Quantum oscillations in a stack of superconducting cylinders in a magnetic field: crossover from the Aharonov–Bohm to the Little–Parks regime
The Aharonov–Bohm (AB) oscillations of the free energy, critical temperature Tc, magnetization M, and magnetic susceptibility χ as functions of the magnetic flux Φ through the hollow in a stack of mesoscopic superconducting cylinders are studied both analytically and numerically. The shape of these...
Gespeichert in:
Datum: | 2000 |
---|---|
1. Verfasser: | |
Format: | Artikel |
Sprache: | English |
Veröffentlicht: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2000
|
Schriftenreihe: | Физика низких температур |
Schlagworte: | |
Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/129095 |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
Zitieren: | Quantum oscillations in a stack of superconducting cylinders in a magnetic field: crossover from the Aharonov–Bohm to the Little–Parks regime / V.M. Gvozdikov // Физика низких температур. — 2000. — Т. 26, № 7. — С. 648-657. — Бібліогр.: 36 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraineid |
irk-123456789-129095 |
---|---|
record_format |
dspace |
spelling |
irk-123456789-1290952018-01-17T03:03:15Z Quantum oscillations in a stack of superconducting cylinders in a magnetic field: crossover from the Aharonov–Bohm to the Little–Parks regime Gvozdikov, V.M. Свеpхпpоводимость, в том числе высокотемпеpатуpная The Aharonov–Bohm (AB) oscillations of the free energy, critical temperature Tc, magnetization M, and magnetic susceptibility χ as functions of the magnetic flux Φ through the hollow in a stack of mesoscopic superconducting cylinders are studied both analytically and numerically. The shape of these oscillations at low temperature T and small level broadening ν is generally nonsinusoidal and has singularities that depend on the superconducting order parameter Δ and stacking sequence. The period of the oscillations is equal to the normal flux quantum Φ₀. The harmonic amplitudes of the AB oscillations decrease exponentially if the diameter 2R of the cylinders becomes greater than the coherence length. Further increase of R results in a complete suppression of the AB oscillations and the development of parabolic Little–Parks (LP) oscillations of Tc(Φ) with half the period, Φs=Φ₀/2. Therefore a crossover from the AB to LP oscillations takes place as the diameter 2R is increased. It is shown that the temperature behavior of the magnetic susceptibility below the superconducting transition is χ ∝ exp(−T/T*), where T*=ℏv₀/2π²R (v₀ is the Fermi velocity, and ℏ is Planck’s constant). Such dependence of χ(T) has been observed recently in Ag wires coated with thin Nb layers in a weak external field [R. Frassanito et al., Czech. J. Phys. 46, 2317 (1996)]. 2000 Article Quantum oscillations in a stack of superconducting cylinders in a magnetic field: crossover from the Aharonov–Bohm to the Little–Parks regime / V.M. Gvozdikov // Физика низких температур. — 2000. — Т. 26, № 7. — С. 648-657. — Бібліогр.: 36 назв. — англ. 0132-6414 PACS: 74.62.-c, 73.20.Dx http://dspace.nbuv.gov.ua/handle/123456789/129095 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
collection |
DSpace DC |
language |
English |
topic |
Свеpхпpоводимость, в том числе высокотемпеpатуpная Свеpхпpоводимость, в том числе высокотемпеpатуpная |
spellingShingle |
Свеpхпpоводимость, в том числе высокотемпеpатуpная Свеpхпpоводимость, в том числе высокотемпеpатуpная Gvozdikov, V.M. Quantum oscillations in a stack of superconducting cylinders in a magnetic field: crossover from the Aharonov–Bohm to the Little–Parks regime Физика низких температур |
description |
The Aharonov–Bohm (AB) oscillations of the free energy, critical temperature Tc, magnetization M, and magnetic susceptibility χ as functions of the magnetic flux Φ through the hollow in a stack of mesoscopic superconducting cylinders are studied both analytically and numerically. The shape of these oscillations at low temperature T and small level broadening ν is generally nonsinusoidal and has singularities that depend on the superconducting order parameter Δ and stacking sequence. The period of the oscillations is equal to the normal flux quantum Φ₀. The harmonic amplitudes of the AB oscillations decrease exponentially if the diameter 2R of the cylinders becomes greater than the coherence length. Further increase of R results in a complete suppression of the AB oscillations and the development of parabolic Little–Parks (LP) oscillations of Tc(Φ) with half the period, Φs=Φ₀/2. Therefore a crossover from the AB to LP oscillations takes place as the diameter 2R is increased. It is shown that the temperature behavior of the magnetic susceptibility below the superconducting transition is χ ∝ exp(−T/T*), where T*=ℏv₀/2π²R (v₀ is the Fermi velocity, and ℏ is Planck’s constant). Such dependence of χ(T) has been observed recently in Ag wires coated with thin Nb layers in a weak external field [R. Frassanito et al., Czech. J. Phys. 46, 2317 (1996)]. |
format |
Article |
author |
Gvozdikov, V.M. |
author_facet |
Gvozdikov, V.M. |
author_sort |
Gvozdikov, V.M. |
title |
Quantum oscillations in a stack of superconducting cylinders in a magnetic field: crossover from the Aharonov–Bohm to the Little–Parks regime |
title_short |
Quantum oscillations in a stack of superconducting cylinders in a magnetic field: crossover from the Aharonov–Bohm to the Little–Parks regime |
title_full |
Quantum oscillations in a stack of superconducting cylinders in a magnetic field: crossover from the Aharonov–Bohm to the Little–Parks regime |
title_fullStr |
Quantum oscillations in a stack of superconducting cylinders in a magnetic field: crossover from the Aharonov–Bohm to the Little–Parks regime |
title_full_unstemmed |
Quantum oscillations in a stack of superconducting cylinders in a magnetic field: crossover from the Aharonov–Bohm to the Little–Parks regime |
title_sort |
quantum oscillations in a stack of superconducting cylinders in a magnetic field: crossover from the aharonov–bohm to the little–parks regime |
publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
publishDate |
2000 |
topic_facet |
Свеpхпpоводимость, в том числе высокотемпеpатуpная |
url |
http://dspace.nbuv.gov.ua/handle/123456789/129095 |
citation_txt |
Quantum oscillations in a stack of superconducting cylinders in a magnetic field: crossover from the Aharonov–Bohm to the Little–Parks regime / V.M. Gvozdikov // Физика низких температур. — 2000. — Т. 26, № 7. — С. 648-657. — Бібліогр.: 36 назв. — англ. |
series |
Физика низких температур |
work_keys_str_mv |
AT gvozdikovvm quantumoscillationsinastackofsuperconductingcylindersinamagneticfieldcrossoverfromtheaharonovbohmtothelittleparksregime |
first_indexed |
2025-07-09T10:35:25Z |
last_indexed |
2025-07-09T10:35:25Z |
_version_ |
1837165264648536064 |
fulltext |
��� �������
�� ��������
����������������������� "!"!�!#��$"%� "&#�' )(+*,�-�.%�&�/"0�1"&�2�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
PRQTSVUXW�Q�Y Z\[^]`_bacadS`W�_eZfUg[h_cUhSi[jW�S�]`klZ`mf[�Q�ngoVp-]^ZVUrqsQr]jW�_bU`t
]Tu
av_cUgqwowp-[h_vUhSxYySwtzU`ogW�_�]{m�_cowaeq}|^]~p-Z\[+[^Z��`owp\m�p�ZVY W���o
� �gSVp-ZfU`Zg�T���sZf��Y W-Z�W��`o��
_eW�W'a�o+����S�p'k�[�p�o�tz_vYho
�
�.�}���g���#�"���������
���d�� ¢¡c£¥¤"��¦-£'§v¨�©«ªv¬�¯®�°d�±³²#ª´ ¢¡�µ´§�¶,·�£� ¸£��º¹»¦�®�¶��b¡¥¯®¼£�¬�±�½¿¾¯À�ÁÂÁc±�·'¶Ã§ÂÄv§ÃÅ�¬Æ·�ǸÈÊɱʲ#ª´ ¢¡�µ´§�¶�±�¹�µÂ¡¼ ¢®¥¦Ã�Ë�Ì�Í.Î�Ï�ÐeÑ�Ò�ÐÓÎbÔ¸Ï ÍÕÏ Ö�× Ø^×ÓÙ"ÚÂÛÃÜ�Ô¸Ï Ý¢ÛÃÚÃÞÆß�à¢ÏÓÚÂácÖb× Ý�â�ÎbÖeÝ�ÛÃÚ�× ß�Î
ã�ácäcáÃÏ ÚÂácÔÆåÊácæ¢Öeß�ÎbÖ¼çjè�é¿ê¢ëÃëÂë�é¸ÖeácÚ¢ÏÓìeácÔÆØ�ÎbÖ¼äbâjèdí�é¸êÂëÂëÃë
î�â¸á.ï"â�ÎÂÖ�Û�à¸ÛÂÚ¢ð�ñ�ÛÂâ¸Í�ò¯ï"ñ�ó�ÛÂìdä�Ï�ÐeÐ�ÎÃô¯ÏÓÛÂà¸ì"Û¢õ�ô�â�áÕõ¥Öcábá.ábà¸ávÖ�ö�ç�é¸äbÖcÏ�ô�Ï�äbÎÂÐ�ôdábÍÕ÷¸ávÖ�ÎÂô¼ß¸Ö�áÕøÊù"é¸ÍÕÎÃö¢à¸ávô¯ÏÓÜcÎÂô�Ï�ÛÂà,úfé
ÎÃà¸Ô
Í#Î�ö�à¸ábôcÏ�ä+ìdߢìdäÃáb÷¸ô�Ï�æ¸ÏûÐ¥ÏÓôeç
χ
ÎÃìjõ¥ß¢à¸ävô¯ÏÓÛ¢à�ì�Û¢õ,ôdâ¸ájÍÕÎÃö¢à¸ávô¯ÏÓärõ¼Ð�߸ü
Φ
ôdâ¸Ö�ÛÂ߸ö�â�ôeâ¸á+â¢Û¸Ð¥Ð�Û�ýþÏ�à�Î^ìdôdÎ�äÃÝ�Û¢õ
ÍÕábìdÛÂìdäbÛ�÷-Ï�äÕìd߸÷¸ábÖdäÃÛÂà¸Ô�߸äbôcÏ�à¸öÆävç-мÏ�à¸Ô�á�Ödì�Î�Ö�á,ì�ô¼ß¸Ô�Ï�ábÔTæ¢Û�ôeâjÎÃà¸ÎÂÐÓç-ôcÏ�ävδмÐ�ç�ÎÃà¸Ôÿà¸ß¸Í#ábÖcÏ�ävÎÂÐûÐûç'×�î�â¸á�ìdâ¢Î�÷¢á,Û¢õ"ôdâ�á�ìdá
ÛÂìdä�Ï�мÐ�ÎÃôcÏ�ÛÂà¸ì+ÎÃô^Ð�Û¢ý ô�ávÍÕ÷¸ábÖdÎÂôe߸Ödá ø ÎÂà�ÔfìdÍÕÎÂÐûÐ�Ð�ábÚ�áÂÐ)æ¸ÖdÛ¢ÎÃÔ¸ávà�Ï�à¸ö ν
Ï�ìTö¢ávà¸ábÖcÎÂÐ¥Ð�çwà¸ÛÂà¸ì¯ÏÓà¸ß¸ì�Û�Ï�Ô¸ÎÂкÎ�à¸Ôwâ¸ÎÃì
ì¯ÏÓà¸öÂß�Ð�ÎÂÖcÏ�ôcÏ�ábì,ôeâ¸ÎÃôÕÔ¸áv÷¸ábà¸Ô+ÛÂà^ôdâ¸á)ìd߸÷¸ábÖdä�Û�à¸Ô¢ß¸ävô¯ÏÓà¸öjÛÂÖcÔ�á�Ö#÷¸Î�ÖdÎÃÍÕáÃôeáÃÖ ∆ Î�à¸Ô+ìdô�ÎÃäbÝ�ÏÓà¸öjìdá � ß�á�à�äÃá¢×�î'â¸á)÷¸ávÖbÏ�ÛÂÔÛ¢õ�ôeâ¸á`ÛÂìdä´Ï�Ð¥Ð�Î�ô�Ï�ÛÂà¸ì^Ï�ìjá � ߸ÎÂкôdÛ\ô�â¸á`à¢Û�ÖdÍÕÎÂÐÿõ¼Ð�߸ü � ߸ÎÃà¸ô�ß¸Í Φ � ×,î�â¸ágâ�ÎÂÖdÍÕÛÂà�ÏÓägÎÃÍÕ÷�Ð¥Ï�ôd߸ԸábìjÛ¸õºô�â¸áXï�ñÛÂìdä�Ï�мÐ�ÎÃôcÏ�ÛÂà¸ì�Ô¸áväbÖdá�ÎÃìdázávü¸÷¸ÛÂà¸ábà¸ôdÏ�ÎÂÐ¥ÐÓç�Ï�õXô¼â¸ázÔ�ÏÓÎ�Í#ábôdábÖ���� Û¢õ+ôdâ¸áwäcç�ÐûÏÓà¸Ô¸ábÖdì�æ¢áÃäbÛ�ÍÕábì�ö�Ö�ávÎ�ôdábÖ�ôdâ¸ÎÃàsôdâ¸á
äbÛÂâ¸ávÖ�áÃà�äÃá�Ð¥ávà¸öÂôdâ�×�å�߸Ö�ôdâ¸ábÖÕÏ�à�ä�ÖdábÎÃìdá)Û¢õ � ÖdáÃì�߸Хôeì,Ï�àjÎ)äÃÛÂÍÕ÷�Ð�ávô�á,Ô¸áb÷¸ÖdáÃì�ìcÏ�ÛÂàTÛ¢õ�ôeâ¸á)ï«ñ~Û¢ìdä�Ï�ÐûÐ Î�ôcÏ�Û�à¸ì�ÎÃà¸Ôjôdâ¸á
Ô¢áÃÚ�á�Ð�ÛÂ÷¸ÍÕávà¸ôÕÛ¸õ�ôdâ¸á)÷¸ÎÃÖ�Î�æ¢Û¸Ð¥Ï�ä���Ï�ôeôcÐ�á�ð
�ÎÃÖcÝ¢ìºò��� �ó�Û�ì�äÃÏ�ХХÎÃôcÏ�ÛÂà¸ìÕÛ�õÕø ù
(Φ)
é�ýÕÏ�ôeâ+â¸Î´Ð¼õ�ôdâ�áÆ÷¸ábÖcÏ�Û�Ô�é Φ
= Φ ��� êÊ×î�â¸ábÖdá´õ ÛÂÖ�áºÎÆävÖcÛÂì�ìdÛÂÚ�ábÖ)õ¥ÖdÛÂÍ�ôeâ¸áºï«ñ�ô�Û��� `Û�ì�äÃÏ�ХХÎÃôcÏ�ÛÂà¸ìÕôdÎÃݸábìÕ÷�Ð�ÎÃäbáºÎÃìÕô�â�áÆÔ¸Ï�ÎÃÍÕábôdábÖ ��� Ï�ì�ÏÓà¸äbÖdábÎÂìdábÔ�×��eô�ÏÓì
ì�â�Û�ý�à)ôdâ¸ÎÃô�ôdâ¸á.ô�ávÍÕ÷¸ábÖdÎÃô�߸Ödá.æ¸ábâ¸ÎÃÚ¸Ï�Û�Ö"Û¢õ�ô¼â¸á�Í#Î�ö�à¸ábôcÏ�ä.ìdߢìdäÃáb÷¸ô�Ï�æ¸Ï¥ÐûÏÓôeç)æ¸á�Ð�Û�ý�ô�â¸á�ì�߸÷¸ávÖ�äÃÛÂà¸Ô�߸äbôcÏ�à¸ö)ôeÖcÎÃà¸ìcÏ�ôcÏ�ÛÂà
Ï�ì χ ∝
