SCIENTIFIC ABSTRACT KHALATNIKOV, I.M. - KHALDEYEV, O.D.

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

N A I- 47-IV K6 v, , T. M 4
AUTHORS: Abrikosov, A. A., KhalatnikOv, I- M- 56-1-28/~6
TITLE: The Scattering of Light in a Fermi Flvid
(Hasseyaniye eveta Y Fermi-zhidkouti)
PERIODICAL: Zhurnal Eksperimentalinoy i Teoreticheskoy Fizikip 19581
Vol. 34t Nr 1p pp. 198-2o3 (USSR)
ABSTRACT: The present paper determines the distribution of the
scattered light to the angles and to the frcquencies.
According to Landau (reference 1) oscillations of a certain
type which are designated as "zero sound" can spread in a
Fermi fluid at suffigiently low temporaturcs. Even at a
temperature of 0,010 a frequency of more than loo cycles
is needed for the immediate observation of zero soundt which
renders the performance of such an experiment very difficult*
But an indirect method can also be saggested whiob consists
of the observation of tho Rayleigh scattering of light in
liquid He3. The observation of the freqaancy distribution
of the scattered light principally makes possible the
measurement of the speed of zero sound. Besides, the
scattering of the light in a Fermi fluid has a number of
Card 113 specific features, wherefore the theoretical investigation

The Scattering of Light in a Fermi Fluid 56-i-2e/56
of this phenomenonp especially of i;he distribution of the
intensities to the frequencies, is of interest. Due to the
very small polarizability of the helium-atoms it may be
assumed that the dielectric constant changes due to the
fluctuation of density. In the ranE:e of those temperature*
and frequencies where >.kT applies the quantum effects
must be taken into account in the averaging of all possible
fluctuations. But for this purpose only the knowledge of the
purely classical case is needed and then a certain
corrective factor has to be introduoed. The fluctuation of
the "random force" contained in the kinetic equation is
determined by the method suggested by Rytov (reference 5)9
.Landau and Lifshits (reference 6). After the solution of
this equation the fluctuations of the distribution function
can then also be determined. The kinetic equation used here
for the case of the Fermi fluid is oxylicitly written down.
The authors are furthermore only interested in the case
that the collisions can be diaregard.ed. In this connection
the exact form of the shook integral doea not have to be
known. But the velocity of modification of the entropy has
to be determined. The course of the cclculatlon is followed
Card 2/3 stel? by step. In this manner formulae for the caloulation

The Scattering of LiCht in a Fermi Fluid 56-l-W56
13 followed atep by step. In this maLner for-iulae for the
calculation of the fluctuations of the distribution
function are found. Finally the formi:aa found for the
distribution of the scattered light to the angles and
frequencies is explicitly written dorn. The frequency
spectriun consists of a central part E.nd of two sharp lines.
The central part corresponds to the Doppler broadening of
the main line. There are 9 references, 7 of w:..ich are
Slavic.
ASSOCIATION: Institute for Physical Problems All USSR
(In5titut fizicheakikh problem Akademii nauk SSSR)
SUBIMITTED: July 3o, 1957
AVAILABLE: Library of Congress
Card 3/3
7z
~...................

~5-1 -37./),-
ikav T
T Yk .:uw.,r-;oi;uctor in a f'-iPh-11-'rvquenc:: ?~.,AA (_:;ver~h.-;rovo'!aik
v v,~s:!,och,-,stctno.,,1 polF..)
;.;-i1O,ACALr 'Zhurnql oksper,imontallnoy i tcor~_'.tichos~,oy fiziki, 1958,
Vol . 35 , fir 1 , pp. d6-~-275 (11;;3H)
ABTZHACT: Bardeen, Cooper and Schrieffer (;3arLiin, Kup~r, Shriffcir) L*'C--
volopel a microscopical theor,11 of sun,-,rc:onductiv!t.'- ('~+?f
In the present paper the question is investigated as to how
superconductors behave in variable wcak ficids, and a new
(not local) equation is derived, which describes the connec-
tion between current ani ficli insteal of the eauation of the
phenomenological theory by F. and G. London. Also the au-3s-
tion of the depth of penetration of a weak stat4c field intD
massive suporconductors and their lepenlence on temperaturp
is dealt with. In the pr~,sent paper the riut~iora investip--~te
the behavior of superconductors in high-fruouoncy fiel,,3 ani
derive an equation describinF this behavior. 7'h._~ parer is
subdivided into 4 sections. lihe first deals the quttinry.,-
Carj 1/2 up of an equntion for the current in surjcrcon,~!.uctoro , 1!f ii". W

