Proximity effect at the interface He II-He I in microgravity environment
The proximity effect causes the existence of some transition area with the gradual variation of the density of superfluid component instead of the sharp boundary at the level where the hydrostatic pressure realizes the phase transition He II-He I. In the microgravity environment the characteristic l...
Gespeichert in:
| Datum: | 2003 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2003
|
| Schriftenreihe: | Физика низких температур |
| Schlagworte: | |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/128857 |
| 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: | Proximity effect at the interface He II-He I in microgravity environment / L. Kiknadze Yu. Mamaladze // Физика низких температур. — 2003. — Т. 29, № 6. — С. 672-673. — Бібліогр.: 6 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-128857 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1288572018-01-15T03:04:01Z Proximity effect at the interface He II-He I in microgravity environment Kiknadze, Yu. Mamaladze, L. 3-й Международный семинар по физике низких температур в условиях микрогравитации The proximity effect causes the existence of some transition area with the gradual variation of the density of superfluid component instead of the sharp boundary at the level where the hydrostatic pressure realizes the phase transition He II-He I. In the microgravity environment the characteristic length of this effect increases, and more convenient conditions arise for measurements in the transition area. The problem of the expansion of thermodynamical potential in power series in the vicinity of He II-He I interface is considered. The critical values of the size of the superfluid area are determined. 2003 Article Proximity effect at the interface He II-He I in microgravity environment / L. Kiknadze Yu. Mamaladze // Физика низких температур. — 2003. — Т. 29, № 6. — С. 672-673. — Бібліогр.: 6 назв. — англ. 0132-6414 PACS: 67.40.Vs http://dspace.nbuv.gov.ua/handle/123456789/128857 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 |
3-й Международный семинар по физике низких температур в условиях микрогравитации 3-й Международный семинар по физике низких температур в условиях микрогравитации |
| spellingShingle |
3-й Международный семинар по физике низких температур в условиях микрогравитации 3-й Международный семинар по физике низких температур в условиях микрогравитации Kiknadze, Yu. Mamaladze, L. Proximity effect at the interface He II-He I in microgravity environment Физика низких температур |
| description |
The proximity effect causes the existence of some transition area with the gradual variation of the density of superfluid component instead of the sharp boundary at the level where the hydrostatic pressure realizes the phase transition He II-He I. In the microgravity environment the characteristic length of this effect increases, and more convenient conditions arise for measurements in the transition area. The problem of the expansion of thermodynamical potential in power series in the vicinity of He II-He I interface is considered. The critical values of the size of the superfluid area are determined. |
| format |
Article |
| author |
Kiknadze, Yu. Mamaladze, L. |
| author_facet |
Kiknadze, Yu. Mamaladze, L. |
| author_sort |
Kiknadze, Yu. |
| title |
Proximity effect at the interface He II-He I in microgravity environment |
| title_short |
Proximity effect at the interface He II-He I in microgravity environment |
| title_full |
Proximity effect at the interface He II-He I in microgravity environment |
| title_fullStr |
Proximity effect at the interface He II-He I in microgravity environment |
| title_full_unstemmed |
Proximity effect at the interface He II-He I in microgravity environment |
| title_sort |
proximity effect at the interface he ii-he i in microgravity environment |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2003 |
| topic_facet |
3-й Международный семинар по физике низких температур в условиях микрогравитации |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/128857 |
| citation_txt |
Proximity effect at the interface He II-He I in microgravity environment / L. Kiknadze Yu. Mamaladze // Физика низких температур. — 2003. — Т. 29, № 6. — С. 672-673. — Бібліогр.: 6 назв. — англ. |
| series |
Физика низких температур |
| work_keys_str_mv |
AT kiknadzeyu proximityeffectattheinterfaceheiiheiinmicrogravityenvironment AT mamaladzel proximityeffectattheinterfaceheiiheiinmicrogravityenvironment |
| first_indexed |
2025-07-09T10:02:45Z |
| last_indexed |
2025-07-09T10:02:45Z |
| _version_ |
1837163209497247744 |
| fulltext |
Fizika Nizkikh Temperatur, 2003, v. 29, No. 6, p. 672–673
Proximity effect at the interface He II–He I in microgravity
environment
L. Kiknadze and Yu. Mamaladze
E.A. Andronikashvili Institute of Physics of the Georgian Academy of Sciences,
6, Tamarashvili Str., Tbilisi, 380077, Georgia
E-mail: yum@iph.hepi.edu.ge; yum270629@yahoo.com
Received December 19, 2002
The proximity effect causes the existence of some transition area with the gradual variation of
the density of superfluid component instead of the sharp boundary at the level where the hydro-
static pressure realizes the phase transition He II–He I. In the microgravity environment the cha-
racteristic length of this effect increases, and more convenient conditions arise for measurements in
the transition area. The problem of the expansion of thermodynamical potential in power series in
the vicinity of He II–He I interface is considered. The critical values of the size of the superfluid
area are determined.