á�ü¸÷
(−
ø � ø ∗)
é¸ý.â¸ávÖcá�ø ∗ =
ª− ¶ � � ê π � � ×���߸äbâÆÔ�áÃ÷¢áÃà�Ô¸ábà¸ävá�Û¸õ χ(
ø
)
â¸ÎÃì"æ¸ávábàÆÛ�æ¸ì�ávÖ�Ú�ábÔºÖ�ávä�ávà¸ô�Ð�çÆÏ�àºï"ö�ýÕÏ�Öcávì
äbÛÂÎÃôdábÔ`ý ÏÓô�âXôdâ¸Ï�à��"ægÐ�ÎÃç¢áÃÖdì�Ï�àXÎjý.ábÎÃÝXáÃü�ô�ávÖcà¢Î¢Ð.õeÏ�áÃÐ�Ô��bè����)òb¶ � Ï�ì)ôeâ¸ájåÊáÃÖ�Í,Ï"Ú�á´Ð�ÛÂäÃÏ�ô¥ç³é»Î�à¸Ôgª− ÏÓì� �Ð¥ÎÃà¸äbÝ� ìäbÛÂà¸ìdôdÎ�à¸ô�ó´×
�ï"!#��Ñ�$&%�' (*)�',+.-¸é
/10�× ê-ë¸×32#ü
4�5�687:9 5<;>=:?A@CB D D 6,9 B =:7:?�B 7�6
?E9 6F@HG#=FIJ?K5�L:MFNO@C=F7<P<5:@89 B 7�QR@�S:D B 7<P<MFN ?�B 7T6
;�6FQ:7<MF9 B @
I B M8D P
U�VXW�Y�Z�[J\
]T^�_�ZJ`,\
Y
acb*deb�f�gJhHijd*k�f�l&mAn�b�o<p�qrhAbsp*g<g<b�f
g&mHk�fut�pvl"q�beb�fun�b*w
k
g<b�n
g<kxl�g<y�n�mHb�lsk{zs|
yTp�f�g<y�}~k�l�d�m�h8h,p*g�mHk
fTl�mAf�w�p�o<mHk�yRlsp�o�g�m,z:mH�
d�m,p�hFhHi�z:p*qTo&mHd�p*g�b�n�f�p�f�k{l�g�o�yTd*g<yTo�b�l�l�y�q
�<b*deg�g<k�l<}�p�h8h
be��g<b�o<f�p�h�}�p1�Tf�b*g�mHd�z:mEbvh,nTl��x�:f���p�o�g�mEd*y.h,p�o*��nTmHz:zFb�o�b�f
g
g<iT�
b�l�k�z�l:y#�
b�o�dek�f�n�y�d*g�m,f{��n
b*wTmEdeb�l�t�p�w{b�q�b*b�f�b*�T�
�#hHk{o�b�n��jt�mEd�t�b*�#t�mHqTmHg�b�n�k
l�d�mChFh�p�g�mEk�f�l�k�zug&t
b�d�o&mEg�m�d�p�h
g<b�}j�
b�o&p*g<yTo�b�� ° yT��k{f~}�k
f�k�g<k�f�mHd�w�p�o&m,p*g&mHk{f�k�z�g�t
b
be��g<b�o<f�p�h�}�p��Tf
beg&mHd�z:mHb�h�n����j�
y�d�t�k
l<d�mCh8h,p�g&mEk�f�l�tTp*w
b
qTb*b�f�kvq#l:b�o�w{b�n mCf p¡z:o�p*deg&p
h¢f�b*g<�sk�o<£�l�¤1¥
�O¦�§*�¨mCf
© k{l�b���t�l:k�f �<yTf�d*g�mHk
f p�o�o&p*i�l ¤Fª#§1�«p�fTn wTp�o<mHk
yTl
}�b�l�k{l�dek
��mHd�hHk{k
��ls¤F¬�#®T§1��¯shFhRg&t
b�l<bsb*�T�
b�o&m,}sb�f�g&l°l&t
k
�
nTmHw
b�o&l:b±p�f�n�q�p�l�m�d�p�hFhAi�f�k{f�l<m,f
y#l:k�mHn�p�h°k�l:d�mFhFh�p*g&mHk{f²��p*g��
g<b�o�f�l�zFk{o>g�t�bug�o�p�fTl�mHg�m�k{f�g<b�}���b�o�p*g<y#o:b³� ° ( � )
�jm�g�t´g�t
b
l<y��
b�o�d*k{f�n
y�deg&mAf��µz�hHy���|�yTp�f�g�yT}
Φ = ¶−·¹¸�ºv» p�l¼p�zFyTf��nTp�}�b�f�g�p
h"�
b�o&mHk
n"�½�8g¼��p�l¾b�l:g�p*q½h,mAl&t
b�n�g&tTp*g¼l�y�d�t�k{l�d�mCh��
h�p�g�mEk�f�l�d*k
y#h,n�q�b�l:y#z:z:mEd�m�b�f�gJhHi¿��bvhFhjyTf�n
b�o&l:g<k
k
nÀp�f�n
n�b�l:d�o&mHq�b�nÀ��mKg&tTmCfÀg&t
b�Á�mCf
ÂJq�yTo��T½ÃXp�f�n�p*y~ÄeÁ�ÃcÅ�p����
�To�k�p*d�t½��ÆXt�b�Á�ÃÀb�|�yTp*g�mHk
f"�¼��t
b�fÇh,m,f
b�pvo�mHÂJb�n¿mCf�g�t
b
k�o�n�b�o���p�o&p�}�b*g<b�o
Ψ
�µm,l�zFk{o&}�p�h8hHiÈmCn
b�f�g�m�d�p�h�g<k~g�t
b
�
d�t�o�k.. nTm,f{��b�oÉb�|
yTp*g�m�k�fÊzFk{oÉp�n�kvy�q½hAi�d�tTp�o���b�nµÄemHfuy#f�mHg�l
k�z�g&t�b�bvhHbed*g�o�k
f�d�t�p�oF��b » ÅË��p�o<g&mHd�hAb¿mCfÌp�}�p*�Tf
b*g�m�dz:mHb�h�nX�XÆXt�yTl��.g�t�b³n
k
y�q#hHbud�t�p�oF��buk�zÉg�t�b�Íck
k{��b�os��p�m,o&l��
¦ » �°m,l�g�t�bµ��t
iTl<m�d�p�h¾o<b�p�l�k{f²l:g�p�f�n�mAf���qTb�t�m,f�nÎg�t�b±z:p*d*gg�t�p*g±|�yTp�f�g�mEg<i
Φ n�b*g<b�o<}�m,f
b�lÊg�t
b��
b�o<m�k�n¨k�z�k�l�d�mFhFh,p��g�m�k{f�l�m,fÇg�t
b¿z�hHy��
Φ
zFk�o�n�m,z:zFb�o�b�f
g�f�k�f�l�mH}���hHiÀd*k�f��
f�bed*g<b�n�l<i�l�g<b�}�l>m,f�g�t�buÁ�Ã�o:b1�Tm,}�b��RÆ"t
buÁ�ÃÎp�����o�k{p�d�t
p�h,l<k���o:k
w
b�n�g<kÊq�bjl�y�d*deb�l&l<zFy#hcmHf�be���#h,p�f�p�g&mEk�fÊk�zÉn�m,z:zFb��
o�b�f�gϣ�f�k��jf�g<i��
b�l>k�z>z�hAy���|
y#p�f
g&mHÂep*g�m�k{f�mHf�l:yT��b�o:d*k�f��
n�y�deg�k{o&l*Ð#g�t�b³Ã.mHg�gJhHb�½ÑXp�o<£�l>k
l<d�mCh8h,p�g&mEk�f�lj¤:Òr�KÓ�§*�Tk�l�d�mFhFh,p��
g�m�k{f�l±mCf�l:yT��b�o�dek�f�n�y�d*g�m,f{�¢z:o&p*deg&p�hjf�b*g<��k
o&£�l�¤�Ô
Õ¥
¥v§1�
p�f�n�m,f © k�l:b���t�l:k�fÊ�<yTf�d*g�mEk�f�p�o&o<p*iTl�¤J¥e¦R�8¥Jª#§1�
Æ"t�bjÃ.mHg�gJhHb�½Ñ"p�o�£�l>ÄeÃcÑÉŰk�l�d�mFhFh,p*g�mHk�f�lÕk�z"g�t
bsd�o<mHg&mHd�p�h
g<b�}��
b�o&p*g�yTo�b³� ° ( � )
t�p*w�b³pÊ��p�o&p*q�k�h�m�d�l&t�p��
b³p�f�n�g�p�£�b
��h,p�d*b�zFk�oÉl&p�}j�RhAb�lÉ�jt
k�l:b�l&mHÂ&b�l¾p�o<bsk�z"g&t
b�k{o&n
b�oÉk{zÕg�t�b
Á�ÃÀd*k�t
b�o<b�f
d*bÖhAb�f���g&t�k�o×�To:b�p�g�b�o���Øjl�d�mFh8h,p*g�m�k{f�l±p�l�p
zFyTf�deg&mHk{f�k�z�z�hAy��¡m,f�g&t�b~Á�ÃÙo:b1�Tm,}�b���mO�Rf�k�o�bÌg�t�b
|
y#p�f
g<y#}��t�p�l:b�m,f�g<b�o<zFb�o<b�f
d*b��Tt
b�f�k{}�b�f�p�n
y�b�g<k�g�t�b
¯¼t�p�o:k�f
k
w�½Ûck�t�}ÜÄJ¯sÛ¼ÅÎb�z:zFb*degÖ¤1¥J¬R§1���jt�mEd�t�m,l�f
k�o��
}�p�h8hHi���o�b�l�b�f�gjm,f�g&t�b�|
y#p�l<m,��p�o:g&mHdvhHb³b�f�b�o���i�l���b*d*g�o:y�}
k�z�f�k{f�l<m,}���hHiÝd*k�f�f�bed*g<b�n�}sb�l<k
l�dek
�TmEdÞl�yR��b�o�dek�f�n�y�d��
g<k�o�l���Æ"t
b²¯sÛÝb�z:zFbed*g�tTp�l´f�yT}�b�o:k
yTl�p����Rh�mHd�p*g�m�k�f�l�m,f
n�mAz:zFb�o�b�f�g�}�b�l�k{l�dek
��mHd¿l�g&o:y�d*g<y#o:b�l�ÐÏd*k�f�n�y�deg&m,f��"��m,f�l<y��
ß à#áJâ¼á&ã�ä�å�æ�çvè é&å*ä�ê&ë*ì�ì�ì
h�p�g�mHf
�"�c}�p*�Tf
b*g�mHd�� p�f�n�l<g&o:k�f��#hHixd*k{o&o:b�h,p�g<b�n½�Xp�o:b*wTmHb*�
k�z��jt�mEd�tÖd�pvf²q�bxzFkvy#f�n�mCf�aÉb�z:l���¥��r��¥e®#�ɯÌ��b�f�b�o<p�h
g�t�bek
o<b*g�m�d�p�hcd*k�f�l&mAn�b�o<p�g&mEk�f�k
z¾g&t�bu¯sÛ�b�z:zFb*deg�mHf�l:y#�
b�o<�
dek�f�n�y�d*g<k�o<l×�jp�l×��m�w{b�f�m,f¨g�t�b�p�o�g�mHd�hAbÖ¤1¥eÒT§1�¾��t�b�o:b�p
f�yT}�q�b�o>k�zÉg&t�b*k{o�b�}�lstTp*w�bjq�b*b�fxzFk�o<}�y#h,p�g�b�n�d*k�f
d*b�o&f��
m,f
��t�k�h8hHk
�Ìl<y��
b�o�d*k{f�n
y�d*g<k�o<l>m,f�pu}�p1�Tf�b*g�mEduz:mHbvh,n½�
Æ"t
b�b�z:zFb*deg�k�z�z�hAy��~|
yTp�f�g�mHÂJp�g&mEk�fÇk�fÇg�t�b�b�f
b�o���i
l���bed*g�o�yT} k�z>b*�Td�mEg�p�g�mEk�f�ljmCf�p�g&t�m,f�t�k�hFhHk{��l�yR��b�o�dek�f��
n�y�d*g�mCf��Ýd*iTh,m,f�n�b�o�p�f�n�k{f�g�t
b�d�o<mHg&mHd�p�h�g<b�}��
b�o�p�g�yTo:b
� ° (Φ)
�jp�lÕl<g�yTn�mKb�n³mCf�¤J¥eÓ�§1�T�Fgc�jp�lÉl<t�kv�jfÊmAf´¤1¥1Ó�§½g�t�p*g
� ° (Φ)
mCl�p�f´k�l:d�mFhFh�p*g�k�o�ixzFyTf
d*g�m�k�fµk�zÉg&t�buz�hHy��xg&t�o�kvy��Tt
g�t�b³t
k�h8hHkv�
Φ =
�
π � � �jmEg�t�g&t
b³�
b�o�mEk�n Φë =
¦
Φ Ä��m,l�g&t�b�mHf�f
b�o�o�p�nTm�yTl�k�zÊg�t�b�d*i#h,mHfTn
b�o*Å��ÏÆ"t
b�p*y�g&t�k
o�l
�To�k{w
b�nÖg�t�bx��b�o�mHk{n�mHd�mEg<iÖk�z�g&t�b�d�o&mEg�mHd�p�h�g�b�}��
b�o<p�g<yTo�b��
� ° (Φ) =
���
(Φ + Φ� ) �rp�f�n�b�l�g&mA}�p*g<b�n�g&t�bjp�}���h,mHg<y�n�b�k
zk�l�d�m�h8h,p*g�mHk�f�l>p�l
� ° ë −
� °
� ° ≈
λ �
� ê
b*�T�
(−
¦
γ
���
ξ ë )
Ä
¥vÅ
ÆXt�b³b*�T��h,mHd�mHgjl�tTp��
bÊk{z>k{l�d�mCh8h,p�g&mKk�f�lÏ�jp�l�f�kvgjzFk�yRf�n�mCf
¤*¥¹Ó�§1�RÆ"t
bjf
k
g&p*g�mHk
f±p�n
k��
g<b�n�m,f��X|½�.Ä�¥vżm,l¾p�l¾zFk�hFhAk��jl�Ð
ξ ë = ¶−� � ¸ π∆( � ) mHl´g�t
b²dek
t�b�o:b�f�d*b�hHb�f���g�t�� λ m,lµg�t
bÛck�t�o¼o&p�n�mHyTl��Rp�f�n�h,f
γ
b�|
yTp�h�l g�t
b��.y#hHb�o¾d*k�f�l<g&p�f�g��
Æ"t
bx��yTo���k
l<b´k{z���o�b�l�b�f�g³��p���b�oum,l�g�kËl�g<y#n
i�ÄJq�k
g&t
pvf�p�hHi�g�mEd�p
hFhAi�p�f�n�f�yT}�b�o<mHd�p�h8hHi#Å�g�t�b³¯¾tTp�o�k{f�kvw�½Ûck{t�}
k�l�d�m�h8h,p*g�mHk�f�l�k{z>g&t�bÊd�o�mHg�mHd�p�h°g�b�}���b�o<p*g�yRo�b±� ° (Φ)
�c}jp1�T�
f�b*g�mHÂJp�g�mEk�f��
(Φ)
��p�f�n�l�yTl�deb��
g�m�qTmFh,mHg<i
χ
mHf�l�yR��b�o�dek�f��
n�y�d*g<k�o�l�m,f�}�k
o<b�n
b*g�p�mCh±p�f�nÇg<kÀl�t�k�� g�t�b�m,oxzFk�o�}jp�h
o<b�h,p*g�mHk
f�g<k�g�t�bµn�b��jpvp�l�#w�p�f�¯sh,��t
b�f�k
l�d�mFhFh,p*g�mHk
fTl�mCf
l<y��
b�o�d*k{f�n
y�deg�k{o&l��¡p�w�b�o�i±p�deg&mKw�bjp�o�b�p�k{zÉo�b�l�b�p�o�d�t±p*g
g�t�bj}�k
}�b�f�gsÄel:b*b��RzFk�o be�Tp�}���hHb��"acb�z:l��#¦��R�r¦�Ór�R¦
Ô³p�f�n
f�yT}�b�o:k
yTl³o�b�zFb�o�b�f�deb�lug&t
b�o�b�mHf.Å��°Æ½kËn
k²g�t�mCl��É��b´dek�f��
l�mCn
b�o¾mCf³��t�p*g¼zFk�hFhAk
�jlÕg�t�bs¯sÛ�k{l�d�mFhFh�p*g&mHk{f�lck�z"g&t�b�z:o�beb
b�f�b�o��Ti�mAf�p�l:g�p*d�£~k�z²��b�pv£RhAi~dek
fTf�bed*g<b�n~yTf�m,p*�Tm,p�h
t�k�h8hHk
� l:y#�
b�o�dek�f�n�y�d*g�m,f{��dei�h,m,f�n�b�o�l����jt�mHd�t~d�pvf~q�b
dek�f�l&m,n
b�o�b�nX�´zFk
o¿mCf�l�g�p�f
d*b��xp�l�p�}�k
n�b�h�l�i�l:g�b�} zFk�o
l<y��
b�o�d*k{f�n
y�deg&mAf��±f�p�f�kvg�yTq�b�l>¤8ª � §1����b>�jmFhFhRl&t
k
��g�t�p*gg�t�b³� ° p�f�n�g&t�b³}�p1�Tf�b*g�mEd�l:yTl�d*b��
g&mHqTmFh,mHg�i χ
mCf�g&t�bu¯sÛ
o<b1�Tm,}�bµp�o�b�k�l:d�mFhFh�p*g&m,f
�ËzFy�f�d*g�mHk
fTl�k�zsg�t�b�z�hAy��¨n�yTb�g<k
g�t�bË|�yTp�f�g&mEg�mHb�l�d*k�l
(
¦
π� Φ̧ Φ ë ) ���#k{o´b�p*d�tÀm,f�g<b1�Tb�o �g�t�bµp�}��rh�mEg<y#n
b�l�k�zsg�t
b�l�b�k�l�d�m�h8h,p*g�mHk
fTlun�b��
b�f�n�k
f²g�t
b
bvhHbed*g�o�k
f�hHbew�bvh�qRo�k�p�n
b�f�m,f��
ν = ¶−̧ τ
�³g�t
b�k
o�n�b�o��p��
o�p�}�b*g<b�o
∆
��p�f�n g�t
b¿l�k
�,d�p
hFhAb�n�l�g�p*d�£�m,f��Ýz:p*d*g<k{o � � �n�b��
b�fTn�mCf���k
f � mHf�g&t
buw�b�o:i�l<p�}�b³z:p�l�t�mHk{f�p�lszFk�o>g�t
bn�b!�jpvp�l<rw�p�fu¯sh,��t
b�f�Ä#" � �%$ ÅÉk{l�d�m�h8h,p*g�mHk
fTlÕm,f�h,p*i
b�o�b�nl<y��
b�o�d*k{f�n
y�deg�k{o&l�¤�¦&��§1�'�Çbj��mFh8h°l�t�k����XmHf���p�o�g�mEd*y.h,p�o*�
g�t�p*g
χ ∝
bv�#�
(−( ¸ � ∗)
���jt�b�o�b�� ∗ = ¶− � � ¸ º π ê ����Æ"t�m,lo<b�l:y½hHgube�Tp*d*gJhHiÖdek
m,f
d�m,n�b�l��jm�g�t²g�t�b�be�#�
b�o�mH}�b�f�g�p�h>kvqT�
l<b�o:w�p*g�mHk
f³k�z"g&t
bsg<b�}j��b�o&p*g<y�o<bsq�b�t�p�w�m�k{oÉk{z g�t�bÏl�yRl�deb����
g�mHqTm�h�mHg�i�m,f�g&t
bu¯Õ�*),+�q´�jm,o:buq�yTfTnRhAbuo�b��
k�o�g<b�nxmHfÎa°b�z1�
¥1Ôr��ÆXt�bÞl�g&p*d�£�mCf�� z:p*deg�k�o-� � m,l�pÞ|�yTp�f�g�mEg<i���t�mHd�t
n�b��
b�fTn�l¨k{f~g�t�bÀnTmHl�g�o�mHq�y�g�mEk�fÌk�z�d*i�h�mCf�n�b�o<l�t
b�mA��t�g�l
p
hHk{f��¿g�t�b�l�g�p*d�£�p�l���b�h8hjp�l�g�t
b²g<i��
b�l�k�zub�hAb*d*g�o<m�d�p�h
d*k�f�g�p*d*g�l>q�b*g<��b*b�fµg�t
b�}��½��g¼f�k{f�g�o�mHwTmHp
hFhHi±}�k�n�m,z:mHb�l¾g�t�b
p�}���h�m�g<yTn�b�k�zÏg�t
b � g�t�k�l�d�mFhFh,p*g�mHk�f�t�p�o&}sk�f�mHd�p�f�n�d�pvfq�bun
b*g<b�o�}�mHf�b�n�q�i�g&t
b�o�bvh,p�g&mEk�fΤ�¦&��§
� � = ∫
−∞
∞
. (ε) /%021 (− 3 º π4 ε̧ ε ë ) " ε
� Äe¦�Å
�jt
b�o�b . (ε)
mHl�pÖk�f
b��FnTmH}�b�f�l<mHk
fTp�h³n�b�f�l�mEg�iÀk{z´l:g�p�g<b�l
o�bvh,p*g<b�n�g<k�g�t�b¼b�hAb*deg&o�k{f³}�kvg&mHk{fÊp�hAk�f��ug�t�b�z:m�bvh,nÊÄep�hAk
f
�
g�t�b³l�g�p*d�£½�Xm,f�k�yRo>d�pvl:b
Åjp�f�n
ε ë mHlsg�t�bug<i���mHd�p�h°b�f
b�o���il�b���p�o�p*g&mHk{f�q�b*g<��b*b�f�g&t
bxb�f�b�o��Ti�hAb*w�b�h�lÊm,f�g&t
b���o�k{q��
hHb�}µ�5��b��jmChFh±l&t
k
�ÜmAf �jt�p*g�zFk�h8hHkv��l�g�t�p*g�m,f�g�t�b
¯sÛ o�b1�Tm,}�b�k�z�pÚl:g&p*d�£ k�z�}sb�l<k
l�dek
�TmEd�d*i�h�mCfTn
b�o&l
ε ë = ¶−��6 ë ¸ �7���X�jt�b�o�b 6 ë l:g&p�fTn�luzFk
o�g&t�b��#b�o&}�m¾}�k
�}�b�f
g�yR}~p�f�n8� mHlsg�t
bub�hHbed*g�o�k�f�}�p�l�l��c��f´d�p�l:buk
z¾g�t�b
n�b5�jp�p�l<rw�p�fʯsh,��t�b�fÊk{l�d�mFhFh�p*g&mHk{f�l¾mHf�h,p�i
b�o:b�nÊdek�f�n�y�d��
g<k�o�l�¤<¦ � �K¦r¥�§�p�f�n l:yT��b�o�dek�f�n�y�d*g<k
o�l ¤�¦&��§
ε ë = ¶−Ω
�
�jt
b�o�b
Ω
m,l¾g&t
b�dei
d�hAk�g�o�k{f�z:o�b�|
y�b�f�d*i½�
9#V*:�;2<�<�Y2<�[>=@?BA�C2<�_�Z&[<^EDGFvY�]�ZH;I<�J:[�<K<�<�YL<�[M=E?