A :3uDcrconductor in a Bigh-Froquency Fic14 OOV,156- 35- 1 - 37/-5,~
-1~
in dependL-nce on A(x); soction two Jpals with Pippard's
limiting case, and section tnree deals with London's doijain
(vk>A(O). In this case, only the ratio between T and &
changes) and Ci 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*-rLhe causes of disagreement
between the experimental date and the values of impedance cal-
culated by the now 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

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FUZOVICALt rspekti rigicbeskim naux, 1)5), Tal 67, wr 4. pp 743-750
(MR)
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STU:Im.k.T. m), .04 %be 7billookly -1-
"r Its% U. Stella& (Tbilisi St.%* University tacml
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bar *111" -0 -all .2 by - Duab.r of y"ag Chit-.*
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b7 floCIV.11m. in ph... tramallion. of lb * a.0 cord lgind.
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%be In conall,rallam of 1b. whl.o-
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80,04mclars is possible which or* supra-comiuctive only vith-
in a Zimilet z*mg~ of temporoturo (&ad act at all %~;4ratures
Va.." the critical at ) 3 T C "', &Ad T. Z. Irwala
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Card 4/11 1bsrmWrVs=Icx of the -praconluctive *%&%a [Pr4ohllch-model)p
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of St. Coul aab I; vwrallan Was dISCUS944 by Cb*.I' Ch-u~hsien "'I
4%1-htio

107 1 ILI LI S/030/60/000/011/005/026
s-6 o fa B021/BO59
AUTHOR: Khalatnikov, I.M., Professor
TITLE: Problems in Low-temperature Physics
PERIODICAL: Vestnik Akademli nauk SSSR, 1960, No. 11, pp~ 28-35
TEXT: Low-temperature physics includes a large number of phenomena of
which superfluidity, superconductivity, antiferromagnetism, and galvano.-
magnetic phenomena in metals are particularly emphasized. Superfluidity in
helium was discovered by P. L. Kapitsa in 1938. Temperature dependence of
the thermodynamic quantities of helium were explained by L. D. Landau by the
existence of a minimum in the energy spectrum. Fluid helium, consisting
of He4 isotopic atoms and obeying Bose statistics, exhibits the property
of superfluidity. At present, research of the properties of liquid helium
is concentrated to the properties of the liquid He3 isotope. This field is
regarded presently as the most promising area of research. The phenomenon
of superconductivity had been discovered by Kamerlingh-Onnes 50 years ago,
but has been explained only in the last few years. Superconductivity of me-
tals is distinguished not only by vanishing resistivity, but also by
extraordinary magnetic properties. The energy spectrum of superconductive
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86229
Problems in Low-temperature Physics 3/030/60/000/011/005/026
B021/BO59
metals has, among others, also been explained by the Soviet acientist
N. N. Bogolyubov on the basis of a system of Fermi electrons. The young
scientist L. P. Gor1kov, who investigated the excitation spectrum by means
of field quantum theoretical methods is also mentioned. Galvanomagnetic
properties of metals have been investigated during the last years at the
Institut fizicheskikh Problem Akademii nauk SSSR (Institute for Physical
Problems of the Academy of Sciences USSR) and at t'~_e_ iziko-tekhnicheskiy
institut Akademii nauk USSR (Institute of_Physics and Technology of the
Academy of Sciences UkrSSR). The dependence of res4stivity, heat conduc-
livity and other electrical characteristics of met;ls on magnitude and
direction of a magnetic field were the subject of 'Investigations for the
purpose of explaining the electron spectTum. The energy spectrum of the
excitation of antiferromagnetics has not been obtained so far. Achieve-
ments may be attained by co-operation of experimental and theoretical
physicists. There is I figur,3.
Card 212