PACS: 67.40.Vs
Introduction
According to the phase diagram of 4He the hydro-
static pressure causes the phase transition He II�He I
but, because of the proximity effect, instead of abrupt
boundary between the superfluid and normal liquid at
the level, where the �-pressure is reached, there is
formed the transition zone where the density of super-
fluid component varies gradually. The superfluidity
penetrates into the normal area [1–3]. The characte-
ristic length of this effect is � g � �6 5 10 3. • cm [1].
Microgravity
The width of the transition zone (its height) may
be estimated as several times � g , i.e., it is of the order
of 10 2� cm. This value is quite macroscopic but never-
theless so small that nobody could carry out the expe-
rimental study of this area. The sole attempt [4] was
unsuccessful.
The more convenient conditions for measurements
in transition area at the boundary He II–He I are
achieved in the microgravity environment since
� � �g
/ /� �
0
3 5 2 5 where �0
8 2 32 73 10� �. • cm • K / ,
�� � �� g/ dP /dT| . I.e., the 105 times decrease of g en-
tails the increase of the width of transition area to cen-
timeters, and 3 107• times decrease of g is necessary to
reach the height of order of 10 cm.
The unit of wave function and « � 0 problem»
The Ginzburg—Pitaevskii (GP) equation for 4He
being under hydrostatic pressure may be written down
in the form (we do not consider some flow and is a
positive function):
�
2 2
2
3 5
2
0
m
d
dz
A B C
� � � , (1)
where A and B are dependent on the distance z from
the boundary (z � 0 is the superfluid area, z � 0 is the
normal one): � �A A z /�
0
4 3( )� (the sign minus is for
the normal area), � �B B z /� 0
2 3( ) .� The asymptotic so-
lution far in the superfluid area ( )z g�� � is
a
/z� ( )� 1 3
0, 0
2 0 0
2
0
2 2
� �
�
�
�
�
�
�
B
C
B
C
A
C
. (2)
It is convenient to introduce the parameter M: M �
� � �C /A B /A 0
4
0 0 0
2
01 and to express coefficients
A B0 0, as
A
M/
/
0
16
4 3111 10
1 3
�
�
�. •
,erg • K
B
M
M/
/
0
39 2 33 52 10
1
1 3
�
�
� �. • erg • cm • K .
Then Eq. (1) may be transformed into the dimen-
sionless form
© L. Kiknadze and Yu. Mamaladze, 2003
� � � �d
d
M M/
2
2
4 3 2 3 3 51 0
�
�
� � � � �
� � � �( ) / , (3)
where � �� z/ gM , � � � gM :
� �gM g
/M/�
( )1 3 3 10,
gM g
// M/�
� �0
1 10
01 3( ) [3].
