SCIENTIFIC ABSTRACT GORKOV, L.P. - GORKOV, V.A.

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• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

Superconducting Alloys at Temperatures Above SO7156-36-1 -48/62
Absolute Zero
ASSOCIATIONt Institut fizicheskikh problein Ak ademiJ nauk SSSR
(Institute of Physical Problems of the Academy of Sciences,
USSR)
5UBMITTED: July 16, 1958
Card 4/4

24(5) SOV/56-36-3-39/71
AUTHORS: Abrikosov, A. A., Gortkov, L. P., Dzyaloshinskiy, 1. Ye.
TITLE: On the Application of the Methods of the Quantum Field Theory
to Problems of Quantum Statistics at Finite Temperatures
(0 primenenii metodov kvantovoy teorii Polya k zadacham kvp-nto-
voy stati8tiki pri konechnykh temperaturakh)
PERIODICAL: Zhurnal eksperimentallnoy i teoreticheskoy fiziki, 1959,
Vol 36, Nr 3, pp 900-908 (USSR)
ABSTRACT: The present paper intends to formulate a variation of the
thermodynamic perturbation theory which permits the full ap-
plication of quantum-field theoretical methods to quantum
statistics at finite temperatures. This method is in principle
based on an extension of the method developed by Matsubara
(Ref 4)- In the Green's functions transition to "imaginary
times" is made by t4 -iTk, and from operators of second
quantization in Schroedinger (Shredinger) representation
transition is made to operators in "interaction representation"
Y+ (~,T); these new Green's functions are expanded
Card 1/2 acco;ding to the imaginary time variable in Fourier series.

SOV/56-36-3-39/71
On the Application of the Methods of the quantum Field Theory to Problems
of (Quantum Statistics at Finite Temperatures
ASSOCIATION:
SUBMITTED:
Card 2/2
This procedure differs from the usual one by the fact that
integration with respect to frequencies is replaced by sum-
mation. over discrete values of the imaginary "frequency" iW n;
otherwise this method is fully equivalent to the usual
diagram-technique in the momentum space at T = 0. In the
following, the analytical properties of the Fourier (Furlye)
components of the Green's functions are investigated and it
is shown that, due to the possibility of analytical continuation,
it sufficev for the treatment of various kinetic and non-
steady problems to know the corresponding equilibrium Green's
functions. The authors finally thank Academician L. D. Landau
and L. P. Pitayevskiy for discussing the results obtained by
this paper. There are 4 figures and 9 references, 5 of which
are Soviet.
Institut f12icheskikh problem Akademii nauk SSSR (Institute
for Phynical Problems of the Academy of Sciences, USSR)
December 4, 1958

24 (5)
AUTHOR: Gorikov, L. P. BOV/56-36-6-41/66
TITLE: The Microscopic Deduction of the Ginzburg-Landau Equations in
the Superconductivity Theory (Mikroskopicheskiy vyvod uravneniy
Ginzburga-Landau v teorii averkhprovodimosti),
PERIODICAL: Zhurnal eksperimentalinoy i teoreticheskoy fiziki, 1959, vol 36,
Hr 61 pp 1918 - 1923 (USSR)
ABSTRACT: The behavior of superconductors in a magnetic field near the
critical.temperature T (London temperature ra4ige) may easily
be described by the phenomenological theory of Ginzburg and
Landau (Ref 1). The author of the present paper shows that the
Ginzburg-Landau equations can be deduced from the theory of su-
perconductivity in the T 0-range. The investigations are based
upon the equations deduced in an earlier paper (Ref 2) which
contain the thermodynamic Green functions; from the latter the
author passes on to Fourier components, and the expression
A*('r) - gF'(-vl 1; -r, 1) goes over into,6'(-#) - TZ'-S+(r,r);
In W
is a function of the interaction constant and the func-
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The Microscopic Deduction-of the Ginzburg-Landau SOV/56-36-6-41/66
Equations in the Superconductivity Theory
tion P+(x,xl) for coinciding arguments; -I. without l'ield 0.
Finally, an equation for the current (r) is deduoed, which,
after introduction of the "wave function"
4-7 T(F)_R/4r T 0, h as th e f orm:
ie! #2
_ _ , 2~y #~
(r) - - F. 9_~. -- The introduction of
r sr:r7 - To
e e* - 2e corresponds to the physi-
the doubled electron charg
eel significance of the "wave function" Y(x) as the wave func-
tion of Cooper pairs. N denotes the electron density in normal
metalj~ (x) is Rieman's zeta function. The phenomenological
constant x is determined like in the old theory. For the crit-
ical magnetic field strength He, and the penetration depth 6 0
IP2e* 2
and e* - 29 it is determined as amounting to x H 6
'~j is Ome 0
and xczro.96 6L/S respectively; 6- i (41rNe 2/mO th
0 L -
LQndon penetration depth, 0 = 0.18*v/kT is the non-locality
f c
Card 2/3 parameter according to Bardeen, Cooper, and Schrieffer (Ref 5)-

The Microscopic Deduction of the Ginzburg-Landau BOV/56-36-6-41/66
Equations in the Superconductivity Theory
For tin xfwO-14 and for aluminum 0.01 is obtained. For tin the
2
formulas for dno (81r/H0) as functions of T/Taare finally givenp
both according to Ginzburg, Yu. V. Sharvin (Ref 9) x%nd accord-
ing to Faber (Ref 10). The author finally thanka Academician
L. D. Landau for valuable advice, and V. L. Ginzburg for diB-
cussions. There are 10 references, 7 of which are Soviet.
ASSOCIATION: Institut fizicheakikh problem Akademii nauk SSSR (Institute for
Physical Problems of the Academy of Sciences, USSR)
SUBMITTED; February 3, 1959
Card 3/3