j
_&V
S/056/60/039/01/19/029
B006/BO63
AUTHORS: Lifohitag Ye. N,, Khalatnikovt I._ M.
TITLE: On the Singularities of Cosmo ngigal-Solutions of the
Gravitational Equations.
"P
PERIODICAL: Zhurnal eksperimentallnoy i teoreticheskoy fiziki,
19609 Vol. 39t No- 1(7), PP- 149-157
TEXT: The usualloy applied cosmological solution of the Einstein gravi-
tational equation is based on the assumption of an entirely homogeneous
and isotropic mass distribution in space though this assumption is at
Most approximately satisfied. In the present paper, the authors wanted
to clarify as to how far the properties of the solution and, above all,
the occurrence of time singularities are connected with this assumption.
'This problem can be tackled most successfully by studying the general
properties of the solutions to gravitational equations in the neighborhood
of singularities. Theeiistence of such solutions is assumed. Two particular
classes of these solutions are given. One of them is a generalization of
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S/056/60/059/003/032/045
Boo6/Bo63
AUTHORS: Lifshits, Ye. M., Khalatnikov~ I. M.
TITLE: Singularities of the Cosmo.logical Solutions of Gravitatio-
nal Equations..kvi
PERIODICAL; Zhurnal eksperimentalinoy i teoreticheskoy fiziki, 1960,
Vol. 39, No. 3119), pp. 600-808
TEXT: The sub-classe8 of cosmological solutions of gravitational equa-
tions derived in Ref. 1 (Part I of the present paper) usually have
singularities. The question as to whether the existence of singularities
is a general property of cosmological rjolutions, irrespective of the as-
sumptions made for the distribution ef matter and the field of gravity,
has not been solved as yet. The solution of this problem is related to
the existence or non-existence of a general solution of gravitational
equations. Thus, the authors were confronted with the following problem:
Within the region of a singularity that is assumed to exist, the form
of the broadest class of solutions to gravitational equations is to be
found, and conclusions are to be drawn as to the universal character of
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88445
8/05 60/039/006/037/063
'~'O: 5-30c) Boo6yzoO
AUTHORSt Bekarovich, I. L.9 Khalatnikovj-.I--X,
TITLE: Theory of the UP tea Theraal Discontinuity on the Interface
Between Liquid Hsi and a Solid
PERIODICALs Zhurnal eksperisontallnoy i tooretiohookoy fiziki, 1960,
Vol. 39, No. 6(12), pp. 1699 - 1712
TEXT: Heat transfer between liquid He II and the surrounding solid is
accompanied by a temperature jump which in related to the complicated
temperature exchange between He II and the phonons of the solid. A
similar effect is displayed by He3 where the surface of the solid performs
small vibrations, and the moved liquid carries away a small amount of
energy. Nonetheless, a temperature jump occurs on the boundary. A
theoretical description of this effect is presented here. The authors used
liquid He3 which was in conlact with the vibrating surface of a solid. At
low temperatures, liquid He can be regarded an a Fermi fluid, and its
condition is characterized by an excitation distribution function which
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4:1~
T
3

