Thermodynamical length scales temperatures correlation for the Ginzburg-Landau theory

Thermodynamical length scales temperatures correlation for the Ginzburg-Landau theory

The emergence of the superconducting state must obey to a variational principle representations, as considered in the classical schemes, the invariance of the extremum values, according to the use of thermodynamical functions, will suggest an internal coherence governing the jumps realized by the sy...

Повний опис

Збережено в:
Бібліографічні деталі
Дата:2006
Автори: Bousnane, Z., Merabtine, N., Benslama, M., Bousaad, F.
Формат: Стаття
Мова:English
Опубліковано: Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України 2006
Назва видання:Semiconductor Physics Quantum Electronics & Optoelectronics
Онлайн доступ:http://dspace.nbuv.gov.ua/handle/123456789/121634
Теги: Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Thermodynamical length scales temperatures correlation for the Ginzburg-Landau theory / Z. Bousnane, N. Merabtine, M. Benslama, F. Bousaad // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2006. — Т. 9, № 4. — С. 63-64. — Бібліогр.: 2 назв. — англ.

Репозитарії

Digital Library of Periodicals of National Academy of Sciences of Ukraine
id irk-123456789-121634
record_format dspace
spelling irk-123456789-1216342017-06-16T03:03:15Z Thermodynamical length scales temperatures correlation for the Ginzburg-Landau theory Bousnane, Z. Merabtine, N. Benslama, M. Bousaad, F. The emergence of the superconducting state must obey to a variational principle representations, as considered in the classical schemes, the invariance of the extremum values, according to the use of thermodynamical functions, will suggest an internal coherence governing the jumps realized by the symmetries, against the non-univoc determination permitted by the variations of the thermodynamical parameters. The uncertainties for macroscopic states must be associated to the existence of “macroscopicity levels”, considering the interaction between cooled and cooling, the macroscopic state of each one, will be considered as a combinatory length scales interactions. The reversed role between cooled and cooling suggests that near transition point Eδ will be spent in c²∆Γ . The thermodynamical functions are obtained each from other by the uncertainty principle. 2006 Article Thermodynamical length scales temperatures correlation for the Ginzburg-Landau theory / Z. Bousnane, N. Merabtine, M. Benslama, F. Bousaad // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2006. — Т. 9, № 4. — С. 63-64. — Бібліогр.: 2 назв. — англ. 1560-8034 PACS 74.25.Bt http://dspace.nbuv.gov.ua/handle/123456789/121634 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description The emergence of the superconducting state must obey to a variational principle representations, as considered in the classical schemes, the invariance of the extremum values, according to the use of thermodynamical functions, will suggest an internal coherence governing the jumps realized by the symmetries, against the non-univoc determination permitted by the variations of the thermodynamical parameters. The uncertainties for macroscopic states must be associated to the existence of “macroscopicity levels”, considering the interaction between cooled and cooling, the macroscopic state of each one, will be considered as a combinatory length scales interactions. The reversed role between cooled and cooling suggests that near transition point Eδ will be spent in c²∆Γ . The thermodynamical functions are obtained each from other by the uncertainty principle.
format Article
author Bousnane, Z.
Merabtine, N.
Benslama, M.
Bousaad, F.
spellingShingle Bousnane, Z.
Merabtine, N.
Benslama, M.
Bousaad, F.
Thermodynamical length scales temperatures correlation for the Ginzburg-Landau theory
Semiconductor Physics Quantum Electronics & Optoelectronics
author_facet Bousnane, Z.
Merabtine, N.
Benslama, M.
Bousaad, F.
author_sort Bousnane, Z.
title Thermodynamical length scales temperatures correlation for the Ginzburg-Landau theory