ÍÉk�f�l�mHn�b�oÊp�l:g&p*d�£Ök
z�yTf�m,p*�#m,p�h¼g&tTmHf�t�k�hFhHk{�Úd*i�h�m,f��
n�b�o�l�ÄJk�o�p²g<y�q�b
Å�k{z�m,f�f�b�o�o<p�n�mHyTl � pvf�n�g&tTmEd�£Tf
b�l&l"BNPO ���°��t�mHd�tÖm,lul�y�q��<bed*gug<kÖp�f�b*��g<b�o<f�p�h�}�p*�Tf
b*g�m�d
z:mHb�h�nÎ� p�hHk{f��Ëg&t�bxp*��m,luk
z�g&t�b�l�g�p*d�£½��Æ"t
b�d*i�h�mCfTn
b�o&l
}�p*i�q�b�y�f�m,zFk�o<}Úm,fÖl<m�ÂJb��ck�o�g�t�b�m,o�t�b�mE�Tt
g&lu}jp*i²w�p�o<i
�
b�o&mHk{n�mEd�p�h8hHixp�hHk�f{�xg�t�bug<y�q�buk�o>q�b³o<p�f�n
k�}uhHixn�mCl<g&o<mHq��
y�g�b�n�|
y#p�f
g�mHg&mHb�l*�L�Àbup�l�l�yT}�b�p�h�l�k±g&t�p�g>g�t
b�g<y#f�f�bvh,mHf
�
qTp�o<o&mEb�o&l³zFk
oub�hAb*d*g�o�k{f�t�k{����m,f{�¨q�beg���beb�fÖf�b�mE�Tt
q�k{o&mHf
�
d*iTh,m,f�n
b�o�l>p�o�bj�sb�pv£�b�f
k
y
�Tt�g�t�p*g¼k
f�b�d�p�f�f�b1�#hAb*d*g¼g�t�b
l&��p*g�mCp�h�w�p�o<m,p*g&mHk{f�l�k
zsg�t�bµl�yR��b�o�dek�f�n�y�d*g�m,f���k�o�n�b�oj��p��
o&p�}�b*g<b�o¾p�hHk{f��³g�t�bÏl�g&p*d�£µÄel<b*b�a°b�z1��ª#¥�pvf�n³g&t
bjn�mCl:d*yRl��
l&mEk�f´m,f���bed��T¬�mHf�g�t�m,l¾d*k{f�f
b*deg&mHk{f½Å��
Ûcb�zFk�o:b�d*k{f�l<m,n�b�o�m,f��¿g&t�b�l�yT��b�o�dek�f�n�y�d*g�m,f�����o�k{��b�o��
g�m�b�lÉk�zÕg�t
bjl�i�l�g<b�}�m,f�|
y�b�l�g�mEk�f½�.hHbeg¾y�l¼z:mHo&l:g¼n�beg�b�o�}jm,f�b
mHg&l�b�f�b�oF��i�l&�
b*deg&o�yT}�p�f�n�g&t�b���p�w
b�zFyTf�deg&mKk�f�lumHf²g�t�b
f�k{o&}�p
h.l�g�p*g<b��TÆ"p�£TmHf��³g�t�b�f×g�t�bRQjp*�TmClÉk{z"g&t�bsd*iTh,m,f�n�o<mC�
d�p�hcdek
k{o&n�mCf�p�g�b�l
(ρ
�
ϕ
�@S
)
g<k�q�bu��p�o<p
hFhHbvh"g<k�g�t�bul<g&p*d�£X�
p�f�n¿l�b���p�o&p*g�m,f���wTp�o<m,p*q½hHb�l�mHf�g&t�bÖ�
d�t�o�k.. n�m,f���b�oÊb�|�y�p��g�m�k{fÊ�UT
Ψε = εΨε
�T��bjt�p*w�b
Ψε(
[
) =
V
(
¦
π)
è � �
b ®¥¦ ϕ WHX (ρ)Ψζ Y (
Q
)
� ÄJªTÅ
¥
ρ
"
Z
ρ
ρ
" W�X
"
ρ
+
¶−ê¦[�
ρ
ê
\ − Φ(ρ)
Φ ë
ê^]
X (ρ) = ε ¦ X W�X (ρ)
�
ÄJ¬TÅ
�UTI_
Ψζ Y (
Q
) = ζ ¤ Ψζ Y (
Q
)
� Ä#��Å
��b�o�b
ρ =
�
+ ` m,l g�t�b o�p�nTmCp�h d*kvk�o<n�mHfTp*g�b
( � ≤ ` ≤
Z NPN �
)
� p�f�n
Φ(ρ) =
�
πρ
ê m,l�g�t
b z�hAy��
g�t�o:k
y
�Tt�p�d�mCo:d�hAb�k{z¾o&p�n�mHy�l
ρ
�.Æ"t
b±�
d�t�o�k.. n�mHf
��b�o¾b�|�y�p��g�m�k{f Ä#�TÅ�n�b�l�d�o<mHq�b�lÊg�t
b�}�k{g&mEk�f¨k�zup�f�b�hAb*deg&o:k�fÖ�jm�g�t
a W � .cb . W
d è æ<è éMegf�è æ<éJè éHh�i%jlknm%jpoUerqts%o8ê�ëeì�ì*ìvê�ä�á<ëvu{êrf�å*w u%xpy
b�f�b�o��Ti
ζ ¤ ≡ ε − ε ¦ X p�hHk�f��¿g&t�b�}jp1�#f
beg&mHd�z:mEbvh,n Äem�� b��,�p
hHk{f���g&t�b^QÏp*�#m,lJÅ���ÆXp�£�mHf
�±mHf�g<kup*ded*k
yTf
gÉg�t�p�g°m,fÊpsg�t�mCf
dei#h,mHfTn�b�o ` ¸ � NPN ¥v�¾��b�z:mHf�n�z:o:k�} �c|½�¼ÄJ¬#ÅÊg�t
b�p�����To�k{��m,}jp*g�bÌb�f
b�o���i l&�
b*d*g�o�yT} zFk
o�b�hAb*deg&o:k�f�lÇmAf�g�t
b
dei#h,mHfTn�b�o�Ð
ε ¦ X = ¶−ê¦[�
π
ê � ê
Z ê +
¥
� ê
\ − Φ
Φ �
ê
� Äe®�Å
Æ#t�b³pv����o�kT��o<mFp�g<b³o&p�nTm,p�h#��p�w�b³z�yTf
d
g�mCkTf��tTmCd{t�l*pv�
g�m,l&z:mEb�lÕg�t�b¼Â1b�o�k�q�kvy#f�n�p�o:iud*k�f�nTmEg�m�k�f�l°p*gÉg�t
b�mHf�f
b�oÉp�f�n
k{y�g<b�o�l�yTo�z:p�d*b�l>k
z¾g�t�budei�h,m,f�n�b�o�� W�� (� ) = W X ( � +
Z
) = � �m,l�TmHw�b�f�q�i
W � (ρ) = √
¦[� " l<m,f
π(ρ −
�
)
�
"
� ÄeÒ�Å
Æ"t
b�|
yRp�f�g<y#}�f�yT}�q�b�o&l�m,f �c|�l*�ÉÄe®�Åup�fTn²ÄeÒ�Å�g�p�£
b
g�t�bxzFk�h8hHkv�jmCf���w�p�hHy�b�l�Ð \ = � � ±
¥
�
±
¦#�������<� �
= � �c¥
�R¦���8�F�xÆ.k~d�p�hAd*y.h,p*g<b�g&t
bÌ|�yTp�l&mH��p�o:g�m�dvhHb�b�f�b�o���i�k{z¨g�t
b
l<i�l�g<b�} y�f�n�b�o�l:g<y�n�i�m,f�g�t�bËl�yR��b�o�dek�f�n�y�d*g�m,f��Þl�g�p*g�b��
k�f�b�t�p�lÌg�k pvn�n�o:b�l&l�g�t�b¡Û"k���kTh,mEyTq�kvwT#n�b¡Á¼b�f�f�b�l
Ä�Û°n�Á�Å>b�|
yTp�g&mEk�f�l�Ð
(
�UT
− �
) � ( [ ) + ∆(
[
) � ( [ ) = ��
(
[
)
�
−(
� T ∗ − �
) � ( [ ) + ∆∗(
[
) � ( [ ) = ��� ( [ ) �
ÄeÓ�Å
�jt�b�o:b � mHl¾g�t�b��#b�o�}�m½b�f�b�o���i½��
m,f
d*bsg�t�b¼g�t�mHd�£�f
b�l&lck�z½deirh�mHf�n
b�o&lÉm,lÉ}syTd�t�hHb�l<lÕg�t�p�f
g�t�b³Û¾Ís�³d*k�t
b�o�b�f
d*b�hAb�f���g�t
ξ
�#g�t
buk
o&n
b�os��p�o&p�}�beg�b�o
∆n�k�b�l�f�k{g�n�b��
b�fTn�k{f�g�t�b�dek
k{o&n�mCfTp*g�b [ �¼ÆXp�£�mHf
��g�t�m,l
m,f�g�k¿d*k{f�l<mCn
b�o&p*g&mHk{fÇpvf�n be�#��p�f�n�m,f��Àg&t�b � − � zFyTf�d��g�mHk�f�l>m,f�g�t�bjqTp�l&m,l k{z,�X|X�XÄ&ª#Å��
� ([ ) = ∑
ε
� εΨε(
[
)
� � ([ ) = ∑
ε
�
εΨε(
[
)
� ÄeÔ�Å
��bÞz:m,f�n~g�t�bÞ|
yTp�l&m,��p�o<g&mEdvhHbÀb�f�b�oF��i�z:o�k{} g&t
bÌÛ°nRÁ
b�|�yTp*g�m�k{f�lsÄeÓ�Å�Ð
� ¦ X = √(ε ¦ X − �
)ê + ∆
ê � Ä
¥ � Å
ÑXo�kvd*beb�nTmCf���g�t�b�f�mCf�pul:g&pvf�n�p�o<n�z:p�l<t�mEk�fX�R��b�p�o�o�mHw�bjp*g
g�t�b±l<��bed*g�o&p�h�n�b�f�l<mHg�i�zFk�o�|�yTpvl�m,��p�o�g�mHd�hHb�ls��mHg&t�p�l<}�p�h8h
nTp�}���m,f���
ν = ¶−� τ
�±pvlÖp�l:y#} k{z�g���k�Ã#k�o:b�f�g�ÂJm,p�fTl
¤<¦v¦�§1�
ρ ¦ (ξ ¤ � ω) =
¥
π
��� � ν
ν
�
+ (ω + � ¦ (ξ ¤ ))
� +
+ � ¦ê ν
ν
ê
+ (ω + � ¦ (ξ Y ))
ê
Ä
¥{¥�Å
Æ.t�b±|�yTpvf
g&m,g&m,b
l � ¦ê p�fTn � ¦ê t�b�o:bxl�g&p�fTnÖzFk�oug&t
b�d*k�t�b��o<b�f
d*b�z:p*d*g<k�o�l�Ð
� ¦ê (ξ ¤ ) =
¥
¦
¥
+
ε� (ξ ¤ )
� � (ξ ¤ )
� � ¦ê (ξ ¤ ) =
¥
¦
¥
−
ε� (ξ ¤ )
� � (ξ ¤ )
�
Ä
¥e¦�Å
��b���y�g�zFk{o�l<mC}j��h,mHd�mEg<i �
=
V��¼l:k²g�t�p*g³g�t�b�|
y#p�l<mC��pvo��
g�m�dvhHbÖb�f�b�o��TmHb�l�mCf�g�t�b�f�k
o&}�p
h³p�f�nÀl�yT�
b�o�dek
fTn
y�d*g�mHf
�
l�g�p*g�b�l q�bed*k�}sb��ro�b�l&�
b*deg&mHw
bvhHi"�
ε ¦ (ξ Y ) = ε(
�
)
\ − Φ
Φ �
�
+ ξ ¤ − µ
� Ä
¥JªTÅ
p�f�n
� ¦ (ξ ¤ ) = √ε ¦ (ξ ¤ )
ê
+ ∆
ê � Ä
¥J¬TÅ
�jt
b�o�b
µ
p�fTn
ε(
�
)
p�o�bjn�beg�b�o�}jmCf
b�nµq�i�g�t�bjo�bvh,p*g�mHk
fTl
µ = �
� −
¶−� π �¦ � " � � ε(
�
) =
¶−ê¦ � � � � Ä
¥#��Å
Øjf�deb�g&t�bÌl&�
b*deg&o�p�h�n�b�f�l�m�g<i�m,l�zFk�yRf�n ��g�t
b~z:o:b*b
b�f�b�oF��i�k
z�p�l:yT��b�o�dek�f�n�y�d*g<k
o�d�p�f²g�t�b�f²q�b�d�p�hAd*y#h,p�g<b�n
�jmHg&t�g�t�b�t
b�h,��k{zÉg&t
b�zFk
o&}�y#h,p�¤:¦�ªT§
�
= ∫ " [��∆(
[
) � ê
λ
−
−
¦��
∑¦ é ¤ ∫
−∞
∞
"
ω ρ ¦ (ξ ¤ � ω)
h,f
¦��������
ω¦
�
� Ä
¥e®�Å
�jt
b�o�b
λ
mHl�g&t
bÚÛ¾Í��Úd*k
yT��h,m,f�� dek
fTl�g�p�f
g�� �jl&mHf
�
g�t�bÌm,f
g�bJ�To&p�h�o<b���o�b�l:b�f�g&p*g�mHk
f zFk
o�g�t
b~hHk���p�o&mHg&t�} m,f�c|½�.Ä
¥e®�Åu¤:¦�¬T§
h,f
d*k{l&t
ω¦
�
= ∫
−∞
∞
" Q ¥ −
dek�l
ω
Q
Qjl�mCf�t
π
� Q Ä
¥eÒ�Å
p�f�n�g�t
bÊÑ.k
m,l&l:k�f�l:y�}j}�p*g�mHk
f�o�y#hHb
∑��!
∞
χ( \ ) = ∫
−∞
∞
χ( \ ) " \ +
¦#" / ∑�
=
è
∞
∫
∞
χ( \ ) b%$ ê π ¦�� Z'& � Ä
¥eÓ�Å
�jt
b�o�b \ � −
¥ O)( N \ ë ����b�z:m,fTnÊg&t
b�k{l�d�mCh8h,p�g�k{o�i³��pvo�gk�zcg&t�b�z:o<b*b�b�f�b�oF��i�m,f�g&t
buzFk{o&}
�+*�,.-
=
¬
π
�
ε ë ∑/ =
∞ a � Ψ/ ( �¾� ∆
�
ν)
d*k�l
º π� Φ
Φ �
Ä
¥eÔ�Å
u10eì d è æ<è é�e f�è æ<éJè é>h i%jpk m%jpo e>qts%oFê<ëeì�ì*ì�êFä�á<ëvu
ê>f�å w
�Fg°m,lcm,}��
k�o:g&p�f�gÕg<kjf�kvg�b¼g�t�p*g°f�k{f�k{l�d�m,hFh,p�g<k
o�i���p�o�gck
z
g�t�b¿z:o:b*b�b�f�b�oF�Ti½��n�beg�b�o&}�mAf�b�nÀq�iÀg�t�b¿z:mHo&l:g�m,f�g<b1�Ro<p�h
g<b�o�} m,f �c|½�³Ä�¥eÓTÅ��jn�kvb�l�f�k�g�n
b���b�f�nÇk�fÀg&t
b¿z�hHy��"�
qTb*d�p*y�l<b
ε � (ξ ¤ )
m,f��X| ��Ä
¥¹ª�žn
b���b�f�nTl k{f \ g�t�o:k
y
�Tt×g�t
bdek�}�qTm,f�p*g&mHk�f \ − Φ ¸ Φ ë �ׯ½��k�z:p�d*g<k{o&l Ψ/ ( � � ∆
�
ν)pvf�n a � t�p�w
b�q�beb�f�m,f�g�o�k{n�y�d*b�n�mCfB�X|½�"Äv¥eÔ�Å�Ð
Ψ� ( �>� ∆
�
ν) = ∫
−∞
∞
Z S�� / (Q )
b −ν �
_��
Q l�m,f�t
(π
�LQ
)
� Äe¦ � Å
pvf�n
a � =
a°bu¤ � � /&0L1 ( 3 ¦ π4 � 6 ë ) §
Äe¦#¥�Å
Æ.t�bÏz�yTf�dvg�mCkTf�� � (Q ) mHl¼n�beg�b�o�}jmCf
b�nµqTiÊg�t�bjm,f�g<b1��o�p
h
� � ( Q ) = ∫
−∞
∞
" \ d�kTl
Q √(ε ë \ )ê + ∆
ê
d*k�l
(
¦
π \ � )
�
Äe¦{¦�Å
ÆXt�yTl²g�t�bÀz:p*deg�k{o
Ψ� ( ( � ∆
�
ν)
���RmEw�b�f qTi �X| �³Äe¦ � Å��n�b�l:d�o&mHq�b�l¼g&t
bunTp�}���m,f���k{z¾g&t
b�¯sÛ�k�l�d�m�h8h,p*g�mHk
fTl k�zÉg�t
b
z:o<b*b�b�f�b�o��Ti�n�y�bug<k�g�t
b�ÛÉÍ��Ê�Tp��
∆
p�f�n�b�f
b�o���iÎhAb*w
bvh
qRo�k�p�n�b�f�m,f��
ν
�RÆ"t�buz:p*d*g<k{o a � mHf �X|½�"Äe¦ � Å�}sk�n
y½h�p*g�b�lg�t�b � g�t�t�pvo�}�k
fTmHd´g�t�o�kvy��TtÖg�t�bxl�g�p*d�£�m,f��¨z:p*d*g<k�o � � ��jtTmEd�tÖtTp�lup�h,o:b�pvn
i²q�b*b�fÖn
b*g<b�o&}�m,f�b�nÎqTi-�c|½�¾Äe¦�Å��¾�8g
n�b��
b�fTn�l�k
fÇg�t
bÖk�f
b��8n�mH}�b�fTl�mHk{f�p�h³n�b�f�l&mEg<iÇk{z�l�g�p*g�b�l
pvl<l�k�d�m,p*g�b�nµ�jmHg�tµg�t
b�bvhHb*deg&o:k�f�}sk
g�m�k{f�p�hHk�f���g�t�bjl�g�p*d�£
. (ε) = ∑¤ δ(ε − ξ Y )
� Äe¦vª#Å
ÆXt�bÝz:p*d*g<k
oÀp�f�p�hAk���k
yTl�g�k�g&t
b � � ��p�l�m,f
g�o�k
n�y�d*b�n
b�p�o&h,mHb�oÉm,fÊg�t�b�g&t�b*k{o�iuk
zcn�b �jp�p�l<�wTp�fʯ>h���t
b�fuk�l:d�mFhFh�p��
g�mHk�f�l�m,f h�p*i
b�o�b�n�dek
fTn�yTd*g<k
o�l�¤:¦ � �K¦r¥�§up�f�n¿l�yR��b�o�dek�f��n�y�d*g<k�o�l�¤:¦&�T§1�
ƽt
b�mAf�g:bJ��o<p�hXmHf��"|½�#Ŧ�¦�Å>depefµq{b�dep�hHdJy�h,pJg:b�nÊbJ�Tp1dJgJhKi
g<k³i�mKb�h,n�¤<¦�¬#§
� � (Q ) = π
ε ë
δ(
Q
−
Q / ) + θ(
S
−
Q / ) ∂
∂
Q � �
∆ √Q �
−