Theory of the Kapites, Thermal Discontinuity 8/056/60/85"06/037/063
on the Interface Between Liquid He3 and a B006/BO63
Solid
an
satisfies the equation of motion 7 .1 an -aL - -~n at . I(n) (n - distribu-
t ar ap ap ar
tion functionj F, - excitation energy which is a function of n;
IN - collision integrall p - momentum). It may be assumed that all points
of the body surface oscillate in phase. Therefore, the distribution
function is only a function of the normal to the surface z. n is not equal
to 110+nV where n 0 is the equilibrium Fermi function at absolute zero;
thus, F- - &0 + f(p,pQnj(p')dp' and f(p,p') - 6t(p)/6n(p'). Spherical
coordinates, G and %, are introduced (e is the angle between p and zi
is the azimuthal angle), /4,is substituted for cos 9, and the
coordinates are measured in units of the nean free path (I - 9 0'01
with w'r-tco (r-j - oscillation frequency) one obtains cquation (8):
i4j1rF 3i1j'TF 3 irInF
+ 0 90 - I - 1 41- 2 cos~(plt . Next,
az 1+F - 7-+Fl Min 1 -+F I"
0 1
the suitable boundary conditions ate determined. When substituting
for ~(z,,a) at z-0, one obtains equation (15):1/
- -Pouz -Pou t- -~v 008~,
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88445
Theory of the Kapitea Thermal Diso3ntinuity 8/056/60/039/006/037/063
on the Interface Between Liquid He and a B006/BO63
Solid
and the condition for reads Iq (/.L-)djv- - -p u /3. The solution
f, n a 7 +~1 0 Z
to (8) is divided into two parts (proportional to u Z and ut) according to
the two terms of (15). The solution corresponding to perpendicular surface
oscillations is called the longitudinal solution, while that corresgbnaixg
to tangential surface oscillations is called the transverse solution. The
two types of solutions are discussed, and several relations are derived
for diffuse reflection in both cases. Thereupon, mirror reflection is
studied, in which case a solution is obtained through a Fourier expansion.
Finally, several formulas are presented for the thermal resistance of the
boundary, which is proportional to T,3. Academician L. D. Landqu Is
thanked for discussions. V. A. Fok is mentioned. There are I figure and
5 references: 4 Soviet and 1 US.
ASSOCIATION: Institut fizicheskikh problem Akademii nauk SSSR (Institute
of Physical Problems, Academy of Soienoes USSR)
SUBMITTED: June 13, 1960
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BEKAREWICII, I.L.j KILUATNIKOV I.M,
Phenomenological deduction of the equations of vortex motion for
He II. Zhur.ekspA teor.fiz. 40 no.3:920-925 Mr 161.
(MIRA 14-8)
1. Ins%Ltut fizicheskikh problem Akademii nauk SSSR.
(Vortex motion) (Helium)

POKROVSKIYI? V.L.; XMIATVIKOV~ I.M.
Superbarrier reflection of high-energy particles# Zhure ekspo
i teoro fiz. 40 no.6:1713-1719 Je 161. (MIRA 14:8)
1. Institut fizicheskikh problem AN SSSR.
(Particles (Nuclear physics))
",fN
al,
V