24 (3)
1UTHORS: Abrikosov, A. A., Gor1kov, L. P., BOV/56-37-1-29/64
Khalatnikov~ I. M.
TITLE: The Analysis of Experimental Data on the Surface Impedance of
Superconductors (Analiz eksperimentalinykli dannykh o poverkh-
nostnom impedanse sverkhprovodnikov)
PERIODICAL: Zhurnal eksperimentallnoy i teoreticheskoy fiziki, 1959, Vol 37,
Nr 1(7), PP 187 - 191 (USSR)
ABSTRACT: The authors compare the experimental data on the measurement of
the surface impedance of superconductors for different fivquen-
cies with the conclusions drawn from the new theory of super-
conductivity. The propeevies of superconductors in a high-fre-
quency field were investigated in a previous paper of the au-
thore (Ref 1) and in a paper by D. C. Mattis and J. Bardeen
(Ref 2). The present paper compares the theory vrith the experi-
mental data on the surfaco impedanae of supercond.uctors. The au-
thors give, above all, formulas for the surface impedance in
various limiting cases which are suitable for a convenient com-
parison -with the experiment. The amount usually measured by ex-
Card 1/3 periment, of the ratio between the impedance Z(tj) in supercon-

The Analyais of Experimental Data on the Surface SOV/56-37-1-29/64
Impedance of Superconductors
ductive state and the real part of the impedance in the normal
state is given by the formula Z(W)/R, /2 in
Pippard's limiting case. An expression for the complex function
Q(w) is then written down, and an expression for the frequency
dependence of the impedance follows subsequently. Now the au-
thors analyze the temperature-dependence for various frequen-
cies at temperatures different from zero. The following cases
are investigated in detail (the quantity 2A denoting the gap,
in the energy spectrum at a given temperature): (a) W,*A(O),
(b)w-A(O): This very case is the most difficult one for com-
paring theory with experiment, for the quantities A,(j and T
are, over a large part of the temperature interval O< T< Too
of the same order of magnitude. The expression for Q(cj) can
only be simplified in the range of low temperatures T40,*
(c)w)>A(O). In this case, only the ratio between T and A
changes, and Q is always large with respect to these two quanti-
ties. The formulas written down in the present paper permit a
Card 2/3 detailed comparison of theory with numerous experimental data.

The Analysis of Experimental Data on the Surface SOV/56-37-1-29/64
Impedance of Superconductors
In the range of very high frequencies cj>>, no experimental
data have become known.up to date.-The causes of disagreemeni
between the experimental data and the values of impedance cal-
culated by the new theory of superconductivity have not yet
been clarified. There are 3 figures and 6 references, 3 of
which are Soviet.
ASSOCIATION: Institut fizicheakikh problem Akademii nauk SSSR (Institute of
Physical Problems of the Academy of Sciences, USSR)
SUBMITTED; February 3, 1959
Card 3/3

24 (8)
AUTHOR: Go
SOV/56-37-3-36/62

TI91LE: The Critical Supercooling Field in the Theory of Superconalxo-.~ivity
PERIODICAL: Zhurnal eksperimentallnoy i tooretiche6koy fiziki, 1959,
vol 37, Nr 3 (9)v PP 833-842 (USSR)
AB'STRACT: The phase transition from the normal to the ouperoonductive
otato occurring at a certain value of the magnetic field strength
is a transition of the first kind for a massive sample. The
value of the critical field H. may be obtained on the basis of
the thermodynamical theory and was calculated by Bardeen,
Cooper., and Schrieffer (Ref 1). Besides the thermodynamical
main field, two further critical field values, however, exist
at a given temperature, viz. the so-called "superheating" field
and the "supercooling" field Eel. These fields determine the
range of the possible hysteresis: If the field is stronger than
H
but weaker than the superheating field, the metal is in a
0
metastable supercondgative phase, and if the field is weaker
than H
but stronger than Hc11 it is in a metastable normal
e
phase. For the determination of these critical field values
thermodynamical considerations are not sufficient, and it is
Card 1/3 necessary to return to the microscopical theory of supercon-

The Critical Supercooling Field in the Theory of SOV/56-37-3-36/62
Superconductivity
ductivity. By using a riethoa developed in an earlier paper
(Ref 2), the author in the pre,;~?nt paper gives derivations of
formulas for the determination of the amount of H.10
Der.ivations are carried nut step by step and axe discussed
in detail. The following is obtained as approximation formula
(variation method): H f--- (e 2 2)(0 A2 /ev), and for T = 0,
01 r/ 0 )P,)1/2
He = lAOT2mpo/irl. Then., H,j/H. = 1-77(3;tT6mc/e)(2'rm/'T~(3
0
(x) is Riemann's zeta, function., ~ (3) = 1.202). If the
product of the parentheses '
jn the right side of the above
equation is denoted byy. then R
Ol/He = 1-77 x~ According to
Ginzburg and Landau (Ref 5) Hc1/Hc = IP2x neax Tc holds;
thus, the ratio varies within this entire temperature interval
only by 25%. The fD11-owing considerations apply to the
determination of Xo7c may be expresued as a'fuaction of the
density of the free electrons n =- p~/31T2 (p Fermi momentum):
3/2/e*
Card. 2/3 0-485 kTO om 40 'n5/6. The eloctron m4ss m and the