title_short Thermodynamical length scales temperatures correlation for the Ginzburg-Landau theory
title_full Thermodynamical length scales temperatures correlation for the Ginzburg-Landau theory
title_fullStr Thermodynamical length scales temperatures correlation for the Ginzburg-Landau theory
title_full_unstemmed Thermodynamical length scales temperatures correlation for the Ginzburg-Landau theory
title_sort thermodynamical length scales temperatures correlation for the ginzburg-landau theory
publisher Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
publishDate 2006
url http://dspace.nbuv.gov.ua/handle/123456789/121634
citation_txt Thermodynamical length scales temperatures correlation for the Ginzburg-Landau theory / Z. Bousnane, N. Merabtine, M. Benslama, F. Bousaad // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2006. — Т. 9, № 4. — С. 63-64. — Бібліогр.: 2 назв. — англ.
series Semiconductor Physics Quantum Electronics & Optoelectronics
work_keys_str_mv AT bousnanez thermodynamicallengthscalestemperaturescorrelationfortheginzburglandautheory
AT merabtinen thermodynamicallengthscalestemperaturescorrelationfortheginzburglandautheory
AT benslamam thermodynamicallengthscalestemperaturescorrelationfortheginzburglandautheory
AT bousaadf thermodynamicallengthscalestemperaturescorrelationfortheginzburglandautheory
first_indexed 2025-07-08T20:15:21Z
last_indexed 2025-07-08T20:15:21Z
_version_ 1837111154938216448
fulltext Semiconductor Physics, Quantum Electronics & Optoelectronics, 2006. V. 9, N 4. P. 63-64. © 2006, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 63 PACS 74.25.Bt Thermodynamical length scales temperatures correlation for the Ginzburg-Landau theory Z. Bousnane1, N. Merabtine2, M. Benslama2, F. Bousaad1 1Physics Department, Faculty of Science, University of Batna, 05000 Algeria 2Electromagnetism and Telecommunication Laboratory, Electronics Department, Faculty of Engineering, University of Constantine, 25000, Algeria E-mail: na_merabtine@hotmail.com; malekbenslama@hotmail.com Abstract. The emergence of the superconducting state must obey to a variational principle representations, as considered in the classical schemes, the invariance of the extremum values, according to the use of thermodynamical functions, will suggest an internal coherence governing the jumps realized by the symmetries, against the non- univoc determination permitted by the variations of the thermodynamical parameters. The uncertainties for macroscopic states must be associated to the existence of “macroscopicity levels”, considering the interaction between cooled and cooling, the macroscopic state of each one, will be considered as a combinatory length scales interactions. The reversed role between cooled and cooling suggests that near transition point Eδ will be spent in ∆Γ2c . The thermodynamical functions are obtained each from other by the uncertainty principle. Keywords: superconductivity, length scales temperature, uncertainty principle. Manuscript received 21.02.06; accepted for publication 23.10.06. 1. Introduction We try by this essay to realize an uncertainty principles dealing with finite variation of thermodynamical parameters, in accordance with the fact that the transition will be described by the ratio of thermo- dynamical length scales of temperatures represented as extremums of the thermodynamical functions. 2. Definitions The importance of the length scales temperatures as dealing with measurement processes was revealing that in general the macroscopic state could be considered as a combinatory length scales interactions, characterizing the critical point of transition. As defined by Landau [1] τ τ τ       ∂ ∂       ∂ ∂ = P Q V T P d lnd . (1) The action of “cold” is formulated as converging deterministically to the appearance of complex pseudo vector, when writing, E S d d ~ τ 1 . (2) The function )(τTT = expresses the absolute scale of the temperature. τ must be chosen in such a way that propagation of superconducting state must be seen as simple as possible, means governed by a variational