25204
S/056/61/040/006/025/031
B108/B209
AUTHORS: Lifshits, Ye. M., Sudakov, V. V., Khalatnikov, 1. M.
TITLEt Singularities of cosmological solutions of gravitation
equations. III
PERIODICALt Zhurnal eksperimentallnoy i teoreticheskoy fiziki, v- 40,
no. 6t 1961, 1847-1855
TEXT: In earlier papers (Refs. 1,2s ZhETF, a, 149, 1960; ZhETF, 12,
800, 1960), Ye. M. Lifshits and I. M. Khalatnikov studied the form of the
cosmological solution of gravitation equations near a point with time
singularity. The general solution of gravitation equations with a
fictitiotr singularity may be represented (by a proper choice of a
synchronous reference system) in a form in which the singularity is
synchronous for the entire space. Such a solution must contain eight
arbitrary solutions of the three spatial coordinates: 1) four "physically
different" functions, necessary to establish the gravitational field at
a certain initial moment, 2) one function determining the initial hyper-
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25204
S/056/61/040/006/025/031
Singularities of cosmological... B108/B209
surface in the geometrical structure, 3) three functions related to the
requirement that the conditions g 00 ' -11 goa . 0 (1) for the metric
tensor (Refs. 1,2) permit any transformation of the spatial coordinates
without involving time. The arbitrary choice of the spatial. coordinates
may be used to bring the first terms of the expansion for the m6trios
near the singularity into a form in which the spatial differential length
is given by the formula
2 6 a b 2 2 2 a 3
'dx a dx dx + (t -1) a & + 2 (t -0 a3 dx dx (5),
dl godxo' ab 33 x3 a.
where the indices a,b assume the values 112; the quantities a ab ta 3a 9a 30
are functions of all three ooorainates. These statements, together with
the results of Refs. 1 and 2 lead to the o6noluaion that the presence of
a time singularity is not a necessary property of cosmological models in
the general relativity theory, and that the general case of arbitrary
distribution of matter and gravitational field does not lead to such a
singularity. The authors thank Academioian D. L. Landau and
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252o4
3/056/61/040/006/025/031
Singularities of cosmological... B108/B209
L. P. Pitayevskiy for discussions. There are 3 Soviet-bloc references.
ASSOCIATION: Institut fizicheskikh problem Akademii nauk SSSR (Institute
of Physical Problems of the Academy of Sciences USSR)
SUBMITTEDt January 259 1961
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S/030/62/000/002/007/008
11101/11110
AUTUOR: Khalatnikov, I. M., Doctor of Physics and Mathematics
TITLE: New studies in the field of low-temperature physics
PERIODICAL: Akademiya nauk SSSR. Vestnik, no. 2, 1962, 111 - 112
T E XT :This is n report on the VIII Congress oil Low- tempera Lure Physics
held in Kiyev on October 13-20, 1961, by the Nauchnyy sovet Do fizike
nizkikh temoeratur,Otdeleniya fiziko-matematicheskikh nauk Akademii nauk
SSSR (Scientific Council of Low-temperature Physics of the Department of
Physics and Mathematics of the Academy of Sciences USSR). This Scientific
Council has been working for eight years. Tile conference was attended by
scientists of Moscow, Leningrad, Khar1kov, Kiyev, Sverdlovsk, Tbilisi, and
other places. The following papers and r3sulto are mentioned; Tunnel
passages of electrons through0a dielectric lying between superconducting
metal (Al, In, Sn, Pb) at 0.1 K. Superconducting modification of Bi, the
suDerconductivity of Bi II being discovered with a transition temperature
of'3.920K at 25,000 kg/cM2. Effect of electron scattering due to spin-orbit
interaction on Night's shift in superconductors. Experimental investigation
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S/030/62/000/002/007/008
New studies in the field of ... B101/B110
of superfluidity of demixed phases of He3_He4 solutions. Investigatio?)
of the scattering of gamma quanta and slow neutrons in Fermi fluid (He to
find the zero sound predicted by L. D. Landau. Piezomagnetic effect in
siderite monocryntzil;t antiferromagnetic resonance in IAnCO and CoCO 3' The
properties of 1114.3I-In alloy between room temperature and 1.3 K were studied
to prove the coexictence of ferromagnetiam and antiferromagnetism below
20XK- I'vIleasurements of the magnetic heat capacity of carbonatee of
transition metals between 60 and 1-50K shoived that the magnetic heat
capacity (spin waves) in MnCO 3 exceeded that of the lattice by one order of
magnitude. No spin waves were observed in FeCO 5" Theoretical study of
quantum oscillations of complex electroconductivity in perpendicular
magnetic and electric fields, and of the de Haas - van Alphen effect for
electrons in the inetal. Theoretical prediction of a new type of oscillation
of the ultrasonic absorption coefficient of metals in a magnetic field,
which had already been proved experimentally in Zn monocrystals..
Development of the thoory of cyclotron retionnneo j.n metalo. E;e. 1) e r I 1:,,e n t 0
concerning the galvanomagnetic properties of Pb showed that the Fermi
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S/030/62/COO/002/007/008
New studies in the field of ... B101/B110
level in Pb consisted of two equal parts with opposite signs. Thermo-
maUnctic and galvanomagnetic effects in InAu, lnSb, and ~,,alvanoma(',netic
effects in Al and In at low temperatures were investigated. Anisotropy
of the effective massea in Al was found by cyclotron rooonatice, and the
Fermi velocities and Lhe effective, electron masses in Sri wore measurod.
Analysis of the dimension effect of the electric resistance in metals
to ascertain the free path of electrons. Prediction for semiconductors
of a new resonance type on band carriers caused by the electric vector of
a high-frequency field at low temperatures. Spectroscopic study of the
resonance effect in wurtzite-type semiconductors at helium temDerature led
to the determination of the tensor of the effective masses. Hall effect
and magnetic resistance of Ge in strong magnetic fields at low temperatures.
Determination of the spin-spin and spin-lattice relaxation times in metal
by "spin echo". Nuclear magnetic resonance in Tl with natural and
enriched isotope content. Moessbauer effect of 23.8 kev gamma quanta on
Sn 119 nuclei. Further reports dealt with low-temT)erature research,
structure of strength, and polymorphous conversions at low temperatures.
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Or
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45
-- 4% "R N,