0 /56-37-3-36/62
F cix, al -oaa i!-jurt thin
j I I f al 5r:~a 0 rjl " Y., as
TIO f
9) and 0.'58 (Ref 10)
il--:Uum 0.22 (Ref '11). Fi--,fher
awad
dependence -,f the
Ths fcV-,o,,7L,,F is
2
'Th,
/T
;v 1--aS in e St
t re
r~:3 cV . GinzlyL~rg for ramax-r-l'-s.
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9'?'or~lr4
AUTHORS-
TITLE.-
30)37
S/57o/6o/oooj1ol7/OO7/Ol2
E032/E114
Gor1kov, L.P., Dzyaloshinskiy, I.Ye., and
r3Ta__y_e_v_sk_3Y_,__L. P.
Calculations of fluctuations in quantities described
by transport equations
SOURCE: Akademiya nauk SSSR. Institut zemnogo magnetizma,
ionoafery i rasprostraneniya radiovoln. Trudy,
no.17(27). Moscow, 196o. Rasprostraneniye radiovoln i
ionosfera. 203-207
TEXT: The authors discuss fluctuations in quantities which
can be described by transport equations, e.g. the equations of
Boltzmann, Fokker-Planck and Landau, in the case of a Coulomb
interaction between the particles. The knowledge of these
fluctuations is essential to the theory of scattering of electro-
magnetic waves in rarefied gases and electron plasma. The method
employed is analogous to that used by L.D. Landau ard Ye.M,
Lifshits (Ref.23 Electrodynamics of uniform media, M., Gostekhizdat,
1957, Ref.3: ZhETF; v.32, 6A, 1957)- It consists in the
introduction into the transport equation of additional random
Card 1/4

030P,37 000/017/007/012
Calculations of fluctuations in S/57 /b0/
E032/E114
terms whose correlations are then determined on the basis of the
general theory of fluctuations. For example, the Boltzmann
equation is modified to read
8-0 + (v + y
at
where the collision integral J is given by
W(Prp"; P'Op') f n0 (pl) (1)' no (pi) -X) (PI)
OS I I
- n (p') -,0 (p) - n (p) N) W) d3 p d3 p(d3p (2)
0 0 1 1
and y is the Itrandom" collision integral. The problem consists
in the evaluation of the average of y(p,r,t)y(p',r',t').
It is shown that this average is in fact given by:
Card 2/4

30937
Calculations of fluctuations in ... S/570/60/000/017/007/012
E032/EI14
y(p,r,t)y(p,',r',tI) = 26(r - r')6(t - t#) X
f 3 3
no(PI) ~E W(P"Pil Pi.,Pl) n 0 (p d Pi d Pi
n0(p) W(P"P)-; pi,pi f) n (p) d 3 pld3p +
0 2
6(p - p')n (P" w(pi,p"; p, pl)no(pl) d3pt d3 1fd3p +
0 SSS 1 1 Pi 1
n0(p)n o(p') w(pl,p'; p. p) d3 pld3 P, (9)
SS 1 1
which is equivalent to the results obtained by B.B. Kadomtsev
(Ref.5: ZhETF, v.32, 943, 1957). It can be shown that the
introduction of the 11ran,dom" collision integral into Eq.(l) does
not upset the -conservation of the number of particles, energy and
momentum. Another transport equation considered is the following:
89 + (v V)N) div ji (10)
Card 3/4 C)t -

Calculations of
wher~e is the
is convenient to
N +
St
30937
fluctuations in ... S/57o/6o/ooo/ol7/007/0l2
E032/Ellk
current density in the momAntum spacs~ Here it
introduce a "random" current y so that
(v div (j + y)
-
Expressions analogous to Eq.(9) are then derived. An account of
the general theory of fluctuations on which these calculations are
based is given in "Statistical Physicst' by L.D. Landau and
Ye.M. Lifshits (Ref.4: izd. 3 M., Gostekhizdat, 1951). The method
.:an be used for fluctuations in the equations for fermi and bose
gase,a. A.A. Abrikosov and I.M. Khalatn_4kov,(Ref.7: ZhETF, v-34,
198, 1958) have used it to study light scattering in liquid He%
k-'knowledgments are expressed to L.,D. Landau and Ye.M. Lifshits
for discussions. S.M. Rytov and B.B. Kadomtsev are mentioned in
c~onnection with their contributions to the theory of fluctuations.
Thsrs are 7 Soviet-bloc references.
card 4/4