Q � ê
�
Äe¦v¬#Å
�jt�b�o:b
θ(
Q
)
mClÖg�t
b ��b�p*w�m,l<m,n�bÞl:g�b���zFy�f�d*g�mHk
f � � ë ( Q )l<g&p�fTn�lxzFk
o�g&t
b�Ûcb�l<l�b�h�zFyTf
d*g�m�k�f*�Ïp�f�n Q � =
¦
π� ¸ ε ë �+�k
�Ìl�y�qTl�g�mEg<y�g�mHf����X|½�"Ŧ�¬#Å�mCf
g<k�� |½�½Äe¦ � Å��R��bjtTp*w
b
Ψ� ( ( � ∆
�
ν) =
= Ψ(
Q � � ν) + ∫�
∞
" Q
Ψ(
Q��
ν) ∂
∂
Q � ë
∆ √S ê
−
Q � ê
�
Äe¦���Å
�jt
b�o�b
Ψ(
Q��
ν) =
b −ν � �
�
Q�l<mCfTt
(π
�*Q
)
� Äe¦
®�Å
Æ"t�b�l�bed*k{f�n�g<b�o<} m,f�Äe¦&��Å�w�p�fTmCl<t�b�lÊ��t�b�f
∆ = � �¼l�kg�t�p*g
Ψ(
Q � � ν)
mHl�g�t�b¨z:p�deg�k{o���t�mHd�tÇn�b*g<b�o<}�m,f
b�l�g�t�b
p�}���h�m�g<yTn�b�lÕk�z½g�t�b�¯>Û�k
l<d�mFhFh�p*g&mHk{f�lÉmAf×g�t�b�l�g�p*d�£³mCfug�t�b
f�k{o&}�p
h¾l�g�p*g<b�� Æ"t
b�n
b��
b�fTn�b�f�debÊk�z � ÛÃìeä k�f�g�t�b³k�l:d�mFh,�h,p*g�m,f��¿z:p*deg�k{o&lud*k�l
(
¦
π� Φ ¸ Φ� ) m,l³p�}�p�f�mAzFb�l�g�p*g&mHk{f�k{zg�t�b¼¯sÛ�b�z:zFbed*g¼¤1¥e®r�O¦�ÒT§cmHfÊ}�b�l:k�l:d*k���mHdsl<i�l�g<b�}jl��{¯¾}���h�mC�
g<y�n�b�l a / p�f�n Ψ� zFk�o<}�p�h8hHi¢p�o�bÖ}syTd�t�g�t�bËl&p�}�b�p�lg�t�k{l�b¼p����
b�p�o�mCf��×mCf�g�t
bsn
b �jp�p�l&�wTp�f�¯sh,��t
b�f�b�z:zFb*d*g°m,f
h,p*i�b�o�b�n�l<y��
b�o�d*k{f�n
y�deg�k{o&l³m,f¨g�t
b�w
k�o�g<b*�¿l�g�p*g�bxq�b�hHkv�
g�t�b�yR����b�o>d�o�m�g�mEd�p�h }�p1�Rf
b*g�m�d³z:mKb�h,nÖ¤�¦&��§*�rÆ"t�b³h,p�g�g<b�osm,l
q�b*d�p�yTl:b�m,f�q�k�g�t�d�p�l�b�lÉk�l:d�mFhFh�p*g&mHk{fµb�z:zFb*deg&l¾pvo�m,l:bjn�y�b�g�k
g�t�b�|
yTpvf�g�mHÂep*g&mHk{f�k{z�g&t�b�b�f
b�o���i�l&�
bed*g�o�yR} m,f¿l�yT��b�o��
d*k�f�n�y�d*g<k
o&l*�±Æ"t
bÀ��o�m,f�d�mH�Tp�h�n�m,z:zFb�o�b�f�d*b¢m,f�g�t�bÀz:mHbvh,n
n�b��
b�f�n�b�f�deb�k�z � *�,�-
(
�
)
m,f�g&t
b�n
bB�jp�pvl<�w�p�f�¯sh,��t�b�f
p�f�nÖ¯¼t�pvo�k�f
k
w�½Ûck�t�} d�p�l:b�l³pv���
b�p�o&l×q�bed�p*y#l:b�k{z�g�t�b
n�mAz:zFb�o�b�f�gjfTp*g�yTo�b³k
z¼g&t�b�|
yTp�f
g�mHÂ*p*g�mHk
f"�c�<f�d�p�l<buk�z>g�t�b
n�b �jp�pvl��wTp�fگ>h���t
b�fÚb�z:zFb*d*g�g�t
bÝl�g&o:k�f�� b*��g<b�o<f�p�h
}�p1��f�b*g�mHd�z:mHb�h�n�m�g�l�bvh,zumHl�p�|
yRp�f�g�mHÂemCf��¿z:p�d*g<k{o��¾��tTmHd�t
i�mHb�h�n�l�p�n�m,l�d�o�b*g<bÖÃ.pvf�n�p*yÀl<��bed*g�o�yT} o�b�l<�
k�f�l&mHq#hHb�zFk�o
g�t�b��
b�o�m�k{n�mKd�mHg�iÀk{z´g�t�b¨z:o�b*bÖb�f�b�o���i � * , -
(
�
)
m,fÇg�t�b
m,f
w�b�o�l<b�}jp1�Tf�beg&mEdÞz:mHb�h�nÙ¥M�c������f d�p�l�bÀk�z�g&t�bǯ¼Û
��o�kvq½hHb�}�yTfTn�b�o�l�g<yTn
i ��g�t�b�b�f�b�o���i�hHb*w�bvh,l
ε ¦ (ξ ¤ )
k{z�c|½�XÄ
¥Jª�Åjp����
b�pvosn
y�bug<k�g�t
b³l�mHÂJbu|
y#p�f
g�mHÂ*p*g�mHk
fxm,f´g�t�b
}�b�l�k�l�dek���m�dµl�pv}��rhHb��°p�f�n²g�t�bµz�hHy��
Φ ∝
� b�f�g<b�o<l�g�t�b
n�mAl�d�o:b*g<b�l���bed*g�o�yT}
ε ¦ (ξ ¤ )
p�l�p���pvo�p�}�b*g<b�o�g�t
b�o�beq�i
}�p�£�m,f���g&t
b±z:o�b*b³b�f
b�o���i � ÛÃìeä (Φ)
m,f �c|½�°ÄJ¦�¬#Å�p��
b�o<mC�
k�n�mHdÀzFyTf�d*g�mEk�fÌk�z�g�t�bÀz:mEbvh,n�mEg�l�b�h�z1��ÑXt�i�l&mEd�p
hFhAi½�³g�t�b
n�b��
b�f�n�b�f�deb�k{f
Φ
mCf�g�t�b³¯sÛÀl:iTl�g<b�}jl�l<t�kvyrh�nÎwTp�f�m,l&t
g<k���b*g�t
b�o���mHg�t~g&t�b�l�mEÂJb�|�y�p�f�g&mKÂ*p*g�mHk�f�m,f g�t
bÇqTy#h,£
h,m,}jmEg��R�:fÊg�t
b�f
b*�Tgs��bed*g�mHk
fTlÕ��bs��mFhFhrl�beb�m,fÊn�b*g�p�m�hRt�kv�
g�t�b�¯>Û«k�l:d�mFhFh�p*g&mHk{f�l�}jp�f�m,zFb�l:g�g�t�b�}�l<b�hHw{b�lÌmHf g�t�b
}�b�l�k�l�dek���m�d�g<y�q�b²yTfTn�b�o´dek�f�l&mHn�b�o�p�g�mEk�f½��q�k�g�tÀmCf�g�t�b
f�k{o&}�p
h"p�fTn�l�yR��b�o�dek�f�n�y�d*g�m,f��xl�g�p*g�b�l��
�RV : ;I<u_�[*`HZJ`,_pF
�"ZH<[D5C2<�[>FvZ<^�[r<u\EAe_�`���� FvZ1`�\�Y2A F�Y�]
].`UD�<�YIA�`,\
Y@F
�c_�[J\@A%Ae\��2<�[
+¾b�p�oÉg�t
b�d�o&mEg�mHd�p�h.g�b�}��
b�o�p*g�yTo�bsk�f�b�d�p�fÊb*�R��p�fTnÊg�t�b
z:o�beb�b�f
b�o���i±m,f���kv��b�o<l k{z
∆
� �'�jl&mHf
�B� |�l��.Ä
¥e®�Å��.Ä
¥eÓ�Å��
p�f�n�Ä
¥¹Ô�Å��T��but�p*w�b
� · −
���
≈
≈ ∆
ê
α(
�
) −
¦
ε � ∑�
=
è
∞ a ���X� ( ( � ν)
d*k�l
¦
π4 Φ
Φ�
+
�����¾�
Äe¦
Ò�Å
a W � .cb . W
d è æ<è éMegf�è æ<éJè éHh�i%jlknm%jpoUerqts%o8ê�ëeì�ì*ìvê�ä�á<ëvu{êrf�å*w u10��
�jt�b�o:b
α(
�
)
mClug�t�b�z:m,o<l�g³d*kvb�z:z:mHd�mHb�f
g³k
z�g�t�bxl�g�p�f�n�p�o&n
ÁÏmHf�ÂJq�yTo��T½Ã.pvf�n�p*y³b*�T��p�f�l&mKk�f½�#�:fug�t�b¼d�p�l�b¼k�z"p�l:y#�
b�o<�
dek�f�n�y�d*g<k�o�k{z�l&}�p
hFh�nTm,}Ïb�f�l<mHk�f�l�m�g�d�p�f�q�bÝzFk�yTf�n
nTm,o�bed*gJhHi z:o�k�} g&t�bÜz:o�b*b b�f�b�o���i n�b*g<b�o<}�m,f
b�n q�i� |½�½Ä
¥1®�Å�Äel:b*b³acb�z1�.¦v®�zFk{o>n�b*g�p�mFh,lJÅ�Ð
α(
�
) = � ( � )
hAf
(� ° ë
+ Ψ
¥
¦ + ν¦
π
�
− Ψ
V
º
Äe¦{Ó�Å
�jb�o:b � ° ë =
� ° ë (� )
m,l�g&t�b�d�o&mEg�m�d�p�h�g�b�}���b�o<p*g<y#o:b�k�z�p
l�}�p�hFh�d*i�h�mCfTn
b�o�k{z�o<p�n�mHyTl �8�
Ψ
l�g�p�f�n�l�zFk{o�g&t
b�nTmH�
�Rp�}j}�p�zFyTf
d*g�mHk�f����
( � ) m,lÏg�t�b±n
b�fTl�mHg<i�k{zsl�g�p*g�b�l�� Æ"t
bz:p�d*g<k{o � � ( �>� ν)
b�f�g<b�o<mCf��Ëg&t�b�z:o�beb�b�f
b�o:��i²be�T��pvf�l&mEk�f
m,fB�c|½�.Äe¦
Ò�Å�mHl¼n�b*g<b�o<}�m,f
b�n�qTiÊg�t�bjm,f�g<b1�To<p
h
�X� ( � � ν) = ∫
∞
Z S b*�R� (− � Q )l*m,f�t�Q � Äe¦{Ô�Å
�jt�b�o:b � = ν̧ π
� p�f�n ( � =
¦
π
� � � ξ(
�
)
�ÞÆ"t
b d*k{�
t�b�o:b�f�d*b�hHb�f
��g�tÇn�b��
b�f�n�l�k
f�g�t�b7�#b�o&}�m�w�b�hAk�d�mHg�i � ëpvf�n g�t�b g�b�}��
b�o&p*g<yTo�b p�ded*k{o&n�mCf�� g<k g&t
b¡o:b�h�p�g�mEk�f
ξ(
�
) = ¶− � ë ¸ π
�¾�
Æ"t
b�d�o<mHg&mHd�p�h�g<b�}j��b�o&p*g<y�o<bÇk�z�g&t�b�l�g�p*d�£�d�p�f�q�b
n�b*g<b�o<}�m,f
b�n�z:o:k�} g�t
b�Á�m,f�Â&qTy�oF�R½Ã.p�f�n�p�yÇbe�T��pvf�l&mEk�f
qTi�b�|
yTp�g&mHf
��g<k�Â&b�o<kÊg�t�bjg�b�o�}ÝmCf�g�t
bul&|
yTp�o�b�qTo<p�d�£
b*g�l
m,fB�c|½�.Äe¦
Ó�Å��RÆ"p�£�m,f��xm,f
g�k±p*d*dek
yTf�g¼pul<}�p�hFh�f�b�l�l¾k�zÕg�t
b
k�l�d�m�h8h,p*g<k�o:i�d*k{o&o�bed*g�mHk
f�g�kÌg�t�bÀd�o<mHg&mHd�p�hxg<b�}��
b�o�p�g�yTo:b
� °∗(
�
)
k�z�p�d*i�h�mCf�n�b�oÖn
y�b¿g�kÞg&t
b�¯¾tTp�o�k{f�kvw�½Ûck{t�}
b�z:zFb*deg��R��bjtTp*w
b
� ° (Φ) =
� °∗(
�
) −
−
¦ � ° ë (� )
� ( � )ε ë ∑/ = è
∞ a � � / ¤<� ° ë ( � )
�
ν
§ ���'�
¦
π� Φ
Φ �
� ÄJª � Å
�jb�o:b�� °∗(
�
) = ( ° ë (� ) − πν
�°Ó�mHl�g&t�b�g&o&p�f�l&mHg�mEk�f�g<b�}��
��b�o<p*g�yRo�b¼k�z½g�t�b¼d*iTh,m,f�n�b�o*�{g&pv£�mCf��×mCf�g�kjp*ded*k
yTf�g°psl<}�p�h8h
n�b���o�b�l�l&mKk�f�n�y�bxg�k�g�t�bxl<m�ÂJb��F|
yTp�f�g�m�¹p�g�mEk�f�hAb*w�b�h¼qTo�k{p��
n�b�f�m,f��"� Æ"t�yTlÊg�t�b�d�o�mHg�mHd�p�h�g<b�}���b�o�p*g<y#o:b�� ° (Φ)
k{l�d�mCh��
h�p�g<b�ljmHf�g&t�b�nTmCo:b*deguz:mEbvh,n��jm�g�t�p���b�o�mHk{nÎb�|�yRp�hÉg<k�g�t
b
f�k
o�}�p�h�z�hHy���|
y#p�f
g<y#}
Φë �°ÆXt�b�pv}��rh,mKg�yRn�b�l�k�z�t�p�o<�}�k�f�mHd�l�m,f-�c|½�°ÄJª � Åun�b��
b�f�n²k{fÎg<��k�z:p*deg�k�o<l a � p�f�n
� � ��k�z��jt�mEd�t a � mCl±��o<k
�
k�o:g&mHk�f�p�h�g<kÖg�t�b�l:g�p�d�£�m,f��z:p�d*g<k{o � � � Æ"t�m,lÊz:p�d*g<k
o³n�b��
b�f�n�luk�fÖg&t�b���p*iË��t�mHd�tdei#h,mHfTn�b�o&l¾pvo�bjl�g�p*d�£
b�n�mHf�g�k³p�g<y�q�b�p�fTnÊk�fÊg�t�b�g<i��
b�k
z
bvhHbed*g�o&mHd�p�hxd*k�f
g�p�deg�q�beg���b*b�f g�t�b�}Ê��Íck�f�l&m,n
b�o��µp�l�p
l���bed�m,z:mHdub*�Tpv}��#hHb��XpÊ}�k�n
b�h°m,f���t�mHd�t�m,n
b�f�g�mHd�p�hcdei�h,m,f��
n�b�o<l�p�o�b�l<g&p*d�£�b�nÇ�
b�o�mHk�n�mHd�p�h8hHi�m,f
g<k�p²g<y�q�bËp�f�n�g�t
b
g<y#f�f�b�h>�<yTf�d*g�mEk�f�lÊq�b*g<��b*b�fÖg�t�b�} p�o:b�n�beg�b�o�}jm,f�b�n�q�i
g�t�b±t�k{����m,f��Ëm,f�g<b1��o&p�h
σ
����y�d�t²p±}�k�n
b�h t�p�ljo�b*deb�f
gJhHi
zFk{y�fTn�l�yT����k�o�gjm,fÎbe�T��b�o&m,}sb�f�g�lsk�f�d�p�o<q�k{f�f�p�f�k�g<y�q�b�l
¤:ª#¥v§1�jÆXt�b�d*k�o�o�b�l���k
fTn�mCf��Þn
b�fTl�mHg<i�k
z±l�g&p*g<b�l���p�l&l:k
d�mH�
p*g<b�n²�jmHg&t�g�t�b�bvhHb*deg&o:k�f�g&o�p�f�l<��k�o�g�p�hAk
f
��g&t
b�g<y�q�b�m,f
g�t�mHl }�k�n
b�h<� m,l �TmHw
b�f q�i g&t
b o:b�h,p*g�mHk�f
. (ε) =
¥ ¸ π(
¬
σ
�
− ε
ê
)
è � ê �#�<f
g�bJ�To&p*g�mHk
fÊk�z � |½�#Äe¦�ž�jm�g�tg�t�mHl . (ε)
i�mHb�h�n�l � � = � ë ( ¬ πσ� ¸ ε ë ) �Xl:k´g�t�p*gsg�t�b³z:p*d*g<k�oa � q�b*d*k�}Ïb�l
a � =
¦ � ë
�
πσ�
ε ë
dek
l
( º π� � 6 � ) ÄJª½¥�Å
Ä � ë ( � )
mHl�g�t
b´Ûcb�l&l:b�h�zFy�f�d*g�mHk
f.Å�� Æ"t�b³d�p�l:bÊk�zsp�l&mHf
�#hHb
d*iTh,m,f�n
b�o�dek
o�o�b�l&�
k
fTn�l�g<k�g�t�b±��o:k�t�mHqTm�g�mHk
f�k�zsb�hAb*deg&o:k�f
g<y�fTf
b�h,m,f
� q�beg���beb�f g&t
b¡p�n
��p*d*b�f�gÌd*i#h,mHfTn
b�o&l*�¿m�� b��F�
σ = � �RÆ"t
bjn�b�f�l�m�g<i³k
z°l�g&p*g<b�l¼mHf�g�t�m,lsh,mH}jmHg¼mClÕ��m�w{b�f�q�i. (ε) = δ(ε)
�T�utTmCd�t�m,}u�#h,mCbvl¼g&t#p�g^� � bv|�y#p
h8l>yRf�mCg�i�pvf�na � =
¦�d*k�l
( º π� ��� ë ) � �jp�w�m,f���p*g�t�p�f�n��"|Tl��XÄe¦�ÔTÅ�p�f�nÄJª#¥�Å��"k{f
bÊdep�f�d*p�hHdJy�h�p1g:b�g<t
b±l�y�}�mHf-�X|r�ÉÄ�ª � Å��X��t�mEdetn
bJg:b�o:}�m,f
b�l¼g&t
bul<t�p��
bjk�zÕg�t�b�k�l:d�mFhFh�p*g&mHk�f�l¾k�zÕg�t�b�d�o&mEg�mC�
d�p�hjg<b�}��
b�o�p�g�yTo:b
δ
� ° (Φ) ≡ (
� ° (Φ) −
� °∗(
�
)) ¸ � ° ë ( � )
m,f
yTf�mHg�lµk�zÊg&t�bÖ|
yTp�f�g�mHg�i��
( � )ε ë �ÏÆ"t
bÖo�b�l�y.hHg�l�k�zÊg�t�bf�yT}�b�o<m�d�p�h�d�p�hAd*y#h,p*g�mHk
fTlÕk{z
δ
� ° (Φ)
zFk{oÉn�mAz:zFb�o�b�f�g°w�p�hHyTb�l
kvzÕg�t
b��
p*o:pe}sb&g:beo:l (
=
¦
π
� � ° ë ( � ) ¸ ε ë pef
n � = ν ¸ π ( ° ë (� )p�o�bËl�t�k��jfÀmHf �.mE�"�u¥
� ��bÖl:b*b�g&t�p�g�m,f��Tb�f
b�o&p�hjg�t�b
l&t�p���b¿k
z�g�t�b¿¯¾tTp�o�k
f�k�wT½Ûck{t�} k�l:d�mFhFh�p*g&mHk�f�l�k�z�g�t�b
g�o&p�f�l&mHg&mEk�f�g�b�}��
b�o<p�g<yTo�b±m,f�g&t
b±l�yT��b�o:d*k�f�n�y�deg&m,f���g<y�q�b
m,luf�kvguk�z�g�t
bxl&m,}��#hHb�d*k{l&mHf�bxzFk
o&}Údek
l
(
¦
πΦ̧ Φ ë ) q�b��d�p*yRl�buk{z¾g&t
bud*k{f�g�o<m�q�y�g�m�k�f�l�z:o�k
}Ìg&t�butTmA��t�b�ost�p�o<}�k�f��
mHd�l�Ä � =
¦R��ªr�³�,�F��Å����Fg�g�pv£�b�l�g&t
b�t�p�o�}Ïk�f�mHd�l&m,f
b�h�m,£�b
zFk�o<} k{frhAi�zFk{o�l�yTz:z:m�d�mHb�f
g1hAi²h�p�o���b ( pvf�n � p�lsk{f�bud�pvfl�beb�mHf �.mO�c��¥
� » �¼Æ"t
b�l<b�|
yTp�f�g�m�g�mEb�l�n
b��
b�fTn¨k�f�� ° � (� )p�f�n�g&t
bub�f�b�o���i�hHbew
b�hXq#o:k�p�n
b�fTmCf��
ν
�#�jt�mEd�t´g�t�b�o�b�zFk�o�b
p*d*g¼p�l¾z:p*deg�k�o�l¾nTp�}���m,f{�±g�t�b�p�}j�Rh�mHg�yTn�b�l¾p�f�n�l<}�b�p�o&mHf
�
g�t�bjz:mHf�bjl:g&o<y�deg�yTo�b�k{zÕg�t�b�l�b�k{l�d�mFhFh�p*g&mHk{f�l*�RÆ"t
b�w�p�hAy�b�k{z
g�t�but
k�����m,f���mAf�g<b1�To&p�h p�h,l:k�l:g&o�k{f��RhHi�p�z:zFbed*g�l g�t�b�l�tTp���b
p�f�nup�}j��h,mHg�yTn�b�l"k�z#g&t�b¾k�l�d�mFhFh,p*g�mHk�f�l��{p�l"k�f
b>d�p�f�g�bvhFhTq�i
d*k�}��Tp�o�m,f
� �rmA�X�¾¥
� ( p�f�n��.mE�"�¾¥
� � �XÆ"t
bub�fTt�p�f�d*b�}�b�f
gk�z
σ
d�t�p�f���b�l´g�t
b²k{l�d�mFh8h,p*g�m�k{f���p*g<g<b�o<fÇp�f�nÀl�g�o�k{f��#hAi
n�b���o�b�l&l�b�l g�t�bjpv}��rh,mKg�yRn�b�l��
Æ"t�bug<b�}j�
b�o<p�g<yTo�b³pvf�n�q�o:k�p�n�b�f�m,f{�
ν
m,f�z�hHy�b�f�d*bug�t�b
p�}���h�m�g<yTn�b�k�z�g&t�b � g�t�t�p�o&}sk�f�mHd�g&tTo�k
y
�TtÖg�t�bxz:p*d*g<k�o
� � ( �>� ν)
���jt�mEd�t�n�bed�o�b�p�l�b�l>o<p���mAnrhHi±p�lÉg�t�b���pvo�p�}�b*g<b�o&l
� p�f�n ( � mHf�d�o�b�p�l:b��¾��f²g&t
b�d�p�l<b��jt�b�fÖ¦ π� �
� ξ( ( )
�
g�t�mHl¼z:p�deg�k{o¾q�bed*k�}�b�l¼p�f�b*�T��k{f�b�f�g�m,p�hczFyTf
d*g�mHk�f
� � ( � � ν) ≈
º
¥
+ �
b*�#�
−
�
( ∗
�
b*�T�
− ν
π ( ∗
ÄJª�¦�Å
n�b��
b�f�n�m,f���k�f�l:k�}�bjdvt�pvo&p�d�g�bvo&m,l¹g�mCdug�b�}��
b�o�p�g�yTo:b³� ∗ =
= ¶− � ë ¸ ¦ π � � �c�Ït�mHd�t�m,l�p�n�bed�o:b�p�l&m,f��ËzFyTf�d*g�mHk
f�k�zsg�t�bo&p�n�mHyTl ���°�FgjzFk�h8hHkv�jlÏg�t�b�f�z:o�k{} � |�l*�°ÄJª � Å�p�f�n²ÄJª�¦�Åg�t�p*g�g&t
b�|
yTpvf�g<yT} ¯sÛ k�l�d�mFhFh,p*g�mHk
fTlÎk{z�g�t�b¿d�o<mHg&mHd�p�h
g<b�}��
b�o&p*g�yTo�b n�bed�o�b�p�l�b be����k
f�b�f
g�mCp�h8hHi �jmHg&t � m,z
¦
π
���
�
ξ(
� ° ë ) �"Øjf´g�t
b�k
g�t
b�ost�p�fTnX�R�jt�b�f��Ìbe��d*b*b�n�lg�t�b¡Ásm,f
ÂJq�y�o:�T½ÃXp�f�nTp*y d*k�t
b�o�b�f
d*b¡hHb�f���g�t
ξ ��� (
� ° ë )
u10eë d è æ<è é�e f�è æ<éJè é>h i%jpk m%jpo e>qts%oFê<ëeì�ì*ì�êFä�á<ëvu
ê>f�å w
Äem�� b��,��mCf�g&t
b�Á�Ã�o:b1�Tm,}�b
Å��cg�t�bÊ��o&p�n�m�b�f�gjg�b�o�}Úm,f²g�t
b
z:o<b*b�b�f
b�o:��iÊbe�#��p�f�l<mHk�f�l&t
k
y#h�nÊq�bjp�n�n�b�nÊg�k³g�t�bjo&mE�Tt
g��
tTp�f�n�l<mCn
bjk
z,�X| �.Äe¦vÒ�Å�Ð
¥
¦��
¶−
3 ∇ −
¦ »��
·
Ψ
ê
� ÄJª{ª#Å
ÆXt�b�Á�mCf
ÂJq�yTo��T½ÃXp�f�n�p*y�k�o<n�b�o���p�o&p�}�beg�b�o
Ψ
m,f �X| �
ÄJª{ª#Å�m,l���o�k{��k{o�g�mEk�f�p�hjg<k
∆
¤:ª
¦�§JÐ
Ψ = γ
� � ∆ ����t�b�o:b
γ
ê
=
Ò
ζ(
ª
) � � ë� � ( � )��¦ π ê � ° ë zFkvosd�hAbep*f�l:y��
b*o:dJk
f{n�y�dJg:k{o�l
p�f�n
γ
ê
= π
� � ë � ( � ) � ¸ ¥e¦ ¶−� ° � zFk
o�n�m,o�g<iÀl�yR��b�o�dek�f�n�y�d��g<k�o�l�� ��b�o�b � ë m,lsg&t
b��#b�o<}�mcw�bvhHkvd�mHg<i½�cp�fTn ζ(
ª
)
m,lsg�t�b
ÂJb*g�p�zFyTf�d*g�mEk�f½� �
= ¶−� ë ¸ ν
��Æ"t�b�z�hAy���k�mHn�|�y�p�f�g&mKÂ*p*g�mHk�f
m,f�p�g�t�m,f�l�yR�
b�o:d*k�f�n�y�deg&m,f���dei�h,m,fTn�b�o¾}�p�£
b�lÉg�t
bjl�yT��b�o��
d*yTo&o:b�f�gÖw
bvhHk
d�mEg�i � = ( ¶−̧ � �
)
}�mAf��
( \ − Φ ¸ Φ� ) � � pvfk�l:d�mFhFh�p*g�k�o�i¿zFy#f
deg&mHk{f�k
zug&t�b�o�p�g�mEk
Φ̧ Φ� ��t�mHd�t¿m,l�p}�p�fTmHzFb�l<g&p*g�mHk
f�k
z¼g&t
b�Ã.mHg�gJhHb�½Ñ"p�o�£�lsb�z:zFb*d*g�¤�Ò��KÓT§�Ä \ m,lp�f�m,f�g<b1��b�o1Å��XÆXt�yTlsg&t
b³z:o�bebub�f�b�o���i�b*�T�Tp�f�l�m�k{f�k{z!�X|X�
Äe¦
Ò�Å�mHf�g&t�buÁ�Ã�o�b1�Tm,}�b�g�p�£�b�l g�t
buzFk{o&}
� · −
� �
≈ Ψ
�
γ
α(
�
) −
¦
ε ë ∑�
=
è
∞ a � � � ( � � ν)
d�kTl
º π4 Φ
Φ ë
+
� � ê
¦
+
� � � � ÄJª
¬TÅ
�Àb�l�b*bsg�t�p*gÉg<��ku��t�i�l<mHd�p�h8hHi³n�mAz:zFb�o�b�f�g�o�bJ�RmH}�b�lÉl&t
k
y#h,n
qTb n�m,l�g�m,f���yTm,l<t�b�n½� �<f g�t�b }�b�l�k�l:d*k���mHd o�bJ�Tm,}Ïb��
¦
π
�
≤ ξ( ( )
��g�t�bÝz:o:b*bÌb�f�b�oF�Ti �TmHw
b�fÚq�i �c|½��Äe¦{Ò�Å
k�l�d�m�h8h,p*g<b�l²�jmHg�t���b�o<mHk
n
Φ ë k�fÌp�d*d*kvyTf�g�k
z�g�t�b¿¯sÛb�z:zFb*deg�� ��f g�t
b Ásm,f
ÂJq�y#oF�T Ãrp�f�n�p*y o�bJ�Tm,}Ïb��
¦
π
� �
�
ξ( ( ° ë ) �sg�t
bÖtTp�o�}�k�f�m�d�k{l�d�mFhFh�p*g&mHk{f�lÊ�TmHw�b�f�q�ig�t�b±l:y#}~k
w
b�o � m,f �X| �cÄJª
¬TÅ�w�pvf�m,l�t"�cp�f�n�g&t
b±��b�o&mEk�nk�zÇk�l:d�mFhFh�p*g&mHk�f�l�q�bed*k�}�b�l�b�|�y�p�h¿g<k g�t�b l�yR��b�o�dek�f��
n�y�d*g�mCf��¿z�hAy���|
yTpvf�g<yT}
Φ = Φ ë ¸ ¦r�¼�:fÖg�t�mHlud�p�l<b´g�t
bk�l�d�m�h8h,p*g�mHk�f�lÉp�o�b¼d*k�}j��hHb*g<b�hAi³n
b*g<b�o&}�m,f�b�n�q�i�g�t�b�l:y#�
b�o<�
dey#o<o�b�f
gjg�b�o&}�� � ê ¸ ¦R��p�lumHf²g�t�b±d�p�l:b�k�zsg&t
b�dek�f
w�b�f��g�mHk�f�p�h>Ãrm�g<gJhHb�½ÑXp�o&£�lsb�z:zFbed*g��XÆ"t
bud�o&mHg�mEd�p
hcg<b�}��
b�o�p�g�yTo:b
k�l:d�mFhFh�p*g�b�lum,f²g&tTm,luo�bJ�#mA}�bxp*d*dek�o�nTmHf��Ëg<k�g&t�b�l�g�p�f�nTp�o&n
Ã.mHg<g1hAb���ÑXp�o&£�l¾b�|
y#p*g�mHk
f
� ° ë (Φ) =
� °∗(
�
) + � �OÒ�ª ξ �
� � � ë ( � )
}�m8f
&
− Φ
Φ
�
�
ÄJª@��Å
Æ"t�y�l³pvf�m,f
d�o<b�p�l�bxk
z � o<b�l:yrhAg&l±mCf�p�d�o�k
l�l�k
w{b�o³z:o�k
}
t�p�o<}�k�f�mHdÀk�l:d�mFhFh�p*g&mHk{f�l�k{z²g�t�bÀd�o&mKg&mHd�p�h�g�b�}���b�o<p*g�yRo�b
� ° (Φ)
�Ïm�g�tÀ��b�o�mHk�n
Φë m,f g�t
b²¯¼t�pvo�k�f�k{w�½Ûck�t�} o:b��
�Tm,}�b�Ĺl�b*b��X|½�>ÄJª � Å�Åug<k²g�t
b���p�o&p*q�k�h�mHd�ÃXmEg�gJhHb� ÑXp�o<£�l
®��-È ¾ ×wîÊâ¢á ï�âÂÎÃÖeÛÃà�ÛÃÚÂð�ñ�ÛÃâ�Í ÛÃìeäbÏ�Ð¥Ð�Îvô�Ï ÛÃà¢ì ÛÂõ�ô¼â¢á äcÖ�Ï ô�Ï äbÎÃÐ�ôûávÍ.÷ÂábÖeÎvôeß�ÖeáþÛÂõ�Î ìeôeÎbäcÝ Û¢õ�â�Û´Ð�Ð�ÛÂý�ìeß�÷ÂábÖeäcÛÃà�Ô ß�äcô�Ï à�ö ädç-Ð�Ï à¢Ô�ácÖeì
δ ø ù (Φ� Φ
!
) ≡ (
ø ù
(Φ) −
ø
∗(
�
))� ø ù� (� )
ò�ìeácáÆË � ×�ò80¢ë�óbó�Ï àTߢà¸Ï ôeì.ÛÂõ"ôeâ�á � ß�Îbà�ô�Ï ô¥ç � ( ë )ε � ò Φ Ï ì.ôeâ�á)õûÐÓߢüTôûâ�ÖeÛÂß�öÂâjÎ)â�Û´Ð�Ð�Û�ý,é�Îbà�Ô Φ� Ô¢ácà�ÛÃôeácìôeâ¢áfõ¥Ð�ßÂü � ߢÎvà¢ôeß�Í�óÃ×�î�â¢áwà¢ß�Í.ácÖ�Ï äbÎÃÐ+äbÎÃÐ�äc߸Ð�ÎÃôeÏ�ÛÃà¢ì�ÛÂõ δ ø ù (Φ)
Ï àfå�Ï öÂìbׯèÃé �� è � ÎbÖ¼áfÔÂÛÂàÂá�õ�ÛÃÖ�Ô-Ï�õ¥õ�ábÖeácà�ô�ÚÂÎ�ÐÓߢácì�ÛÂõXô¼â¢áw÷¢ÎvÖeÎÃÍ.ácôeácÖeì
=
ê
π � � ù� ( � )� ε � é Ä = ν� π � ù� ( � )
é °
= � πσ � ε � é¿Îbà�Ô � µ � =
ècëÂëÃë¸Ñ
=
ë�×�è�é Ä
=
èÃé °
=
ë¸×�è#ò¯åÊÏ�ö¸×�èÃé ó��
=
ë�×�èÂé Ä
=
èÃé °
=
ècëºò�å�Ï ö�×�èÃé Ä ó��
=ë¸× êÃí�é Ä
=
èÂé °
=
èbë�ò�å�Ï ö�×�èÃé ° ó��
=
ë¸× í-é Ä
=
èÃé °
=
è¯ë�ò¯å�Ï ö�×�èÂé Å ó��
=
èÂé Ä
=
èÂé °
=
èbë)ò�å�Ï ö�×�è�é � óÃ×
a W � .cb . W
d è æ<è éMegf�è æ<éJè éHh�i%jlknm%jpoUerqts%o8ê�ëeì�ì*ìvê�ä�á<ëvu{êrf�å*w u10��
k�l�d�m�h8h,p*g�mHk�f�l��mHg&t��
b�o�mHk�n
Φ mCfug�t�b�Á�m,f
Â1q�yTo��T½ÃXp�f�n�p*yo<b1�Tm,}�bjn�b�l:d�o&mEqTb�n�q�iB�X|½�"Ä&ª ��Å��
�#V��BFK=�YL<�ZJ`���F
ZJ`,\
Y���CL<�[HA�` AJZ><�Y�Zs_�^�[&[H<�Y�Z��F
Y�] A1^2AJ_&<pC�Z1` �r`��F`HZM?�\@Ae_�`�� � F�ZJ`,\
Y2A
�jp*wTmHf�� p*g�tTp�f�n�b�|�yTp�g&mKk�f�l�zFk{oµg�t�bËz:o:b*b�b�f
b�o���i½�
k�f�bÀd�p�f~d�p�hHdey½h,p*g<b�g�t�bÀ}�p1�Rf
b*g�mHÂep*g&mHk{f � pvf�n~g�t
b
l<y�l<d*b��
g�mHq�mFh�mEg�i
χ
q�i³g&pv£�m,f{�´n�b�o&mHw�p*g�m�w�b�l�Ð
�
= −
∂
�
∂
� �
χ =
∂
�
∂
� � ÄJª�®�Å
Ͱk�f�l&mHn�b�osz:m,o<l�gsg�t
b³}�p1�Tf�b*g�mEÂep*g&mHk�f½�c��f´g�t�b�¯sÛ¿o<b1�Tm,}sb
��b�f�g<b�o<l�g�t
b�z:o:b*b³b�f�b�oF��i"�Xp�lsk�f
bÊd�p�f�l�b*b³z:o�k{} �c|�l��
Äe¦v¬#Å�p�f�n�ÄJ¦
���Rg&tTo�k{y���t�pul�g�o�k�f{�.hAi�k�l:d�mFhFh�p*g�k�o:ixzFyTf�d��
g�mHk�f�d*k{l
(
¦
π4 Φ̧ Φ ë ) �Xl<k´g�t�p*gjn�b�o&mEwTp*g�m�k{f�m,f �X|X�cÄJª�®�Åm,l¾g&o�mEwTmCp�hXpvf�nµi�m�bvh,nTl
� * , -
= −
¬
π
�
ε ë
¦
π
Φ ë
∑�
=
è
∞ a / Ψ� ( ( � ∆
�
ν)� ����
º π� Φ
Φ ë
�
ÄJª�Ò�Å
��g¾mHl¾mHfTl�g�o�y�d*g�mHw
bsg<k�qTb1�Tm,fug&t
b�p�fTp�hHi�l&m,lck
z"g�t�bÏl�tTp���b�k
z
g�t�bÏzFy�f
deg&mHk�f � * ,�-
(Φ)
�jmEg&t³d*k{f�l<mCn
b�o&p*g&mHk{fÊk{z g�t
b�h,m,}jmH�
g�m,f��¢d�p�l�b
∆ = σ = ν =
�
= � �Ïl&m,f
d*b�g&t�bÖl:yT} m,f �X| �
ÄJª�Ò�ÅÖm,f�g�t�m,lÎd�p�l:b�d�p�f�q�b�d�p�hHd*y.h,p*g<b�nÌp�f�p�hAi