The GP equation is founded on the expansion of
the thermodynamical potential in power series. If this
expansion is performed in respect to the ratio of wave
function to its equilibrium value then it becomes in-
valid at the He II–He I boundary where this ratio be-
comes infinite [3]. This problem does not exist for
Eq. (3) and for corresponding expansion in power se-
ries in respect to � gM because gM is temperature
and coordinate independent (if we compare gM with
a , the quantity �z in Eq. (2) is substituted by
( ) ( )� �0
3 2 3 101 3/ M/g
/ /
). These quantities have
the dimension of temperature, but the latter is tempe-
rature and coordinate independent.
In these units the asymptotic solution (Eq. (2)) has
the form � �a
/� 1 3.
Critical sizes of superfluid area
The superfluid area must content the superfluid
component enough to entail the superfluidity in nor-
mal area. That is why the size (the height) of the
superfluid area Hs has the critical value Hsc such that
if H Hs sc� then the density of the superfluid compo-
nent is zero in the whole vessel (more exactly for the
case M � 1 see below). It is determined by the equa-
tion:
J h I hsc
/
n
/
03
5 3
03
5 33
5
3
5. .
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
� ��J h I hsc
/
n
/
03
5 3
03
5 33
5
3
5
0. . , (4)
the first variant of which is obtained in [1]; hsc � 2 29.
when hn � � [2,5] and hsc � 2 55. when hn � 0 [5]
( ,� � �H z Hn s Hn is the size of normal area,
h H/ gM� � ). Let us consider the case h h hs sc sc� ��
and hn � 0. Employing the method suggested in [6]
we obtain the approximate solution of Eq. (3) of the
form � � �� c J j/h/
s
/
03
5 3 5 3
. ( ) where j � 2 8541. . The
analyses of the coefficient c shows that in the case
M � 1 the size hsc is not critical and that there exist
two other critical sizes: hmin above which the super-
fluidity becomes possible, and htr above which the
superfluidity becomes stable, h htr � min:
h h
M
M
I
I Isc
/
min
( )
�
��
�
�
�
�
�
�
�
�
1
1
4
2
2
2
1 3
3 10
,
h h
M
M
I
I Isc
/
tr �
��
�
�
�
�
�
�
�
�
1
3
16
1 2
2
2
1 3
3 10
( )
,
(5)
where I xJ x dx
j
1 03
2
0
0 91627� �� . ( ) . ,
I x J x dx/
j
2
6 5
03
4
0
0 37001� �� . ( ) . ,
I x J x dx/
j
3
7 5
03
3
0
016790� �� . ( ) . .
Acknowledgements
We would like to thank the Organizing Committee
of CWS 2002 for the invitation, which stimulated this
work and for the support of attendance of one of us
(Yu.M.) at the workshop, and G. Kharadze and
S. Tsakadze for their interest and attention. The work
is partly supported by the grant 2.17.02 of the Geor-
gian Academy of Sciences.
1. L.V. Kiknadze, Yu.G. Mamaladze, and O.D. Cheish-
vili, Pis’ma ZhETF 3, 305 (1966); in Proceedings of
the Xth International Conference on Low Temperature
Physics (1966), VINITI, Moscow (1967), p. 491; L.V.
Kiknadze, Yu.G. Mamaladze, Fiz. Nizk. Temp. 17,
300 (1991) [Sov. J. Low Temp. Phys. 17,156 (1991)].
2. V.A. Slusarev and M.A. Strzhemechny, Zh. Exp. i
Teor. Fiz. 58, 1757 (1970).
3. A.A. Sobianin, Zh. Exp. i Teor. Fiz. 63, 1780 (1972);
V.L. Ginzburg and A.A. Sobianin, Usp. Fiz. Nauk
120, 153 (1976).
4. G. Ahlers, Phys. Rev. 171, 275 (1968).
5. L.V. Kiknadze, Thesis, Tbilisi State University (1970).
6. Yu.G. Mamaladze, Bulletin Acad. Sci. of Georgia
109, 45 (1983).
Proximity effect at the interface He II–He I in microgravity environment
Fizika Nizkikh Temperatur, 2003, v. 29, No. 6 673
|