S/030/60/000/009/012/016
B021/BO56
AUTHORt Gorikov, L. P., Candidate of Physical and Mathematical
Ic es
TITLEs Problems of the Physics of-Low Temperaturesl\ -
30
PERIODICAL: Vestnik Akademii nauk SSSR, 19 0,po. 9, pp. 110 - 112
TEXT: From June 23 to 28, 1960, the 7th All-Union Conference on Low
Temperature Physicq took place at Kharlkov. The opening address was
delivered by P. L. Kagitsa, who said that the physics of low temperat-ares
had developed into a large field of science. Since 1938, when P.L.Kapitea
discovered the phenomenon of He II super-fluidity and 1941 when
L. D. Landau explained thiB phenomenon, He II has been the object of
numerous experimental and theoretical iLvestigations. Furthermore, the
following lectures are mentionedt E. L. kndronikashvili, R. A. Bablifte, V/
u. G._,&maladz , B. G. MatigZan, K. B. Mesoye , and D. S. Tsakadze spoke
about the further research of vortex prcperties; Y1. P. Peshkov - results
obtained by experiments with critical velocities in _apjL~ag es,
M. Khalatnikov - analysis of the phenomenon of the "Kapitsa-temperature
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Problems of the Physics of Low Temperatures S/030/60/000/009/012/016
B021/BO56
origin"; k. YBog21LtIbov - the problem of au2erconductivit
BelluglLy and A. A. Galkin - the discovery of the anisotropy of the
absorption coefficien of longitudinal sound in tin..A,- i~L k
L_ ~~_jj
results obtained by measuring thermal conductivity; A,. A. Abrikosov and
L. P. GorIkov - the influence exerted by the so-call~~d--"~a-z~a-m-a:-gn-eTnl-
T~-P`uriiies on superconductivity; B. G. Lazarev, Ye, Ye. Semenenko,
A. 1,, Sudovtsov, Ye. I. Nikulin, N. M. RLe , and A,. P. Smirnov - the
Lnov
possibility of the existence of superconductive metal modifications in
form of foils; I. M. Lifshits - problems of the physics of metals5
N. Yo. Alekseyevakiy, Yu. P. Gaydukov, I. M. Lifshits, and
V. G. PescLa~ki - th e, anisotropy of the energy spectrum of tin;
M~ S, Khaykin - the so.."lled cyclotron resonance in tin, which had been
fEV-b7i-eT4i`Z`ay predicted by,~. Ya. Azbel I already several years ago,
E. A. Kanerp A. A. Galkin A. P. Korolyuk, N. B. Brandt, and
the further development in this field,. A report was given
on problems of magnetism by A. I. Astror, I. Ye. Dzyaloshinski , and
R, T. Minaya. 100 reports were submitted to the conference.
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83199
S/056/60/039/002/036/044
4-.77#o B006/BO70
,&TJTHORSt Abrikosov, A.A , GorIkov. L. P.
TITLEs The Problem of Kni&ht ShiftYin Superconductors
PERIODICAL3 Zhurnal eksperimentallnoy i teoreticheskoy fiziki, !960,
Vol. 39, No. 2(8), pp, 480 - 483
TEXT: A number of scientists have interested themselves in the theory of
Knight shift in semiconductors (displacement of the nuclear resonancp
frequency as compared with that of dielectrics). The purpose of the pres-
ent paper was to explain the experimental data, The Knight shift is due
to the paramagnetism of the conduction electrons- Since the electron wave
function is anomalously large in the neighbourhood of tho nucleus, the
magnetization of the electrons causes a change in the magnetic field
acting upon the nucleus; the deviation of the effective field from the
external one is given by AH - (BR/3N at)l'(OW~H, where 1f(0)12 is the
probability density of the electron at the position of the nucleus, N at
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83199
The Problem of Knight Shift in Superconductors S/056/60/039/002/036/04A
B006/BO70
is the number of atoms per unit volume, ;Cis the electronic susceptibil-
ityj and H is the external field. The authors first discuss the results
and methods of other related works, and show that a homogeneous field
can exist only in such semiconductors whose dimensions are very small
compared to the depth of penetration, F, of the static field, (The ex-
perimental work was done with an emulsion of a semiconductor), A con-
sideration of massive semiconductor in a homogeneous field (e.g. Ref, 1)
corresponds to no practical situations. Also, the results obtained by
other authors (Refs. 3,4) relating to the effect of impurities are
criticized and the errors indicated. The authors of the present work have
elaborated in earlier publications a method for the theoretical
investigation of semiconductors with impurities,. Here an expression for
the spin magnetic moment of the electron system in a homogeneous magnetic
field is first written down and transformed. The impurities aye taken
into account in a manner completely analogous to Refs. 7 and 8. The ex-
periments show, in particular, that for T - 0 the susceptibility T
vanishes and therefore ther.~ can be no Knight shift,, (The authors of
Refs. 3,4 found the opposit:.- result; also experimentally;( was not found
to be zero for T - 0).. In V-1is connection, the authors also comment on
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The Problem of Knight Shift in Superconductors S/056/60/039/002/036/044
B006/BO70
the interpretation of the experiment of Reif (Ref. 5). For low tempera-
tiires, the field was no more homogeneous, as is also indicated by the
large width of the resonance line. A discussion is also given of the
characteristics of transition from the supraconducting to normal state
for particles which are smaller than the depth of penetration of the
field. The authors finally thank Academician L, D, Landau for discussions
There are 9 references: 3 Soviet and 6 US.
ASSOCIATIONs I-nstitut fizicheskikh Droblem Akademii nauk SSSR ~~it~ute
of Physical Problems of the Academy of Sciences of the USSR
SUBMITTEDs March 23~ 1960
Card 3/3

". X_~
8
S/05Y60 0039/006/052/063
B006 B063
AUTHORS Abrikosov, A. A., Gor'kQ -v,..-L.--P,-
TITLE: Theory of Superconductive k1loys With Parazagnetic
Impurities
PERIODICAL: Zhurr,al eksperimentallnoy i teoreticheskoy fiziki, 1960,
Vol- 39, No. 6(12), pp. 1781-1796
TEXT: Experiments on the effect of paramagnetic impurities upon the
critical temperature of superconductors have shown that an admixture of
such elements leads to a decrease of To? whereas an admixture of ferro- J
magnetic elements (e.g., to titanium - Ref. 4) results in an increase af
Tc. A study of this phenomenon has been made on the basis of a microscopic\J111-
theory of superconductivity. The mechanism of superconductivity is related
to the formation of bound electron pairs in the singlet state. Exchange
interaction between electrons and spinning impurity atoms leads to non-
conservation of the electron spin, which indicates the formation of
Cooper pairs. Thus, the spin of the impurity atoms is likely to complicate
Card 1/4

88460
Theory of Superconductive Alloys 3/056/60/039/006/052/063
With Paramagnetic Impurities B006/,063
the occurrence of superconductivity and causes a decrease in TC. This
assumption was confirmed by a theoretical study described here. It is
assumed that the interaction of an electron with an impurity ato% is
described by an expression in which the exchange term 'UM = u1(')
r
-.> A
S is the momentum of the impurity atom, and a
r SU) is contained;
+ U2()(
is the electron spin matrix. The Hamiltonian describing the interaction
between electrons and impurity atoms is assumed to be given by
+1%1) _ (j+jA(--11 _ - )y)
Hint V a v r ra (.99cond-quantization representation).
First, the dependence of the transition temperature T0 on the impurity
concentration is described. Following a previous paper, the superconductor
is described by two Green functions. When the impurity concentration is
small (Q>l, i.e., T. /T co(< 1 , then
T2 = (6/jj)ln(nT Ir /2Y). At a certain critical concentration of the
c S c0 a
Card 2/4