g�m�d�p�hFhAi �
�
beg�g�m,f���g<k�ÂJb�o�k�g�t�b�l:bË��p�o�p�}�b*g<b�o<l�m,f �"|½��ÄJª�ÒTÅ����sb
tTp*w�b
� ÛÂìeä (Φ) =
� Û�ìcä+ +
� Û�ì¼ä− � ÄJª�Ó�Å
�jt�b�o:b
� ÛÃìeä± =
¦
ε �
πΦ ë ∑�
= è
∞
(−
¥
)
�
�
l�m,f
¦
π�
Φ
Φ ë ±
� 6 ë +
¥
¦
�
ÄJª�Ô�Å
ÆXt�b�l:y#}Àm,f � |X�RÄ&ª�Ô�Å�mClcb*�Rp*d*gJhHi³p�l&p*�j�Cg<k�k{g&t³zFyTf�d*g�mEk�f
k�z�mHg&lxp�o���yT}�b�f�g�mHf�g&t�bÖ��p�o�b�f�g�t�b�l�m,l��ÏÆ"t
b�o<b�zFk{o�b²g�t
b
}jp1�Rf�beg&mHÂep*g�m�k{f � Û�ì¼ä (Φ)
k�zsp�l�m,f
�#hHb³d*i�h�m,f�n
b�ouÄ
σ = � Åp�gÉÂJb�o�kug�b�}��
b�o<p�g�yTo:b�p�fTn´hHbew�b�h#qTo�k{p�n
b�f�mHf
�
ν
m,l¾p�l:y#}
k�z>g���k�l�p*�j�Cg<k
kvg&t���o�k{z:m�hAb�l*�°p�l�mAl�l<t�kv��f�mHf-�.mE�"� ¦R� ( �
ÆXt�b��
b�o<l&m,l:g�b�f�g�d*yRo�o�b�f
gup�f�nÎg�t�b³d*k�o�o�b�l���k
fTn�mCf��Ë}jp1�T�
f�b*g�mHÂJp�g�mEk�f¿zFyTf�deg&mHk�f � ÛÃìeä (Φ)
k�zup�g�t�mHf¿f
k�o�}jp�h�o&m,f��
Äez:m,o<l�g�kvq�g&pvmHf�b�n�q�i��¼y#h,m,£�¤:¦
Ò�§�Å���b�o�b±l�g<y�n�mHb�n�m,fÎg�t
b
�Tp��
b�o�¤Fª{ª#§¼p�f�n�h,p�g�b�osn�m,l�dey#l<l�b�nxmHf�n�b*g�p�m�h m,f´p³o:b*wTmHb*�
pvo:g&mHd�hAb�¤Fª
¬#§1� +�k
f�b*g�t�bvhHb�l&l���p�luk
f�b�d�p�f�l�bebxz:o�k
} �X| �
ÄJª�Ò�Å���g�t
b�}jp1�Rf�beg&mHÂep*g�m�k{f�k
zÖg�t�bÀg<y�qTb�mAl�l:g&o�k{f��RhHi
pvz:zFb*deg�b�n�q�i�g�t
bup�n�n�mHg�m�k{f�p�h z:p*d*g<k�o a � (σ)
�rÆ"t
buo�k�hHbjk
z
g�t�bjl:g&p�d�£�m,f���z:p�d*g<k{o a � (σ)
mHf�g�t
b�l�t�pv�
b�k
z � Û�ì¼ä (Φ)
m,l
f�k
f�g&o<mHwTmHp�hÏp�f�n�m,l�mFhFhAy�l:g�o&p*g�b�n�q�iÖg�t�b�o�bvh,p*g�m�w�bxg&o<p�f�l<�
z:mE��yRo�p*g�mHk�f�l�k�zÖg&t�b�k�l:d�mFhFh�p*g&mHk{fÚ��p*g<g<b�o<f�l�l<t�kv��f mCf
�.mE�Tl���¦r� ( pvf�n�¦r� � �¼�<f
d�o�b�p�l<m,f��Ëg&t�b´g<b�}j�
b�o&p*g<yTo�bxp�f�nhHbew�b�h¼q#o:k�p�n
b�fTmCf��¿nTp�}��Ög�t�b�p�}���h,mHg<yTn�b�luk{z�g&t
b�t�pvo��
}�k{f�mHd�l���}�p�£�m,f���g�t
b�zFk�o<} k�z�� ÛÃìeä (Φ)
d�hHk{l�bÖg<kÀl<mC�
f�bvh,mH£�b��rp�l>k{f�bud�p�f�l�bebum,f �rmA�X�X¦R� · �XÆ"t
b³l<t�p��
buk
z¾g�t�b}�p1��f�b*g�mHÂJp�g&mEk�f k{l�d�m�h8h,p*g�mHk
fTl²mHf�g�t�b¿l�yT�
b�o�dek
fTn
y�d*g�mHf
�
g<y�qTbud�p�hAd*y½h�p*g�b�n�k
f�g�t�buqTp�l&m,l>k�z � |X�cÄJª{Ò�ÅjzFk�osnTmCz:zFb�o��
b�f�gcw�p�hAy�b�lÕk{z½g�t�b���p�o<p�}�beg�b�o&l
∆ � σ � ν
��p�f�nu��m,lcl&t
k
�jf
m,f �rmO�c�"ª#�cÆXt�b±}�p1�Tf�b*g�m�¹p�g�mEk�f�k
z¼g&t�b�l�g�p*d�£�k�z>d*i�h�m,f��
n�b�o�l¼m,l>m,fTt�b�o�b�f
gJhHi�o<b�h,p*g<b�n�g<kÊg�t�b�l�k��Cd�p�h8hHb�n´�
b�o&l�m,l�g<b�f
g
d*yTo&o:b�f�g �
= · � ¸
(
= π � � ) �¨Æ"t�mClÌd*yTo<o�b�f
gÝz�hHk
�jl
p�o�kvy#f�nÊg�t�bjt
k�hFhAk�� p�f�n�g�t
b�o�beq�i³d�o:b�p�g<b�lÉg�t�bj}�p*�Tf
b*g�mC�
ÂJp*g<mEk{fr�XÆ.t
b*o:bezCk{o�bjk
l:demCh,hAp*g<mEk
f�l>kvz¾g<t
bu}�p1��f�bJg�mEÂJpJg<mEk
fxp*l
pÉz,y
fvd1g�mEkvf>kvzTz�hKyv�jp�hAlFk¼mK}���hKi¼kvlFdJmChHhAp&g<mOkvf{l�kvz�g<t�bc�vbJo:l:mHlFgFbef�g
dJyTo�oFb�f�g��Ï��mEg<tÇg�t�b¿p*}���hAmEg:yTn�b � ÛÃì¥ä (Φ) = · � Ûbìeä (Φ)
���¾�
Æ.t�b¼k{lFd�mCh,hAp*g<mEk{f
lÕkvz½g<t
b�lFyTl�dJbe�
g<mEq�mCh�mEg:i�dep*f�q�b¾d�p�hKd*y�hAp*g:ben
q�i�g<p�£
mAf{��g<t
b�n
beo�mKw�p1g<mEw{b
χ
* , -
(Φ) = ∂� ÛÃì¥ä (Φ)
�
∂
� �¾�<f
g�t�b³f
k�o<}�p�h°l:g&p�g�b��#yRf�n�b�o>g�t
bud�kTf#n#m,gJmFkTf#l
∆ = σ = ν =
=
�
= � ��g&t
b¡}jp1�Rf�beg&mHÂep*g�m�k{f zFy#f
d*g�mHk
f � Û�ìeä (Φ)
m,l
�TmHw�b�f�q�i�g�t�b�l&p*�j�Cg<k�k
g�t�zFyTf�d*g�m�k{f´k�z �X|½�cÄ&ª�ÓTÅ�p�f�n�m,l
®��-È�� ׸î�â�á.ï�â�ÎbÖeÛÃà�ÛÃÚÂÌûñ�ÛÃâ¢ÍwÛÃìeäbÏ�Ð�Ð�ÎbôdÏ ÛÂàÂì"ÛÂõ�ô¼â¢á.Í.ÎböÂà�ábôeÏ�ÜdÎbô�Ï ÛÃàºÛ´õ
Î�ìeôeÎväcÝXÛ´õ â¢ÛÂÐ�ÐÓÛÂý�à�ÛÃÖ�Í.ÎÃÐ�ädç¸Ð�Ï à�Ô¢ácÖeì ú �����
(Φ� Φ � ) ò�öÂÏ�Ú�ácà^æ�ç Ë � ×ò80J/�ó�ý�Ï ôeâ
∆ =
ë ó Ï àºß¢à¸Ï ôeì"ÛÂõ�ôeâÂá � ß�Îbà�ôeÏ�ô�ç ú (
ë
) =
ê ε � · � Φ
! ׸îÊâ¢á
à�ߢÍ.ácÖ�Ï ävÎ�Ð�äcÎ�ÐÓäbߢÐ�ÎbôdÏ Û�à�ìÕÛ¢õ ú �����
(Φ � Φ � ) Ï à^å�Ï öÂìv×"è�é ð�è ° ÎvÖ�á)Ô�ÛÃà¢áõ�ÛÃÖ Ô¸Ï�õ¥õ�ábÖeácà�ôþÚÂÎÂÐÓߢácì Û¢õ ôeâ�á ÷¢ÎvÖ�ÎvÍ.ácôeácÖeì
=
ê
π � ø ù� ( � )� ε � éÄ
= ν� π � ù� (� )
é °
= � πσ� ε � é�ÎbàÂÔ ��µ � Ñ =
ë�× ë�èÃé Ä
=
ë�× ë�èÃé °
=
ë�×�è é
� µ � =
ècëÂëÃë ò¯å�Ï ö�×.èÂé ó��
=
ë¿× ë�èÂé Ä
=
ë¿× ë�èÂé °
=
èÂé ��µ � =
ècëÂë
ò¯å�Ï ö�×�èÂé Ä ó �
=
ë�× ë¸èÃé Ä
=
ë¿× ë�èÂé °
=
ë¸×�èÃé � µ � =
èbëÃë)òcå'Ï öÊ×'è�é ° ó�×
u10�x d è æ<è é�e f�è æ<éJè é>h i%jpk m%jpo e>qts%oFê<ëeì�ì*ì�êFä�á<ëvu
ê>f�å w
l�t�k{��f�m,f �.mE�"�X¦#� (r�XÆ"t�yTl
χ
*�,.-
(Φ)
m,f�g&t�m,lsd�p�l�bu��k
y#h,n
tTp*w�b³n�bvhHg�p��8zFyTf�deg&mHk�fx��b�p�£�l�p*gsg�t�b��<yT}j��lsk{z g�t�b³l<p����
g<k
kvg&txp�f�nxpÊf
b1�Rp*g�mHw
bud*k{f�l:g&p�f�g>wTp�hAy�buq�beg���b*b�f�g&t�b�}µ�
Æ.b�}��
b�o&p*g�yTo�bµp�f�n
ν
�°p�l���b�hFh p�l
∆
p�f�n
σ
�°l&}sb�pvo�g�t
b
l�mCf���y.h,p�o¿zFb�p*g<y�o<b�l�m,f � * ,�-
(Φ)
�µp�l�k{f�bÀd�p�f�l:b*bÞmCf�rmO�½��¦R� ( p*f�n8�#m3�½�{ªr� · ��}�p�£
mHf���g&t�b χ
*�, -
(Φ)
p�t{p�o�}skvf�mEde�
h�m,£�bµzFy#f
d*g�mHk
f²g<kvk½� +¾b�p�o�g�t�b�g�o<p�f�l&mEg�mHk�f�g�b�}��
b�o<p�g<yTo�b��
�To�k{w�m,n�b�n�g�t�p�gËmEgËmClËt�mE�TtÌb�f
k
y
�TtÌg&t�p*g�g&t�b�t�mE�Tt�b�o
tTp�o&}sk�f�mHd�lÉd�pvfÊq�bjf
b1�.hHbed*g<b�n½�T��bÏt�p*w�b�z:o�k{} �c|½�#Äe¦{Ò�Å
pjl�m,}j�RhAb�p�f�p�hAi
g�m�d�p�h#b*�T��o�b�l�l&mHk{fÊzFk�oÕg�t�b�l�yTl�d*b���g�mHqTm�h�mEg<i Ð
χ ≈
¦
ε ë
¦
π
∆
Φ ë
ê a è � è ( � � ν)
dek
l
¦
π Φ
Φ ë
ÄJ¬ � Å
¯¾ded*k�o<n�mAf��xg�k�� |X�cÄ�ª�¦�Å�g&t
bug<b�}j��b�o&p*g<y�o<buq�b�t�p�w�mHk{osk
z
g�t�bjl�yTl�deb��
g�m�qTmFh,mKg�i�f�b�p�o¼� ° mHl
χ ∝
be�T�
−
(� ∗
ÄJ¬.¥vÅ
�
y�d�t�pÊg�b�}��
b�o�p*g�yTo�b±n�b���b�f�n�b�f
deb�k
z¼g&t�b�}�p*�Tf
b*g�m�d
l�yTl:d*b���g&mKq#mCh�m�g<iÝt�p�l²q�b*b�fÝzFk�yRf�n~o:b*d*b�f�gJhHiÌm,f�b*�R�
b�o<mC�
}�b�f
g&lÊk{f�p�q�yTf�nrhAb´k�z�b�hAb*deg&o&mHd�p�hFhHi¨mHl�k�h,p�g�b�n¨¯c�*),+¾q
�jm,o�b�lΤJ¥eÔ�§1� �Xw
b�o�i¿��m,o�b�m,f�g&t
b�q�y�fTn�hHb���p�l±p²w
b�o<i
d�hAb�p�f�¯Õ�±d*i#h�mHf�n
b�o¾d*k{p*g<b�n���mHg&t³g&tTmHf�l�yT�
b�o�dek
fTn
y�d*g�mHf
�+¾qÀh,p*i�b�o*��Æ"t
b�p*y�g&t�k
o�lÊk
z�a°b�z1��¥1ÔÖp�h,l�kËk�qTl�b�o�w�b�n¿p
d�o<k
l&l:k
w
b�o¾mHfÊg�t
bsg�b�}��
b�o�p*g�yTo�bsq�b�t�p*w�mHk�ock�z½g�t�b�l:yTl�d*b����
g�m�qTmFh,mHg<i²�Ït�mHd�tÖn
k
y�q#hHb�l×g�t
bxo�p*g�mHk�� ¸ � ∗ →
¦ ( ¸ � ∗ m,fg�t�b�be�#�
k�f
b�f�g�k�z
χ(
�
)
��t�b�fÖ� N � ∗ � �Àb�d�p�fÖo�b�h�p*g�bg�t�mHlÀ��t�b�f
k�}�b�f
k�f�g<k�g&t�b~z:p*deg�g&tTp*g�g&t�bÝ|�yTpvf
g&mHg<i
ξ(
�
) = ¶−� � ¸ π
��t�p�l¾p�n�kvy�q.hHb�}sb�p�f�m,f���mHf³g&t
b���o�kvq#hHb�}
m,f�|
y�b�l�g�mHk
f"���.m,o<l�g��¼mHg�m,lÊg�t�bxd*k�t
b�o�b�f
d*bÖhAb�f���g�t�g�t�p*g
n�beg�b�o�}jm,f�b�l�g&t
b�pv}��#h,mEg<y#n
b�lµk{zug&t�b�¯>ÛÝk�l�d�mFhFh,p*g�mHk
fTl��
�
b*dek
fTn½�.g&t�b�hHb�f
��g�t
ξ
�
(
�
) = ¶− � ë ¸ π
��mHl�£�f�kv�jf´g<k�q�b
g�t�b�hAb�f��Tg&t�g&tTp*gun�b*g<b�o<}�m,f
b�l�g�t�b�l<��p*g�m,p�h¼l�d�p�hAb�k�zsg�t�b
��o�kv�#m,}�m�g<i�b�z:zFb*d*g��.�<fÊg�t�b�d*k�f�g<b*�Tg¾k
zÉkvyTo>p�fTp�hHi�l�mClÉg�t�m,l
}�b�p�f�l¾g&tTp*gsp*g¼g�t�b�g<b�}���b�o<p*g�yRo�b��
=
� ∗ g�t�bj¯É��d*i�h�m,f��n�b�osq�b*d�p�}�b³d*k{}���hHbeg�bvhHi�l:y#�
b�o:d*k�f�n�y�d*g�mCf��Ën
y�b³g<k�g�t�b
��o�kv�#m,}�m�g<i���mHg&t¿l�yR�
b�o:d*k�f�n�y�deg&m,f��7+¾q�d*k�p*g�m,f��"�¼l&m,f
d*b
p*gug�t�mHlug�b�}���b�o<p*g<y#o:b
ξ
�
(
� ∗) =
¦
π
�±�c¯¼lup�o:b�l�y#hAg��°g�t�b
z�hHy���m,l�b*�#�
bvhFhHb�n²z:o<k
}�g�t�bµmHf�g<b�o<mHk�o�k�zsg�t
b��jmCo:b��Õp�f�n
g�t�b³d*i�h�mCf�n�b�o�d�p�f²f
k�hHk{f���b�o�g�o�pv��g&t�b�z�hAy��Öm,f�g�t�b³¯É�
d*k�o�b��ÀÆ"t�b�o:b�zFk�o:b g&t
b d�o�k{l&l:k
w
b�o�k
qTl�b�o�w
b�n«m,f g�t�b
¯É� ),+�q�dei#h,mHfTn�b�o&l�}�p*i�q�b�dek�f�l&mHn�b�o:b�n~p�l�p�d*k{f�l:b��
|
y�b�f�deb�k{z¨g�t
b�d�o:k�l<l�kvw�b�o�mHf�g�t�bÀg�k��
k�hAk���i�k
zÖg�t�b
l�i�l:g<b�} p�lÌg&t�b�g<b�}j��b�o&p*g<y�o<bÚn�b*d�o:b�pvl:b�l�Ð��
t
k�h8hHkv���
d*iTh,m,f�n
b�o�l>�jmEg&t�p³z�hHy��xg&o&p����
b�n�mAf�l<mCn�b�g�t�b�f�k{o&}�p�hX¯É�
d*k�o�b�ÄezFk�o�g<b�}��
b�o&p*g�yTo�b�lu� ��� ∗ Å×q�bed�p�}�b±d*k�}j�RhAb*g<b�hAil�yT�
b�o�dek
fTn
y�deg&m,f
���jt�b�f � q�b*dek
}�b�luhHb�l<l�g�t�p�f � ∗ p�f�nb*�R�
b�h.g&t�bjz�hHy��xz:o:k�}�g&t
bj¯É��dek�o�b��
� V��¾\�YT_ �H^2A�`�\
YIA
Æ"t�b�k{o&mE�Tm,f�p�h½¯sÛËb�z:zFbed*g¾�jp�l¾zFk�o<}�y#h,p*g<b�n�mHf�¤1¥J¬T§°p�l
p²�Tb�n�p�f�£
b�fÀb*�T�
b�o&m,}sb�f�g�m,f �jt�mHd�t�g&t�bÖm,f�g�b�o�zFb�o�b�f
d*b
��p�g<g<b�o<f�k�z½g<�sk�bvhHb*deg&o:k�f�lc}�kvwTmCf��×p�o�k�yTfTn�g&t
b�l�k�hAb�f
k�m,n
m,f²g�t�b�p�qTl�b�f�d*b�k{z�px}�p1�Tf�b*g�mEdxz:m�bvh,nÖn�b��
b�f�nTl�k�f²g�t�b
z�hHy��Ög�t�o:k
y
�Tt²g�t�bµl�k�hAb�f�k