ABRIKOSOV, A.A., doktor fiziko-matematicheakikli nauk; K-HALATNIKOV I.M.
doktor fiziko-matematicheskikh nauk, prof.
Aca4emician Lev Davidovich Landau. Fiz.v shkole 22 no.1:2l-z7
ja-F 162. (11M 15 -.3)
(Landau., Lev Davidovich., 1908-)

AERIKOSOVv A.A., doktor fisika--mat6maticheakikh nauk, prof.' KHAIATNIWV
I doktor fiziko-matematicho5kikh naukj prof ~a
S~=etry of the world. Fiz,v shkole 22 no.5t4-13 B-0 162,
WRA l5sl2)
(Particlea (Nuelear physics)) (Symetry)

TAMK, I.Ye., akademik; ABRIKOSOV, A.A., doktor fiz.-matem.nauk;
KHALATNIKOV I.M., doktor fir.-matem.nauk
Nobel prize wi=er foi 1962. Test.AN SSSR 32 no.12:63-67 D 162.
(KERA 15,12)
(Undgu, lav Davidovicbp 1908-)
I

S/056 62/'043/'00,'z,/'O,r5/063
B 1 04X1 02
AUTHORS: Patashinskiy, A. Z., Pokrovskiy, V. L., Khalatnikov, i.
TITLE: Regge poles in nonrelativistic quantum mechanics
P-_--R!CD I CAL: Zhurnal eksperimental'noy i teoraticheskoy fiziki, v. 43,
no. 3(g), 1562, 1117-1119
'i_- Ii method of examining the position of the poles in the complex
Momentu~n *planelfor a lar(,e class of potentials was worked out. - This method
iq cloo'l-1.1y related to that previously established by V. L. Pokrov3kiy and
nikov (ZhETF, 40, 1713, 1961). The ronanulytical potential
1. i~.:. Khalat
U U, < 0 for r a is s tudied on t,',.e basis of a semi-
0.
claosical approximation to Schr6difieer's radial equation. From the
equations X,J', (xl)lj.(x.) xH(,"'(x)1II,( 11 (x), x2jal = 2niE,
/a'= 2m (E - U(~). (3)
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5/0:i6 '62/043/M/059/063
Reje Ie poles i noLrllelativis'ti c. B104YB
102
it is conclud that three series of ales exist. Tha first series is to
tVieft- of Vj~ X, ~,Fig. 1), tho second in the unpar semiplane abovo tho
il point x atymptotically approacIning the line Im -1 at U < E < 0. T h,~
0
third sorieg is missing when U 0 E < 0, but approximately symmnetric -~-Ath
h c o n d :3 o r i e u wh e n '"' > 0 . Ar, analytical potential V(r) 'aiiving
singularitles in the complex momentum plane is examined. 'tiller, --->>U0 the
Doles are-near to those values of I at which the level lir~e has two ;:.oints
of inverpion,ir V~ej/k and r (Fig. 2). There are twe. oeries of poles in
1 2
the UDP4~ s Iem1plane. The first series extends to the left and downward of
i ; ,, 1 2
the po nt q~= kr , k = 2mT.1, approaching the real axis asymptotically. Th,_
0
second s'drie6 ~is situated right. and left of the point, 9 = kr 0 where the
asymptotO,s Im(V - kr )~n/ln(n), Re(~ - kr )-In,(V - kr')/ln(n). The
0 0 0
i Position !of the poles in the case of-minU (r)< E