88460'
Theory of Superoonduotive Illoys S/056J60/039/006/052/063
With Paramagnetic Impurities B006/BO63
paramagnetic impuritieV, which is detormined by the condition -r a or
= 2r/nT cc thereis no superconductivity any longer throughout the tempera-
ture range. The cri'tibal path is given by 1 8 or = VT s or -10-4 cm. In
addition, the thermodynamio and electromagne tic properties of alloys within
the range of critical concentration have been studied, i.e. at T 2:~T
8 a or
It is noted that ihe expr;ssion for the ratio between the specific heats
of the superbonduotive and the normal phase contains no exponential term
a~ Ma meaus,that there is not gap in the spectrum of these super-
.conductors and, consequently, no absorption threshold for electron magnetic
radiation at T - 0. Finally, the dependence of the spectrum gap at T 0
on the imj?urity concOntration is described. The gap disappears at a
concentration that is somewhat lower than the critical one (ni
~2e_~'An ''r--0,'91 n ), and the spectrum remains oo*n',,inu'ous at higher
or .- , . or
c orAcentrationa-. L. D. Landau is thanked for discussions. N.N. Bogolyubov,
V,L*,Ginzburg, A. B. Migdal, V. M. Galitskiy, and A.~ 1. Shallnikov
arei mentioned. There are 4 figures and 17 references; 9 Soviet and 8 US.
Gard 3/4

88460
Theory of Superconductive Alloys S/056/60/039/006/052/063
With Paramagnetic Impurities B006/B063
ASSOOIATION:. Inatitut fizicheikikla problem Akademii.nauk SSSR (Institute
-of Physical Problems, Ac4damy.of Sciences USSR)
SUBMITTED: ~5; 19060.
Card 4/4

S/030/61/000/009/009/013
B105/1101
AVTEORi Gor1kov, L. P., Doctor of Physics and Mathematics
TITU s Problono of the thoory of solido and of quantum statistics
PERIODICAM Akademiya nauk SSSR. Vestnik, no. 9, 1961, 121-122
A
TEM A well-attended joint symposium on the theory of solids and new
statistical methods was held by the Odeaskiy universitet (Odessa
University) and the Institut fizicheskikh problem im. S. 1. Vavilova
Akademii nauk SSSR (Institute of Physical Problems imeni S. I. Vavilbv of
the Academy of Sciences USSR) in Odessa from May 21 to 30, 1961. The
present state of the semiconductor theory, general problems of quantum
statistics, and the theory of metals and semiconductors were discussed.
A. A. Abrikosov and L. P. Gorlkov (Moscow) reviewed past achievements, and
G. X. Eliaehberg (Leningrad) discussed general statistical problems. In
additiong the latter lectured on the derivation of the kinetic equation
for excitation in the Fermi liquid (theory of the liquid isotope He3 at
low temperatures). 1). N. Zubarev (Moscow) spoke of generaliz4ng the
notion of statistical operator in quantum statistics to cover the case of
Card 1/2

S10301611000100910091013
Problems of the theory of solids and ... B105/BlOl
nonequilibrium processes. The following reports are mentioredt I. M.
Lifshits (Xharlkov) on arguments backing the statement that the so-called
Fermi liquid effects are not important in studies of the energy spectrum
of electrons in mets.191 L. D. Landau on the essential role played in a
number of cases by excitation interactions in the theory of.Fermi liquidsl
V. G. Bkobov (Leningrad) on ultrasonic attenuation in the magnetic field
of metals in the presence of impuritiesi V. G. Vaks, A. I. Larkin, and
V. M. Galitskiy (Moscow) on so-called collective excitations in super-
conductors. V. L. Pokrovskiy (Novosibirsk) on the theory of super-
conductivity in an anisotropic metal; L. Y. Keldysh (Moscow) reviewed the
principal problems and latest findings in the iheory of semiconduotoral
Fs. I, Hashba (Kiyev) on hia findingo Oonoorning wurtzltu-typlo semi-
coiductors; G. S. Pikus (Leningrad) on the effoct of deformations on the
electronic spectrum in samiconductoral A. 1. Larkin and V. G~ Vaks on the
theory of superconductivity as utilized to set up a model of elementary
particles; A. A. Vedenov (Moscow) and R. SaRdeyev (Novosibirsk) on the
mechanism of energy transfer in plasma from a particle beam to plasma
oscillations. The latter researchers succeeded in setting up a kinetic
equation covering this process.
Card 2/2

GOR'KCV, L.P.; GALITSKIY, V.M.
.
Superfluidity in a Fermi system in the presence of pairs with
nonzero angular momentum. Zhur. eksp. i tepr. fiz. 40
no.4:1124-112? Ap '61. (MIRA 14!7)
1. Institut fizicheskikh problem AN SSSR-
(Superfluidity) (Fermi surfaces)

GORIKOV, L.P.; MELIK-RUDEUDAROV, T.K.
Theox7 of Me ouperfluidity of an imparfect Femi gan. Zhur.
ekap. i toor. fiz. 40 no.5-0452-33458 My 161. (KM 14:7)
1. Inatitut fizicheakikh problem AN SSSR.
(Qu~ntim Veld theory)
(Electron gas)

S/056/61/041/005/025/038
a100 //,v/, 3 B102/B136
AUTHORS: Bychkov, Yu. A., Gorikov, L. P.
TITLE: Quantum oscillations of the tbermodynamic quantities of a
metal in a magnetic field according to the Fermi fluid model
PERIODICAL: Zhurnal eksperimentallnoy i teoretichesk,~y fiziki, v. 41,
no. 501), ig6i, 1592-1605
TEXT: L. D. Landau's theory of the Fermi fluid (ZhETF, 50, 1058, 1956;
ibid. 25-9 97, 1958) is applied to investigate the de Haas-van Alphen
effect for the electrons in a metal. ' The Fermi fluid is assumed to be
isotropic and the long-range part of the Coulomb interaction to be
screened. To determine the energy spectrum of the electrons, the
authors start from an investigation of the properties of the Green
functions of electrons in a magnetic field:
G (r, r'; t - t') b,p I < T t) qi'A I'))>.
The field operators yc,(x) and ~,*(xl) include field dependence. In the
Card 1/7