principle held on E, W, F, ( ) ( ) ( ) PSVPVS WFE ,,, δδδ == . The indeterministic description concerning the propagation of superconducting state began by the non- existence of the derivative as τ∂ ∂T ~ τd dT . (3a) According to this view, the relation [2] TQ∆∆ ~ (3b) rises. During the propagation, near the transition point, the deterministic description as hopped is called to assume a jump. (3b) will be rewritten as STT ∆∆ ~ and Semiconductor Physics, Quantum Electronics & Optoelectronics, 2006. V. 9, N 4. P. 63-64. © 2006, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 64 ST∆∆ ~ 7.63828×10−12. This uncertainty seems informing that in the neighbourhood of transition, as to our knowledge about the temperature of the body, will be lost under a given degree of precision. As viewed at this level, the thermodynamical scale of temperatures will not follow the law (1). It will be written: )(lnˆlnˆln τ ττ TF d TdF d Td == (4a) and )(lnˆln10637.7 12 τ τ TF d Td =× − , (4b) STHF ˆˆˆ −= . (5) Ŝ is equivalent to multiply by ∆Γln . Those considerations makes that the entropy near the transition point, will be well known when T is lost. The functions lnTn( τ) are polynoms. The situation is so, when the difference between temperatures of Helium (He) and Mercury (Hg) in the Kammerling-Onnes experiment is in the order of 7.63828×10−12. Cooling every time seems to be limited by the interaction between length scales of temperatures. The free energy will be denoted TScF −∆Γ−= 2 . (6) This law seems signifying the equivalence statistical weight-cold, which regularize the relation between the cooled and cooling. ∆Γ− 2c is expressing the reversion of cold. Equation (4b) is rewritten as ( )( )−∆Γ=× − τ τ TcT ln d lnd1063828.7 212 ( ) ( )( )τTT lnln∆Γ− . (7) This expression shows that the interaction between two temperature length scales T and τ is governed by the potential ( ) ( )( )τTT lnln∆Γ− , we write it ( )τ,Ts . ( )[ ]τ τ Tc ln2∆Γ ∂ ∂ gives the momentum causing the uncertainties of T∆ on the temperature and S∆ on the entropy. 3. The thermodynamical function expressions We must have the following notation ( ) ( )( ) ( ) ( )( ) τ η τ η τ φ φ d d d d d d ri ri erSTerE = . (8) This expression is replaced by an expansion Series hold on E and S as follows =+ ∂ ∂ ∂ ∂ + ∂ ∂ ∂ ∂ = 0ττ φ φ η η E r E r E τ φ φ η ητ =+      ∂ ∂ ∂ ∂ + ∂ ∂ ∂ ∂ ∂ ∂ = TTS r S r ST , −      ∂ ∂ ∂ ∂ + ∂ ∂ ∂ ∂ =− == r S r STTSE T φ φ η ηττττ d d 0       ∂ ∂ ∂ ∂ + ∂ ∂ ∂ ∂ − r E r E φ φ η η , ττττττ ==== −= TT TSEF 00, , (9) which is the expression of ( ) ( ) ( )[ ]ττττ δδδ STTSE +== 0 for ( ) 0 0 ==ττδE , we’ll have ( ) ( )τττττ δδ STTSF T −−=∆ == 0, , which implies that 0ττ φ φ η η == ∂ ∂ ∂ ∂ + ∂ ∂ ∂ ∂ E r E r E . ( ) 0ττδ =E and 0, τττδ ==TF seems not reaching zero in the same time but will be linked by FEδδ as . The variation of the free energy, generating propagation of order parameter, when near the transition point Eδ will be spent in ∆Γ2c , meaning the existence of intrinsic states of the order parameter, where the roles between cooled and cooling are reversed. The expressions FE∆∆ must mean an indetermination concerning the free energy density submitted to a length scale temperatures interaction. 4. Conclusion The interaction between length scales of thermo- dynamical parameters, may be considered as a measurement process, inducing a non-deterministically picture, and breaks the fence between cooled and cooling, which will be expressed as the appearance of macroscopic levels for each one. According to this, the action of cold will be limited by the levels of macroscopicity of the sample, near the transition point. It seems that the ranks of macroscopicity will depend on the standard scale τ , which itself is under the action of T, then becoming an own results. The thermodynamical functions will have not objective picture but will be obtained as uncertainties each from other. References 1. L. Landau, E. Lifshits, Statistical physics. Edition MIR, Moscow, 1967. 2. L. Landau, E. Lifshits, Quantum mechanics. Edition MIR, Moscow, 1967.

Схожі ресурси