m,n �ÕÆ"t�mCl�g�t�bek
o<b*g�mEd�p
h¼��o�b�n�mHd��
g�m�k{f���p�l�l:k
k{f�d*k�f�z:m,o�}�b�n�m,f�p�o:b�p�h°b*�T��b�o�m,}�b�f
gjn�k�f�b
q�i�;t�p�}�q�b�o&l²¤8ª@��§*�jÃ.p*g<b�o´k{f �Ïn�m,z:zFb�o�b�f�gx}jp�f�mHzFb�l�g&p��
g�m�k{f�l�k�z�g�t�b�¯sÛÞb�z:zFb*deg³mHf�l�kTh,mHnTlut�p*w
b�q�b*b�f�l:g<y�nTmHb�n
p�f�n�}jp�f�i¿b*�Tp�}���hHb�l´�sb�o�bËzFk�yTf�n�m,f��jt�mHd�t�w�pvo�mHkvy#l
��t�i�l�mEd�p
h°��o�k
�
b�o�g&mHb�l>b*�Rt�mHqTmHgsk�l:d�mFhFh�p*g&mHk{f�lspvlszFyTf�deg&mHk{f�l
k�zÉg�t
b³z�hHy�����mHg�t���b�o<mHk
n
Φ ë Äe}jp�f�ixo:b�zFb�o�b�f
d*b�l>k{f´g�t�bl�y�q
�<b*deg�d*k�f�g�pvmHfÖo�bew�mHb*� p�o�g&mKd�hHb�l�¤1¥#�r�8¥e®��3ª
¬#§�Å��c¯Ìg&t
b��
k�o:iÖk�z�g&t�b�¯>ÛÌk{l�d�m�h8h,p*g�mHk
fTl×k{z�g&t�bxz:o�b*b�b�f�b�oF��i�m,f�p
}�beg&p�hro&m,f{�µp�f�nÊg�t�b�o:b�h�p�g<b�n³��o:k
q#hHb�}Çk
zcg&t
b��
b�o&l�m,l�g<b�f
g
d*yTo&o:b�f�g&l¼m,f�l�y�d�t�l�i�l:g�b�}�l¾�jp�lsz:mHo&l:g>dek�f�l&mHn�b�o:b�n�mAf´g�t�b
��p��
b�os¤:¦
Ò�§¾Äel�bebjp�h,l�k�a°b�z1��ª�®umCf³g&tTmHlÉd*k�f�f�b*d*g�mHk
f.żp�f�n
�jp�l>h,p*g<b�o"��b�f
b�o&p�h�m�Â�b�nÊg<k�g�t�bsd�p�l�b�k�z"l�yT�
b�o�dek
fTn
y�d*g�mHf
�
o&mHf
��mCf�aÉb�z1�¾¥eÓ��.��t
b�o�bu¯¾tTp�o�k
f�k�wT�:Û"k�t�}~k{l�d�mFhFh�p*g&mHk{f�l
k�z>g�t�b³g�o&p�f�l&mHg&mEk�fÎg<b�}j��b�o�p�g<y�o:b�� ° (Φ)
t�p�w
b³q�beb�f���o:b��
n�mKd*g<b�n ��Æ"t�b�g&t�b*k{o�b*g�mHd�p�h¼d*k�f�l&m,n
b�o�p*g&mHk{fË��m�w�b�f�mAf¨g�t�m,l
��k
o�£�n�bew�b�hHk{��l�zFyTo�g�t
b�oÖg&t�bÀo�b�l:y#hHg�lÖk�zÎg�t�bÀ�Tp��
b�o&l
¤1¥eÓ#�K¦
Ò�§*� �#k{o>g�t�m,ls�
yTo&�
k
l�b��#��b³t�p*w�bul�g<yTn�mHb�n´g�t�b³z:o:b*b
®��-È�� ×"î�â�á�ï�â�Î�Ö¼Û�à�ÛÃÚÂð�ñ�Û�â�Í Û�ì¼äbÏ�ÐûÐÓÎbô�Ï ÛÃà�ì�Û�õ.ôeâÂá�Í.ÎböÂà�ácô�Ï ÜdÎbô�Ï Û�à
Û¢õjÎwìeôeÎväbÝ�Û´õ+â�ÛÂÐ�Ð�ÛÃý ìeß�÷¢ácÖ¼äbÛÃà¢Ô�ߢäcô�Ï à�öfäcç¢Ð¥Ï à�ÔÂábÖeì ú � � �
(Φ� Φ � )ò�ìeácájË � ×�ò80J/�ócóÆÏ�àXßÂà¸Ï ôeì,Û¢õ.ôeâ�á � ßÂÎÃàÂô�Ï ô ç ú ( ë ) =
ê ε� · � Φ
! ×�î�â�á
à¢ß�Í.ácÖ�Ï�äcÎÃÐ�äcÎÃÐ�äbß�Ð�Îvô�Ï ÛÃà¢ì"ÛÂõ ú ��� �
(Φ� Φ � ) Ï àÿåÊÏ�öÃìb×�èÂé ð�èÃé ° ÎvÖeá.Ô¢ÛÃà�áõ�Û�Ö Ô�Ï�õ¥õ�ácÖeácà¢ô ÚÂÎÃÐ�ß�ácì Û´õ ô¼â¢á ÷ÂÎÃÖeÎbÍ.ácôeácÖdì
=
ê
π � ø ù� ( � ) � ε � éÄ
= ν � π � ù� (� )
é °
= � πσ� ε � é Å =
ê
π∆� ε � é.Îvà¢Ô � µ � Ñ =
ë�× ë¿è�é
Ä
=
ë�× ë¸èÃé °
=
è�é Å
=
ë¿× ëví�é � µ � =
èbëÃëÂë�ò�å�Ï ö�×�èÂé ó��
=
ë¿× ë�èÂé Ä
=
=
ë¢× ë¸èÃé °
=
èÂé �Õµ � =
èvë�ë¿é Å
=
ë¸× ëví�ò¯å�Ï ö�×�è�é Ä ó��
=
ë¢× ë¸èÃé Ä
=
ë¸× í-é
°
=
èÂé Å
=
ë�× í�é � µ � =
ècëÂëÃë�ò¯å�Ï ö�×�èÂé ° óÃ×
a W � .cb . W
d è æ<è éMegf�è æ<éJè éHh�i%jlknm%jpoUerqts%o8ê�ëeì�ì*ìvê�ä�á<ëvu{êrf�å*w u10�0
b�f�b�o��Ti�k
z³pÖl:g&p*d�£�k
z³l:y#�
b�o:d*k�f�n�y�deg&m,f��¿d*i#h,mAf�n
b�o&l±mCf
be��g<b�o<f�p�hX}�p���f�beg&mHdjz:mEbvh,nÊ�jmHg&t�m,fÊg�t
b�}�mHd�o<k
l�dek
��mHd�۾��
}�k�n
b�h�p�f�n�tTp*w�b³d�p�hAd*y#h,p*g<b�n�p�f�p�hAi
g�m�d�p�hFhAi�g�t�buk�l:d�mFhFh�p��
g<k�o:i³��p�o�gck
z½g�t
bsz:o<b*b¾b�f�b�oF�TiÊÄJl<b*b �"|½�TÄ
¥JÔTÅ�Å�� ��bstTp*w
b
p
h,l:kËzFk�yTf�n�b*�#��h�m�d�mHgub*�T��o�b�l<l&mHk
fTluzFk�o�g�t�b�¯sÛÀk�l:d�mFhFh�p��
g�mHk�f�l�k�z¼g&t�bÊd�o&mEg�m�d�p�h¾g<b�}���b�o�p*g<y#o:b�� ° (Φ)
Äp�X| �°Ä&ª � Å�Å��g�t�bÝk
l<d�mCh8h,p�g�k{o�i¡��p�o�g�k�z�g�t
b�}jp1�Tf�beg&mEÂep*g�mHk�f Ä%�c|�l��
ÄJª�Ò�Å&"Ä&ª�ÔTÅ�Å��³pvf�n�g�t
b�l�yTl:d*b���g&mKq#mCh�m�g<i
χ(
�
)
f
b�pvoÎg�t
b
g�o&p�fTl�mHg�m�k{fÖg�b�}��
b�o<p�g�yTo:b²Ä%� |½�>ÄJ¬ � Å�Å���Æ"t
b�k�l:d�mFhFh�p*g�k�o:in�b��
b�fTn
b�f�deb�k�z³p�hFhjp*q�k
w{b�|�yTpvf
g&mHg�m�b�lÊk{f�g�t�b�z�hAy��
Φ�jmHg�t�g&t
b³zFy#f�nTp�}�b�f
g�p�h¾�
b�o�mHk�n
Φ ë l:g�b�}�l��Xm,f�g&t�b�hHk�f��o<y�f"��z:o�k�} g�t
b��Tp*y
�Tb¿mCf
wTp�o<mCp�f�d*b�k�z�g&t
b�g&t�b*k{o�iÀk
z
f�k
fTl�m,}j�RhAi²dek�f�f�bed*g<b�nÖl:k�h,m,n�l��¾��f²k�yTou�Tp�o�g�mHd*y#h,pvo�d�p�l:b
g�t�m,l¼z�hHyT��n�b��
b�fTn
b�f�debup�����b�p�o�l�n�y�b�g<k�g�t�b³|
yTp�l&m,��p�o�g�mH�
dvhHb�b�f�b�oF�Ti��TmHw
b�f~q�i �c|½��Ä�¥¹ª#Å��³Æ"t�b�o�b�l�y.hHg�l²k{z²p
f�yT}�b�o<mHd�p�h�p�f�p�hAi�l�m,lsk{z>g&t
b�l�buk
l<d�mFhFh�p*g&mHk{f�lsm,lsl&t
k
�jfxmCf�rmA��l��½¥1�ª½�TÆ"t
b�l<bs�TmEd*g<y#o:b�l°n�b�}�k
fTl�g�o&p*g<b�l:g&o�k{f��RhHi³f
k�f��
l�mCf
yTl�k{m,n�p�hÖk�l�d�m�h8h,p*g�m,f�� �Tp*g�g<b�o<f�l�zFk{oÇg�t�bÈzFy#f
d*g�mHk
fTl
� ° (Φ)
p�f�n � ÛÂìeä (Φ)
mCf�g�t
bÊd�p�l�b³k
z�hAk��Ýg�b�}��
b�o�p*g�yTo�b�l
pvf�n¡l�}jp�hFh�hAb*w
bvh�q#o:k�p�n
b�f�m,f��"��
y�d�tÚf�k
fTl�m,f�y�l:k�m,n�p�h
qTb�t�p*wTmHk
o�k�zsg�t�b�k�l�d�m�h8h,p*g�mHk
fTlumCl�d�p*yTl�b�n�q�i�g�t�b�l<}�p�h8h
n�b*d�o�b�p�l:b�k�zÖg�t�bÌt�pvo�}�k
fTm�d p�}���h,mHg<y�n�b�l���mHg�t�g�t�b�m,o
f�yT}�q�b�o � mHfÖg&tTmClud�p�l:b����:f�d�o:b�p�l&m,f���g�t
b�g<b�}��
b�o�p�g�yTo:bpvf�n
ν
p�l´��b�h8hup�l
∆
n�p�}j��l´g�t�b¨p�}���h,mHg<y�n
b�l´k�zÊg�t
b
tTp�o&}sk�f�mHd�lspvf�n�l&}�b�p�o<l>g&t�bul&m,f���y.h,p�o<m�g�mHb�lsm,f�g&t
buk{l�d�mCh��
h�p�g�mEk�fÀ��p*g�g<b�o�f�l���}jp�£�m,f��Àg�t�b�}�dvhHk�l:bÖg<k¿l&m,f�bvh,m,£
b²k�o
dek�l<mCf�b�h�mH£�bjmHf�l<t�p��
b��RÆ"t�b��Ïp�i±m,fÊ�jt�mHd�tÊg&t�bsd*i#h�mHf�n
b�o�l
pvo:b�l<g&p*d�£�b�n�m,f�g<kÀp�g<y�q�b¿p�h�l�kÀl�g�o�k�f��#hAi�pvz:zFb*deg&l�g�t
b
k�l�d�m�h8h,p*g�mHk�f���p*g�g<b�o&f�l�g&t�o�kvy
�#t�g�t
bÖz:p*deg�k�o a � k{z��X| �Äe¦#¥vÅ�� Æ"t�mCl³z:p�d*g<k
o³m,f¨g<y#o<f�n�b���b�f�n�luk�fÖg&t
b�l:g�p�d�£�m,f��
z:p�d*g<k{o!� � �RmEw�b�f�q�i7�c|½�¾Äe¦TÅÊp�fTnÖn
b*g<b�o&}jmHf�b�n²q�i²g�t
bn�b�f�l&mHg<i�k�z�l:g&p�g�b�l . (ε)
o�b�h�p*g�b�n�g<k�b�hAb*deg&o:k�fÌ}�k
g�mEk�f
p�d�o:k�l<l�g�t�b±l�g�p*d�£ÖÄep�hHk{f���g�t�b±g�y�q�b
Å�� Æ"t�b±n�b��
b�f�n�b�f�deb
k�zÉg&t
b�k�l�d�m�h8h,p*g�mHk�f���p�g<g�b�o�f�k
f�g�t�but
k�����m,f��xm,f�g<b1�To<p�h
σqTb*g<�sb*b�f×dei�h,m,f�n�b�o�lcm,fupsl�g�p*d�£um,fups}�k
n�b�hTn�b�l:d�o&mHq�b�n�q�i
g�t�b�z:p�deg�k{oÊk�z��X|"�sÄ&ª.¥vÅ�m,lÊo&p*g�t�b�oÊl<k
�Tt�m,l:g&mHd�p*g�b�n�p�f�n
d�p�f³q�bjl�beb�f�z:o<k
}Ìp�dek�}���p�o<m,l�k
f³k�z^�.m3�#l*�R¦R� (�p�f�n�¦r� � �ÆXt�b�¯¼t�pvo�k�f�k{w�½Ûck�t�} b�z:zFb*d*g±t�p�l³q�beb�f�k�qRl�b�o�w
b�n¿o�b��
deb�f�g1hAium,f�d�m,o�deyrh�p�oÕd�p�o�qTk
f³f�p�f�kvg�yTq�b�l¾¤Fª � §1�T�8gÕ�jp�lcp�h,l<kl�t�k{��f�g�t�p*gËl�g�o�yTd*g<y�o<p
h�n�m,l�k
o�n�b�o²b�z:zFbed*g�mHw
b�hAi�qTo:b�pv£�l
d�p�o:q�k�f³f�pvf
k
g<y�q�b�lÉm,f
g�k�p�l<b�o<m�b�lÕk{z"d*i�h�mCf�n�b�o<l ÄJk{oÉn�kvg�l*Å
l<b���p�o&p*g<b�n�q�i�g<yTf�f�b�h�m,f{�ÀqTp�o&o<mHb�o<l��ÏÆ"t
b²g�o&p�f�l<}�m,l<l&mEk�f
�To�k{q�p*qTmFh,mHg<i�q�beg���beb�f�g�t�budei�h,m,fTn�b�o&l>�jp�l>b�l�g&m,}�p�g�b�n´g<k
wTp�o�iu�Ïm�g�t�mAfÊg&t
b�h�m,}�mHg�l � � �&� ¥e � �F¥Ï¤:ªr¥v§J�TÆ"t
yTlÉf�p�f�k�g<yT�qTb�lsp�ls��b�h8h°p�l>d*k�p*g�b�n´�jm,o�b�lsp�o:b���k
k{n´d�p�f�nTmHn�p*g<b�lszFk�o
g�t�b���t
i�l�m�d�p�h#o<b�p�h,mHÂep*g�m�k{fuk�z½g�t�b�}�k{n�b�hRpvn�k���g<b�n³m,f×g�t�m,l
�Tp��
b�o��
Û"b�mCf
�x|�yTp�f�g�yT}~m,fxf�p�g<y�o:b��.g�t
bu¯>Û�k�l:d�mFh8h,p*g�m�k�f�l¼k
z
g�t�bud�o�mHg�mHd�p�hcg<b�}���b�o�p*g<y#o:b³� ° (Φ)
wTp�f�mCl�t´b*�T��k
f�b�f
g&m,p�h8hHi
�jt�b�f!�Àm,l°mCf
d�o�b�p�l:b�nug�k�wTp�hHy�b�lÕk{z½g&t�b>k{o&n
b�ock
z.g&t�b�Á�Ã
dek�t
b�o�b�f
d*bÊhAb�f��Tg&t½� �#yRo�g�t�b�o>mHf�d�o:b�pvl�bjk
zg� o�b�l�y#hHg�l¼mCf�p
nTm,}Ïb�f�l<mHk�f�p�h�d�o:k�l�l<k�w�b�o±z:o�k�}¡g&t
b�¯¼ÛÌk�l�d�mFhFh,p*g�mHk�f�lÊg<k
g�t�b�Ã.mHg�gJhHb�½Ñ"p�o�£�lck
f�b�l*��ÆXt�b�Ã"Ñ�k
l<d�mFhFh�p*g&mHk{f�lct�p*w
b�t�p�h�z
p�l×h�p�o���b±p��
b�o&mHk{n²mAfÎg�t
b�z�hAy��"�
Φ = Φ ë ¸ ¦r�cp�f�n�t�p�w
bg�t�bjl&t�p���b�k�z°��b�o&mHk
nTmEdu��p�o&p*q�k�h�p�lÏÄel:b*b �X| �.ÄJª&�TÅ�Å��#ÆXt�b
Ã"Ñ k
l�d�mFhFh,p*g�mHk
fTl g�pv£�bÙ��h,p�d*b m,f g�t�b Á�à o:b1�RmH}�b�
≥ ξ ��� (
�
)
��m,f²�jt�m�d�t²g�t�bx|
y�p�f�g�yT}¡l<m�ÂJb�b�z:zFb*deg&lupvo�b
m,o�o<b�hHbew�pvf�g¨p�f�nÝ|�yTp�f�g<yT} ¯sÛ¡k{l�d�m,hFh,p�g�mEk�f�lÖp�o�b¢l�yT���
��o�b�l<l�b�nX��Æ"t
b�ÃcÑ¿k
l<d�mFhFh�p*g&mHk{f�l�pvo<mCl:bxn
y�b�g<k�be��g<b�o<f�p�h,�
z:mHb�h�n��8m,f�n
y�d*b�nÚk{l�d�m,hFh,p�g�mEk�f�l�k�zÖg&t�bÌl�yT�
b�o�dek
fTn
y�d*g�mHf
�
d*yTo&o:b�f�gsk{z g�t
b�ÍÉkvk��
b�os�Tp�m,o�lspvo:k
yTf�n�p³t
k�hFhAk��ÈmHf�g�t�b
d*iTh,m,f�n
b�o��°��mHf�debug&t�b�ÍÉk
k{�
b�o���p�m,o<lsd�p�o&o:i�n�k�y�q½hAbub�hAb*d��
g�o�k
fTmEd�d�tTp�o���b��Tg�t
b���b�o<mHk
n�k{zÕg�t�b�l�b�k
l<d�mCh8h,p�g&mEk�f�l¼mHf�g�t�b
z�hHy��Öq�bed*k�}�b�l�tTp�h,z�pvl×h,p�o:��b�p�luzFk{o�g&t
b�|�y�p�f�g�yT}�¯¼Û
k�l:d�mFhFh�p*g&mHk{f�l*�L��b�p�h�l�k�zFkvyTf�n�g�t�p*g�f�b�p�o¾g�t�b�g�o<p�f�l&mEg�mHk�f
g<b�}��
b�o&p*g�yTo�bug�t
b³}�p1�Tf�b*g�mHd³l�yTl�deb��
g&mHqTmFh,mHg<i
χ(
�
)
k�z¾g�t�b
l�yT�
b�o�dek
fTn
y�deg&m,f
�Údei�h,m,f�n�b�o�mCl���m�w{b�fÚq�i �X| ��ÄJ¬ � Å���jt�m�d�t �Tg�t�o:k
y
�Tt´g�t
buz:p*d*g<k�o¾k
z,� |½�½ÄJ¬.¥vÅ��rn�mHl&��h�p*i�l¾g�t�b
f�k{f�g�o<m�w�mCp�h�b*�T��k{f�b�f�g�m,p�h¾g<b�}���b�o�p*g<y#o:b�n
b��
b�fTn
b�f�debÊk{q��
l�b�o�w�b�n�mHf�¯É� )�+¾q±��m,o:b�l�¤*¥JÔ�§J�
�<f�d*k{f�dvhHyTl&mEk�fX����b���k�y.h,nÇh,mA£�b�g<k�l<g&o:b�l&l�i
beg�pvf��
k
g�t
b�o�m,}��
k
o<g&p�f�g��
k�m,f�g�k{z²kvy�oÖdek�f�l&m,n�b�o&p*g�m�k{f �±ÆXt�b
��t�i�l�mEd�l�q�b�t�m,f�n�g�t�bµ|�yRp�f
g�yR} ¯sÛ�k�l�d�m�h8h,p*g�mHk�f�l�m,f²l<y��
�
b�o�dek
fTn
y�d*g<k{o&l���m,fÖb�l<l�b�f
deb��¼mAl×w�b�o:i�}sy�d�tÖl&mH}jmFh,p�oug�k
g�t�p*g��jt�mHd�t ��k
w
b�o�f�l�g�t
b�n ��w{¯ k�l�d�m�h8h,p*g�mHk
fTl�m,fÇg�t�b
w�k
o<g�be�¡l�g�p*g<b����:f l&��m�g<b�k�zÖg�t�bÌz:p*deg�g&t�p�g�g�t
b�¯¼Û
k�l:d�mFhFh�p*g&mHk{f�l¿p�o�b��
b�o&mHk
nTmEdÌm,f g�t
bÌn�m,o�bed*g�z:mHbvh,n½��g�t�b
n�p�}j��mCf��¨z:p�deg�k{o&l
Ψ� p�fTn a � b�f�g�b�o�m,f�� �c|½�¼Ä�¥eÔ�ųpvo�bp�£�mAfµg<k³g&t
bjp�����o:k���o&mHp�g�bjz:p*d*g<k{o&l¾m,fµg�t
bjn ��w
¯¿k�l�d�mFhFh,p��
g�m�k{f�lËmCf�l:yT��b�o�dek�f�n�y�d*g<k
o�l�¤<¦K��§J���#k�o²be�#p�}���hAb��³g�t�b
z:p*d*g<k�o
Ψ� n�beg�b�o�}jm,f�b�n´q�i��X|X�XÄe¦&��Å��Xp�zFg�b�o g�t�b�l�yTq�l:g�mC�g<y�g�mHk�f
ε ë = ¶−Ω
��q�b*d*k{}�b�lÉm,n
b�f�g&mHd�p�hTg<k�g�t�bÏp�����o�k{��o<m,p*g�b
z:p*d*g<k�oÝmHf�g�t�b nI��w{¯ k�l:d�mFhFh�p*g&mHk{f�l~n
b�l�d�o<mHq�m,f�� g�t�b
n�p�}j��mCf��xk{z g�t
b � g&txp�}���h,mHg<yTn�bun�y�b�g<k�g&t
b³l:yT��b�o:d*k�f��n�y�deg&m,f��Ì�Tp��
∆( ( )
�±�FgËm,lÖm,}���k
l�l�mHq#hHb¿g�kÌl�mHf��#hAb�k
y�g
b*�R�
b�o<mC}�b�f
g�p�h8hHi�g&t�b¾d*k�f
g�o&mHq�y�g�mHk
f�k�z
∆
g<k�g�t
bsn�pv}���mHf
�
k�z½g�t
b�nI��w�¯Ök
l<d�mFhFh�p*g&mHk{f�lcm,fÊl:y#�
b�o:d*k�f�n�y�d*g<k�o�lcq�b*d�p*yRl�b
k�zÊg�t�b¨l���p�g&mHp
h�}�k�n
y#h,p�g&mKk�f k�zÊg&t�b²k�o�n�b�o���p�o&p�}�b*g<b�o
∆(
[
)
d�p*yTl�b�n´q�i�g&t
buw
k�o�g�mHd*b�lj¤:¦
Ó�§1� ��m,f�debug&t
b�o�bup�o�b�f�k
w�k
o<g&mEdeb�ljmHfÎg�t
bʯsۢl�i�l:g<b�}�y�f�n�b�osd*k{f�l<m,n�b�o<p*g�m�k�fX�Xg�t�b
d*k�}��Tp�o�p�g�mEw�bsb*�R��b�o�m,}�b�f
g&p
h.l:g�yRn�m�b�lÉk
z"g�t�b�nTp�}���m,f���k{z
g�t�b�¯sÛ p�f�n n'��w�¯Ük{l�d�mFhFh�p*g&mHk{f�l�d�pvf��To�k
w�mCn
bÌg�t�b
m,f�zFk�o�}jp*g&mHk�fxf
b*d*b�l&l<p�o�ixzFk
osl<b���p�o&p*g�m�k{f´k�zÉg&t�b ��w�k{o�g<b*�
}�p*g<g<b�o ��dek
f�g&o<mHq�y�g�mEk�f²g<k�g�t�b�n�pv}���mHf
��k�zsg&t
b�nL��w
¯
k�l:d�mFhFh�p*g&mHk{f�l¼m,f´l:yT��b�o�dek�f�n�y�d*g<k
o�l>m,f�g&t
b�}�mH�Tb�n�l�g�p*g<b��
� _��TYT\�� � <�]E=@D <�Y�ZHA
Æ"t�b�o:b�l�y#hHg�l"k�z#g&tTmCl"��k{o&£ut�p*w�b¼q�b*b�fun�mHl�deyTl&l�b�n��jm�g�t
}�iuyTf�g&m,}sb�hAi�n
b*deb�p�l�b�nÊz:o�m�b�f�nׯshAb*�#p�f�n�b�o>�
b�}sb�f�kvwTmHd�t
a°k�Âet�p*w�l&£
i½�sg<k��jt�k{} �³��k�y#h�n h�mH£�b�g<k�b*�#��o�b�l�l�}�i
n�beb��
b�l:g±zFb*b�h�m,f{��l×k�zs�Ro�p*g�mHg�yTn�b��¼���sk{yrh�n�p�h,l�kÖh�mC£
bxg�k
g�t�p�f�£ �<h��3i�p �¼o&mKw�b zFk
o¿t�b�h���zFyrh�d*k�}�}�b�f�g�l�k{f�g�t�b
}�p�f�yTl�d�o&m,��g¼pvf�n�zFk�o yTl:b�zFy.h½dek�f
w�b�o<l&p*g&mHk{f�l*�
u10�u d è æ<è é�e f�è æ<éJè é>h i%jpk m%jpo e>qts%oFê<ëeì�ì*ì�êFä�á<ëvu
ê>f�å w
èÃ×��¸×"ØX×"Ù"ÛÃÖeÔ�Û�à�é�ï�×"ØX×"Ù"ÛÂÐ�Ô�Í.Îbà�é�Îbà�Ô��¸×�Ø�Îv÷¢ìbé ©«ª�¬¢¯ÈR����¶ÂÈ
� �ãe£�×��&(�é�êÂê��¢ë�ò�èF������ób×ê¸×�ï.׺Ù�ácÖdæÂábÖ+Îbà�Ô�Ù ×É2.ácß�äcâ¢ácÖÃé ©«ªv¬�¯ÈÉ�.�b¶¢È � �ãe£ ×°(&%�éºècí��ÂíòÃè:�&�¢ë�ó�×0¸×
)×�ã.×.��â�ábÎjÎvà¢Ô�Ø^×»î³Ï à�Ý�âÂÎÃÍ�é ©«ªv¬�¯È½����¶�È � �£¼£ ×#$��¸é"êJ0Ãê �òÃè:�&�e/�ó�×
� ×�Ò,×�ÒÕ×«Ø Û�ì¼â¢äcâ�Î�ÐÓÝ¢ÛÃÚ�é#��×�Ù«Ï ábÔ�ß'é½!�×#�Âô¼Öeߢà�Ý�é"ã.×���ÛÂà�äbÝÂâ�ácábÖeáÂé
,×���߸ϥéÕ!�×"Ò"ÎÃà� .ÎvácìeábàÂÔ�ÛÃà¢äcÝ�é�Îbà�Ô��.×�ñ�ÖdßÃç¢à�ìeácÖeÎÃácÔ�áÂé � ��
£��¸¡¼��� $ � é�0Êè8�ºò�èF�J�Ãí¸óÃ×
í¸×¼!"×¾�Âô¼Öeߢà�Ý�é,ÒÕ×�ñ�Öeß�ç¢à�ÔÂÛÂäcü�éÕÒÕ×,ÒÕ×�Ø�ÛÃìeâ�äcâ�Î�Ð�Ý�ÛÃÚ�é¾!�×#Ò"ÎÃà
.ÎÃácìeácà�Ô�Û�à�äcÝ�éÕÎbà�Ô��Õ×,ñ�Öeß�çÂà¢ì¼ácÖ�ÎvácÔ¢áÂé�� _ �b°bªÂÈ���È#©»ª�¬Â�×c%1(-é
êJ0&0e/ òÃè8�1���-ó��jÒÕ×+ñ�ÖdßÃç¢à�Ô¢ÛÃäcü�éu!�×���ôeÖeß�àÂÝ�éjÒÕ×TÒÕ×^غÛÂìeâÂÌ
ävâÂÎÂÐ�Ý�Û�ÚÊé�!�×�Ò�Îbà� .ÎbácìeávàÂÔ�Û�à�äcÝ�é�Î�à�Ô �Õ×\ñ�Ö¼ßÂçÂà�ìeácÖ�ÎvácÔ¢áÂé
�
_ �v°bªÂÈ���È¿©«ª´¬Â ×�%&(�é�êJ0&0J�ºò�èF�J����ób×
��×¼!"×>!«×,ï�æ¸Ï�Ð¥Ï Û¸é° "×,ñ�ߢô¼Îbà�Ô'é#î�×�åÊÛÃß�Öeà-Ï ávÖbé�ñ�×° ÊÎvà¢à�ácô�Ï ácÖÃé��-×
Ò.Ï Ô¢ÎÃÐeé.��×��ÂácÔ¢ácì¼Ý¢Û¸é"Îvà¢Ôgñ�×#2.Î�ÐÓÜcÛ�ô¼ôûÛÊé ©�ªv¬ÂcȽ����¶ÂÈ � �£e£ ×"! � éí�ècëÃêºò�èF�J�&�¸ób×/�×$#w×,ï�×¾��Ï ôeô�ÐÓágÎbà�Ô�ã.×¾2,×� ³ÎbÖeÝ�ìbé#©«ª´¬Â¯È ���b¶�È � �ãe£�×%��éÉ�òÃè:���Ãê�ó�×
�¸×�ã.×� XÙ�Ö�ÛÂõ¥õ�ÎÃàÂÔÿã�×v2)×� ÊÎÃÖeÝ�ìbé�©»ªv¬�¯È�����¶¿×'&<$&(¸é¸í(�&/)òÃèF�(�)�¸ó�×�¸×v��׿ï«ÐÓácü¢Îvà¢Ô�ácÖbé ©«ª�¬¢¯È��.�b¶¢È+* )J$¸é�ècí � è#ò�èF���&0¸ób×èbë�×��Êׯï"Ð�ácü�Îbà�Ô�ácÖgÎbà�ÔsË»×, .Î�Ð�ácڢϥé ��Ⱥ©�ªv¬Â.-c©� �¡�®Ó0/ %1%-é1�ÂëÃí
òÃè:���J0�ó�×
èÂèÃ×v �×�Ù�׸Ô�á�Ù"ácà�àÂábìvé2��È{��È43"°c ÂÅ�·�°b®�È�)��1)-é��ÆòÃè8�5�-è´ó�×
ècê¸×¸ÒÕ×�Ø+׸Ò�Ï à�Û�Ý�ß�Öbé��46 ø ©³(&(�é�èF���ºòbè:���e/�ó�×
è:0¸×.��×.��×.�Ââ�ÛÃâ¢à`Îbà�Ô
Ø+×"î�Ï à�Ý¢âÂÎÃÍ)é ©«ª�¬¢¯ÈX����¶ÂÈ�* %e$��e/
� ®¥Äî�Å ×
* %J$¸é*�(�&/�ò�è:�&�J0�ó�×
è � ×��Õ×�ï�â�ÎbÖeÛÃà�ÛÃÚ)Îbà�Ô¼2)׸ñ�ÛÃâ�Í�é ©«ªv¬�¯È����b¶ ×2&5&0�Êé � �ÂíÆòbè���í1�¢óÃ×ècí¸×�ï.×�ÙÕ×Êï�ÖdÛ�à�ÛÃÚÆÎvà¢Ô7�.×{��×
�Ââ�ÎbÖdÚ¢Ï à�é ���öÂÈ ú §ÃÅ�ȳ©«ªÃ¬�¯È ����é
/víÂí
òÃè:���e/�ó�×
è8��×.�b×»ÒÕ×
9"Ö�Ï Ú�ájÎbà�ÔXï�×½��×�ã�Û�Ü�â�ÎbÚÂì¼ÝÂç�é;:�¦�£ûÈ<��È ú §ÃÅ�È�©«ª�¬¢�×r(-é
ècêÃíÂíºò�èF�J�Ãê¸ób×
è</�×
!�×1��×���Î�à�ö�é ����¶�È ú §ÃÅ�ÈÊ©"ªv¬¢ × � %-é+�<� � òÃè8�4�bê¿ób×è=�¸×�Ë�×r��×�ñ�Û�ö�Îbäcâ�ácÝ'é.ÙÕ×"ï.×.Ù�ÛÂöÃÎ�Ô�ÜcáÂé"Îbà�Ô±�c×?>�×
9"߸Ð�Ï Ý�é�©�ªv¬Â¯È
·�£� ¸£��Ã�·Ê§ X ®�Å'®@-�Ä�/ (*$¢é¿ê��*/)òÃè8�*/bí¿ób×
è:�¸×gã.×XåÊÖeÎÃìeìeÎvà-Ï ôeÛ¸é³ �×XÒ�Ï ì¼Î�à�ÏeégØ+×��«Ï Ô�ácÖdÛ�ì¼ôbé+ï�×�!"×gØ�ÛÃôeÎ�é �×���Í.ábÏ�æ¢ÏÓÔ¢ÐdéA9#×���ý.Ï ácôeäc΢é7#w×,#`ácà¢Ô�Ð�ácÖvéÆÎÃàÂÔ�å�×� ÊÛÃæ�ábÐûмé
�
_ �b°bªÂÈ4��ÈÊ©"ªv¬¢ ×e%1(-é¿êJ0¸è</)òbè����4�ÂóÃ×
ê¢ë�×ÊÒÕ×'ØX׳٫Ú�Û�ÜdÔ¸Ï Ý¢ÛÃÚ�éÊ·�§Â¶Âȳ©«ªv¬�¯È�·¸§ X ®�Åj·�£� ¸£��Õ)J(¸é�èdí(�Ãëºò�è���� � ó��®ûÄî�Å ×�)�!�é�è:/&�ºòbè:���(��ó�×
ê�èÃ׸ÒÕ׸ØX×�Ù�ÚÂÛÃÜcÔ¢Ï�Ý�ÛÂÚ�é ® _ È � ® _ µÂÈ ø �ä��-ÈB&0!Êé'è�è�ê5�ÆòÃè8�1��ê¿ób×êÂê¸×4��×�ã.×v��äcâ�Ö�Ï ábõ¥õ�ábÖbé ø ª´�b§�¡ ¬ÿ§v¨"·2���¢�b¡¼°c§´¦´Å2�°ãû®¥¶Â®¼£�¬�é���ÎvߢÝ�Î-éÊØ�ÛÃìeÌ
äcÛÂýwò�èF�e/Ãë�ó�×
êJ0¸×��-×)ñ�ÎbÖeÔ¸Ï à'é)ã.×%9"ß�Í�Í.ábÐdéÕï.×)Ë�×C�ÃÎÃäcÛ�æ�ìbé,Îbà�Ô���×#î�ácý�ÛÃÖeÔ�ôbé
©«ªÃ¬�¯È�����¶ ×'&=!e$�é¸íÃí(�)òÃèF�(���¸ób×
ê � ×c�c×c��×,Ù�Ö�ÎvÔ¢ìeâ�ôeábÏ�à�ÎÃàÂÔx�c×ÕØ ×Õã�ç¢Üdâ¸Ï Ý'é ø ¢Ä X ��ÿ§v¨,:�¦¿£�� ��¡e X �±·2�¢¤«�±Æ·Ê��¡d®��cd±Æ ¦ÂÅw©"¡e§ÃÅ���°Ã£� é"��Îbß�Ý¢Î�é�Ø�ÛÃìeävÛ�ý ò�èF�e/�èÃóXòcÏ à
ã�ߢìeìdÏ ÎbàÊó�×
êÂí¸×�ÒÕ×�ØX×�Ù"ÚÂÛÃÜdÔ-Ï Ý�ÛÃÚÆÎÃàÂÔjØX×ÊÒ�×�Ù�ÚÂÛ�Ü�Ô¸Ï Ý¢ÛÃÚÂÎ�é ©«ªv¬�¯È�����¶ × * ��!�é
�e/�è8�)òbè����5�¢óÃ×
ê(��×"ÒÕ×"ØX×.Ù�ÚÂÛÃÜcÔ¢Ï�Ý�ÛÂÚ^Îvà¢ÔgË»×�غÎ�à�à-Ï à�ácà'é ® _ È � ® _ µÂÈ ø ��¤«�-È (�éèÂèF0��Æòbè�����ëÂóÕ� ·�§Â¶ÂÈ��ÊÈ � §�D ø ��¤«�-È¿©»ª�¬Â ×�(¸é¸íÂíÃêºò�èF���Âë�ó���×êe/�×v�c×+>�×+9"߸Ð�Ï Ý�é��46 ø © � �ãe£¥ÈE&�&¢é¸êJ/Ãíºòbè:�J/Âë�ó�×ê��¸×"î�×E��׫ñ�×E�ÃÎ�à�ìeìeábàÊé���×
.ÎvÖ�ÖdÏ ìeÛÃà'é.��×"ØX×F �çÂÔ¢ácà�é. �×�غábácìeÛÃà�é
Îbà�ÔÆØX×v��÷¢Ö�Ï à�ö¢õ�ÛÃÖeÔ�é�©«ªv¬�¯È����b¶Ê× * �¹$¿é'è�è0�¹���ºò�è����5�¢óÃ×
êJ�¸×�î"×�ØÆÎÃà¢ÏÓÚ�é�ÒÕ×���×"GÊâÂß�ÖeÎÃÚ¢ÐÓácÚ�éT�v×T2,×�Ò�ÎböÂà�ábÖbé�Îbà�Ô� �×�# ç¢ÔÂávÖbé
��ÈE��ªÃ�b¤�È�·�§ X ®�Å¿ �5�-é³ò�èF�J���¸ó�×0¢ë�×4�¸×�ã�ÛÂÐ�Ð�æÂß�â-ÐÓácÖ"Î�à�ÔÆï.×¢ï.×'>�Ô¸Ï à�ôûì¼ÛÂÚ�é � ø � �,©«¡e§Ã°c�c�vÅ�®û¦��¢�± � ø � �
���°�CH ú ±��¢ ´�¢��¡ � ¾cÀ�½¿¾¯½ÃÈÊ�¢Å¿¨�òbè����1�¢óÃ×0�èÃ×� �×{��×�غä)Ë�ߢácà�é�ØX×'ñ�ÛÃäbÝÂÖdÎbô¼â�é�2)×' )×�!�ÛÃæ�Ô¢ácâ�é+�Õ×�ÙÕ×+�"Û�ÛÃà�é
Îbà�Ô¼��×�ÙÕ×��ÊÛÂÏ�ìbé ©�ªv¬Â¯È����öÂÈ � ��£e£ ×4! � é¸íÂë&���ºò�è:�&�J��ó�×0Âê¸×v��×v �×�Ù�ÛÃÖ& Ý�Û�ÚÊé4I�ªÂÈ+6«µv¼�-È ø �c§Â¡�È ® _ È � (¸é�èF��èJ�ÆòÃè:�ÃíJ��ó�×0J0¸×< )×"å�×.!�â�ácߢà�ö�éE��×�Ù"ábõ�ácà'é"Ë"×E9Õ×"ã�ábÏ Ô�ábÐ�é�Îvà¢ÔK#z×< )×#��â-Ï â�é
©«ªÃ¬�¯È�����¶ × *"� $¸é+��ë´í´ë�ò�èF�����¸óÃ×0 � ×�ï�×�ï�×EG¸ÚÃç�Îbö¢Ï à+ÎÃàÂÔ��v×�ÒÕ×E9"ÖcÏ ÚÂáÂé ® _ È � ® _ µÂÈ ø �ä�� ×�)�&ÂéB�)�e/ò�èF�J�Ãí¸ó�×0Âí¸×�ã�×�Ù�×�!�âÂÎÃÍ�æ�ábÖeìbé-©«ªv¬�¯È����b¶�È � �£e£�×4��é�0Æòbè:���Âë�óÃ×0(��×�Ø ×�ñ�ßÂôeô�Ï Ý�ácÖbéE��×��¥Í.Öeç�é�Î�à�Ôrã.×��ÊÎbà�Ô�Îbß�ácÖbé ©�ªv¬Â¯È � �£¼£ ×'L<�&(�é0(�víÆòÃè8�5��0¿ó�×
a W � .cb . W
d è æ<è éMegf�è æ<éJè éHh�i%jlknm%jpoUerqts%o8ê�ëeì�ì*ìvê�ä�á<ëvu{êrf�å*w u10vw
|