S/056/61/041/005/025/038
Quantum oscillations of the... B102/B138
following, the Fourier components G(r, r7.1; E) of (1) through the time
difference _(.~-t')_._9,3~~t_q~onsidered in thfa Dyson equation
B+ P --LA) 2] G (r, I (r, r'; P) G (r', r'; P,) d3r'
2m C
A r'). (6)
p ia/ar, 11 -chemical potential of the electrons in the magnetic field,
(r' P'; &) is the so-call
ed self-energy part, caused by particle interaction
in the Fermi fluid. The vector potential is defined by AM - f-HY,0,01.
For small F_ and 11=0 the function (;O(P'*', t) has a pole near the Fermi
surface: GO(FE, - a/(t_-v(p-p.) + 16(E )). The spectrum of the Fermi fluid
is def ined by & - v(p-po), i. e. from the eigenvalues of the operator which.
stands within the brackets of (6). The electron interaction Hamiltonian.
in secondary-quantization representation is given by
e OHy Hyip (r) d3r, (7)
1
2.c P 2MC, 1
A = _ia/ax . The authors show that the^ electron energy spectrum in the
Px
magnetic field can be determined from (5) with regular quasiclassical
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26,710
5/056/61/041/005/025/038
quantum oscillations of the... B102/B138
qijantization, as proposed by I. M. Lifthits and A. M. Kosevich (ZhETF, 29,
760, 1955). Where the electrons are near the Fermi surface as in the -
de Haas-van Alphen effect
G (P, P'; V) 4l,. (P) q~ (P') 6 (0. - P'X) (P, - P;) G~ (PI, F),
ri
(p, P-) = a /(P- + 2-ni* - (n + '/2) p2 / 2m* A O(e)), (15)
is found, with 4)1"-eH/~*'c; the constants a, e and po contain terms which
3/2
are functions of H The singularity near the Fermi surface is
determined by GO(P-0,90 a g(-,E). The Green function in
E-V(P-Po 16 (,.-y + P
coordinate representation is given by
G (r, r'; e) = eXD f- 1 (elf 12C) (X - X') (Y + YT Y
L-ellp"OLn hze ip,(z-z') dp,
(~Acj P2)~z+ 4/2m'-(n +11.),o* -r~, /2m' + i8(r)
exp 1 (effl2c) (x x') (y + y')) 6 (R, (17)
Card 3/7

S/056/61/041/005/025/038
Quantum oscillations of the ... B102/B138
where L nW is a Laguerre polynomial. The formulas derived are then
applied to study the influence of the Fermi-fluid effeeta upon the
oscillation of the thermodynamic quantities of a metal in a magnetic field.
The variation of the particle densit K with the chemical potential p is
first investigated for In Fourier representa--
tion
d(o G., (r, 1; a)) G, (1, r; (o) A
~'dwd(#'~ dJs,,Ps~d-s,&s,,P1G,,, (r, sj; w) G., (s4, r; W) x
(2n? ~
X Fa,a,, cea. (S1, 6); S2 P (l)", SS, (J)'; S4 0)) Gp., (1, sg; (sa, (o')
which can be trans-f
ON
2
2g2
a + (pl, p.-) GO (PI, (0) GO (P2, w) d'pj (29)
For H 0
a po dp~ (29')
a~L P.. -D m* diL
Card 4/7

2010
S/056/61/041/005/025/038
Quantum oscillations of the... B102/B136
and 01V I jfW (!LP;!), q-L' A
Ni- 4,2 djL 2 W P))
hold. For the oscillating part of the thermodynamic potentialQ
~4jn*2 W* M. %W.
3 )f cos (2,nr
is found, which agrees in full with the formula found by Lii6hits and
Kosevich. Finally the influence of electron spin on the oscillations,
i.e. of the interaction between the magnetic field and magnetic moment
of the spin, is studied. It is found that
2
a IV if j; ~ (I, L\
_L , _~ ,) 4
d1t 2 W 20, 2 W* 21*
and for the oscillating part of the thermodynamic potential
2,n'2 ca'k', 3 A+~ff [Z 3 A
IC( 1), ) + 21 (34)
Card 5/7

267 ILO
S/056/61/041/005/025/038
Quantum oscillations of the ... B102/BI36
for the oscillating part of the magnetic moment
CO
MOCII M, Cos(-Ltr sin ar CP;
2a, A3 H r1h
where eA/M*'c, c VT and J/P* - 4n2V3PP*Y. The results show that the
Lifshits-Kosevich procedure can be followed in order to determine
oscillation periods. Deviation from the usual formulas occurs for the
oscillation amplitudes and is due to the variation in the effective magneton
excitation caused by electron interaction. Without taking account of spin
susceptibility an expression for Mosc may be found from the usual
representation of the electron system as a quasi-particle gas. This
conclusion agrees with that of Luttinger. L. P. Pitayevskiy (ZhETF, 211
1794, 1959) and A. A. Abrikosov and 1. M. Khalatnikov (UFN, 66, 177, 1958)
are mentioned, Academician L. D. Landau is thanked for discussions. There
are 4 figures and 11 references: 8 Soviet and 3 non-Soviet. The latter
read as follows: J. M. Luttinger. Phys. Rev. 121, 1251, 1961;
E. Sondheimer, A. Wilson. Proc. Roy. Soc., A210, 173, 1951; Higher
transcendental functions, I., N.Y., 1953, p. 24.
Card 6/7

26710
S/056/61'/041/005/025/038
Quantum oscillations of the::~ B102/B138
ASSOCIAT ION ~ Institut fizicheskikh problem Akademii nauk SSSR (Institute
of Phyeical Problems of the Acalemy of Sciences USSR)
SUBMITTED, May 31, 1961
0 >~
Card 7/7

27876
S/020/61/140/001/012/024
1A 7) B100109
q-*) ~ O'd MO I/ //,t ", "
AUTHORi Gortkov, L. P.
TITLEt The forces acting on a small particle in an acoustic field
in an ideal liquid
PER I (jD1 CAL iAkndoiniya nnuk B33H* DOklady, V. 140p lio. 1, 1901, 60-91
MIT i The author ouggostb a method for calculating the average forces
acting on a particle in any acoustic field in an ideal liquid. The di-
mensions of the particle are small as compared with the wavelength of the
acoustic fields It is shown that it is sufficient to solve the linear
scattf~ring problem. As a small particle in the theoretical investigation
the authors considered a compressible gas-filled sphere, which could be
moved by the forcus of the acountic field. For the velocity potential of a
wave scattered by the sphere, the expre3sion
_f - RD
3pr pj, d i v (Vn (7)
Card 1/4

27876
3/020/61/140/001/012/024
The J'orces acting on a smalloot B100109
is obtained, R is the radius of the sphere; SO is the density of the gas
of the spherel is the density of the liquidt Y. is the density of the
compressed spherel -> is the vblocity of the incident wave; f 1 - c._~/J~;
vTI 0
f2 - 2(~o -y)/(25,0 +9). The first term in (7) expresses the "ejection"
of mass owing to the compression of the gas in the incident.wave. By means
of this formulat thgfollowing equation is obtained for the potential
U(r-') of the forces F acting on the_sphe.re:
V2
3 17.11
U 2nR p jg~jo- A 12
(12)
where a is the velocity of sound, 12 and v2 are averaged values of
p7r n
pressure and velocity at the point where the particle is located. This
formula holds for a plane traveling wave. The formula
Card 2/4

27876
S/020/61/140/001/012/024
The forces acting on a small**. B104/BlOg
,'J (r) QR' 0 __Ul
2 11
Wig hiLenhity ept the radiatiun Ejource, holds for spherical
Vlave'9. This indicates that e. g. for f 2-> 0, f1 5 312 f2the particles are
attracted by or repulsed from the radiation center, as depending on their
distance from the center* is the condition for the applicability
of the results obtained here% -The author thanks Academician L. D. Landau
for a discussion tind valuablo advice. Thero aro 3 roferonceat 1 Soviet
Und 2 non-0oviet. The refer(inoo to English-language publications reads as
follows: L. V. King, Proc. Roy. Soc., AjAj, 212 (1954).
ASSOCIATION: Institut fizicheskikh problem im. S. 1. Vavilova Akadomii
nauk SSSR (Institute of Phyaical Problems imeni S. I. Vavilov
of the Academy of Scienceii USSH)
Card 3/4

I
,U~~-ISKOV: -4.1eksey Alekseyevich-, GORIKOIT Lev Petrov* h DZYAWSHINSEIY~
Igor' Telchiyellyevich- L.Yu.;' tel-hn.
red.
["Quantum field theory methods in statistical physics] Metody
kvantovol teorii polia v statisticheskol fizike. Moskva.. Fizmat-
giz, 1962. 443 P. (IMA 15:7)
(Quantum field theory)

9/056/62/042/002/043/055
B108/B138
AUTHORS: Gorlkov~p L. P.,,Pitayevskiy,.L. P.
TITLE. Transit*ion of liquid Hd into the superfluid state
PER16DICAL: "Zburnal eksprimentallnoy i teoretichaskoy fiziki, v. 42,
no. 2, 19621 600-605
3 3
TEXT: The Cooper effect in He j i.e. transition of He to the superfluid
state, is investigated.- Theoretically, this effect is due to pairing of
excitationd1whic.h.attiact each other.when they are in a state with a
suffici6ntly~-la.tge Iorbit~l'.angular momentum (1>1). The transition tempera-
tur& founa iia
T' =(2/n)_yia6
3m*pAo (21 + 1) AM 21
(14)
+
)2/3 2 2/312 (m02 iA 2 2
(I =tf((2-n mm 0 1 ON/811) c/m c ) - N number of atoms pez-
uni volume, m - maeB of'He3 atom, M% - effective mass of excitation,
Card 113

3
Transition of liquid He into
S/056/62/042/002/043/'O,-,")
B108/B138
compressibility of liquid 11d, C-2 - compressibility of ideal Fermi
0
gas with mass m and density N. In fact, pairing of the excitations,takes
place at not too great 1 (probably at I . 2), i.e., at temperatures much
higher than calculated from the asymptotic formula (14). However, an
estimation with the aid of formula (14) (which is applicable only for
o-4
large values
1),
of
using I = 2, yields T 00'0 2 * I
OK. On the basis of
W..hf,r estimations it is concluded that T0 probably lies between B-10-3 and
-40K.- E. E. Shnoll and N. D. Vvedenska, collaborators of the
-.-Lenr!.ticheskiy insti-tut (Institute of Mathematics), are thanked for cal-
c-%1a.1_!onB, S. P. Kapitsa and Academician L. D. Landau for discussions and
'"MiAs. Mention is-made of N. N. Bogolyubov et al. (Novyy metod v teorii
svr-.r1chprovodimosti (A new method in the theory of superconductivity, Izd.
AN SSSR, 1958). There are 2 figures wid 7 references: 4 Soviet and 3
non-Soviet. The three references to English-language publications -read as
follovs- 'V. I. Emery, k. IA. Sessler. Phys. Rev., 119, 43, 1960;
K. A. Bruecner, 1. L. Cammel. Phys. Rev., _LO2, 1040, 1958, 1 A. C. Anderson
et al. Phys. Rev. Lett., 6, 331, 196A%.
Card 2/3

3/05 6/62/04 2/~;,D2/04;5/055
Transition of liquid He into !- B108/B!38
ASSOCIATION: Institut fizicheskikh problem Akademii nauk SSSR (institute
of Physical Problems of the Academy of Sciences USSR)
SUM"ITTED: September 15. 1961
11-K
Card ~i/3

~j "to
S/096/62/042/004/027/037
B108/B102
AUTHCRS: Abrikosov, A
TITLE: Spin-orbit interaction and the Knight shift
in superconductors
PERIODIUL. Zhurnal eksperimentallnoy i teoreticheskoy fiziki,
V. 42, no. 4, 1962, 1088 - 1096
TEXT: it is shown that consideration of spin-orbit interaction may provide
a quantitative explanation of the frequency shift of nuclear magnetic
resonance in superconductors at absolute zero. This Knight shift is
proportional to the paramagnetic susceptibility of the conduction electrons.
-in a polycrystalline small superconductor the electrons undergo scattering
from the grain boundaries. Owing to spin-orbit interaction, scattering
changes the paramagnetic susceptibility of the superconductorp thereby
leading to the Knight shift. Formulas of the type
co
%S
2/3vl
Card 1/2

S/056/6')/042/004/027/037
Spin-orbit interaction ... B!08/BI02
are obtained for the paramagnetic susceptibilities.4t, is theenergy gap in
the spectrum of the pure supercoraduc-Lor at a given temperature. Theory
and experimental data are in good agreement. There are 6 figures and 12
references: 3 Soviet and 9 non-Soviet. The four,most recent English-
lariguage references read as follows: R. A. Ferrell. Phys. Rev. Lett.,
262, 1959; P. W. Anderson. Phys. Rev. Lett., ~, 325, 1959; J. Bardeen,
J. R. Schrieffer. Progress in Low Temp. Phya., 2, Amstordain, 1961;
G. :J. Androes, 1.11. 1). Knight. Phys. Rev., 121, 779, 1961. .
ASSOCIATION: Institut fiziche3kikh problem Akademii nauk SSSR
(Institute for Research on Problems of Physics
of the Academy of S6ienoes USSR)
SUBMITTED: November 4, 1961
Card 2/2

AUTHORS: Abrikosov,
TITLE, The nature
PERIODICAL: Zhurnal eksperimentallnoy
no. 6(12),
h 240
8/05 62/043/006/045/067
B187Y3102
A. A., Gor1kov, L. P.
of impurity ferromagnetiam
i teoreticheskoy fiziki, v. 43,
1962, 223072233
TEXT: The ferromagnetism discovered by Matthias et al. (Phys. Rev. 115,
1597, 1959; Phys. Rev. Lett. 1, 44, 92, 1958) in nonmagnetic metals doped
with paramagnetic atoms was first explained by the exchange interaction
between the impurity atoms and the conduction electrons. This concept was
refuted, however, in a paper by Yosida (Phys. Rev. 106, 893, 1957) who
argued that such an interaction cannot caus *e a'uniform polarization of the
electron spin. The latter is assumed to occur only in the neighborhood of
the impurity atoms and to decrease rapidly with the distance from the atom
concerned; but this concept is not correct as the decrease does not take
place rapidly. The contribution of all impurity atoms to polarization has
therefore to be taken into account. The electron density with different
qpin. orientation as a function of the number of randomly distributed
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3/056/62/043/006/045/067
The.nature of impurity... B187/B102
impurity atoms is calculated on the basis of this concept and with the aid of
a formula of Yosida. It is shown that spin polarization of the impurity atoms
causes uniform electron polaiiZation. Furthermore, the thermodynamic
propertien of thin Enodal are fiti)died, ft*tj Coilo 10,e-judbrld
fV011, Ilj!J JhLurhal Wid frOO ollorglen Wtiiv oylitem. It is found to be
proportional to the impurity concentration. For temperatures above the
Curie temperature a formula is given for the paramagnetic susceptibility.
ASSOCIATIO'N; Institut fizicheskikh problem Akademii nauk SSSR (Institute
of Physical Problems of the Academy of Sciences USSR)
SUBMITTED: July 3, 1962
Care 2/2 %"0

S/020/62/144/002/005/028
B100102
GorIkov, L. P., and Pitayevskiy, L. P.
------------
TITLE: Formation of a shock wave on reflection of a weak
discontinuity from sonic line
PERIODICAL: Al:ademiya nauk SSSR. Doklady, v. 144, no. 2, 1962,
293 - 296
TI~7q': Iho formation of a shock wave was studied under the condit'ion
-,,.,here a weak discontinuity is reflected from a 14ne, alon6 which the
-flow, velocitv couals the local velocity of sound 'sonic line). Herein
is assumed that 'he jump of the :irst derivatives of the'velocity of 'he
we&'- discontinuity on the coordinates is negative. Tn 'his case, the
I - U - - 6
discontinuity reflected from 'he sonic line has the form of a shock wave
rihose intensity is exponentially small near the point, of reflection. If
"'-e velocity derivatives are positive, they give rise to weak logarithmic
singularities such as have been studied by L. D. Landau et al. (D,,N, 96,
725 (11954)). There are.2 figures.
Card 1/2

S/020/62/144/002/005/028
Formation of a shock.... B100102
PRE'SENTED: December 15, 1961, by L. D. Landau, Alcademician
SUBYITTED: December 6, 1961 4
Card 2/2

-18031-63 -FJWTW/nC6r)./zD8
ACCESSION M : %~'P3-0007'14 S/i3258/631003/002/0246/0250
171 'kov L. (Moscow)
MR; Gor
TI:1 U.: Nonllniii4 oscil it i
ons of gas column
SOURCE: InzhenL:rny*y zhurnal, v. 3, no. 2, 1963, 246-2jO
TOPIC TAIGS: : rD.,;6nanC0;, shocIt wave, Oscillation, nonlinear eAffect
ABSTIIA-CI-: A sizziple anialysis has been presented to solve che probLen. of nonlinear
oscil Iztion of a pas aol=m in a tube with One e3ld closed by a soLid plug and the
other by an osclillatinig piston. The amplitude of the sinuso-idialLy oscillat-ing
T)i.':tO'r, is UmiLi-,S by the assimption Auj