SCIENTIFIC ABSTRACT AGRANOVICH, V. M. - SHVARTS, A. A.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000100520017-5
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: June 5, 2000
• Sequence Number: 17
• Publication Date: December 31, 1967
• Content Type: SCIENCEAB

L26635-66
A series of such states was found in surface excitons with E 0, D 0. Fre-z
..quency values of suvface excitons were determined by the tensor of crystal
permittivity taking into account spatial dispersion. Their connection with
volume exciton frequencies was established. Orig. art has: 28 equations..
-SUB CODE: '20 SUBH DATE 04Feb65/. ORIG"REP: 005
Lcard V2

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L. 4j~j~- IT- THDo
AILL NXi B6015889 SOURCE CODE: bi[5-1-58/6i
AUTHORSs AjE!n2!Loht V. X.; Ovander, L. N.i Toshioho B. S.
OROt none
TITLEs On a theory of the nonlinear polarizability f crystals
SOURCHt Obninsk. F12iko-energaticheq~& inatitut. Doklady, FEI-25P 1965- K teorii
TOPIC TAGS: tensor, oryataly electromagnetic radiationg Hamiltonian, Green functiont
Maxwell equationp Fourier eeriesp exciton, phonon interaction, coulomb interaction,
nonlinear effect, particle interaction, charged particle
ABSTRACT: The tonsor of nonlinear polarizability of crystals 9 iji for the exciton
region of the spectrum is found by a method similar to one used earlier (V. M.
A:gmnovich and Yu. V. Konobeyev. FTTP 5~ 2524, 1963). The interaction between
charged particles of the crystal and the natural radiation field existing in the
crystal is not assumed to be weak. The ten8or of nonlinear effects is proportional to
the corresponding anharmonicity coefficients. The general formula for the tensor of
nonlinear polarizability
dip Xiv &~-(i ~d'
41 (d W 141,
4x-
together with
Um it
CarLl 2

AT6015889
fM/r
XJO a/
0 ev W;
permits the tensor of nonlinear effects to be expressed in terms of
and the tensor components The case of limitingly weak excitoxi-phohon
interaction is examined. The formula for the tensor for the excitDn- region of the
spectrum takes the form
IV
..6yeRwA,w, CYj
The obtained equations are found to be more nuitaiie than earlier ones in the vicinity
of the exoiton absorption bands as well as outside the absorption bands if the teneor
cannot be replaced by The authors thank V. L. Ginzburg and L. Ps
ij! ij-
Pitayevskiy for discussion. Orig. art. has: 38 formulas.
SUB CODEt 20/ SUM DATE: none/ ORIG REP: 013/ OM B", 004
Card 2/2 b1

ACC NKs AP6018813 SOURCE CODE: UR/0056/66/050/005/1332/1342
AUTHOR: Altranovich, V. M.; Ovander. JL. N.: Toshich, B. S. 4-1,
ORG: none
TITLE: Theory of the nonlinear polarizability of crystals
SOURCE: Zhurnal eksperimental'noy i teoreticheskoy fiziki, v. 50, no. 5, 1966, D32,
TOPIC TAGS: 13A1461- exciton Ax4oe CXY-77,4,1S 7-eoVTaA1j
00eysr'94- OR7'.1c AP0_WX'0*'j -oPr;e-
ABSTRACT: A new method is proposed for calculating the nonlinear crystal polarizabilit.
tensor cijl (kw, Ww', k"w"), which determines the third-order nonlinear optical pro-
cesses in the exciton spectral range. The main difference between the new method and
previous methods is that in determining cijl, real electromagnetic waves in a medium
are used for the states in the zeroth approximation. The properties of such waves
(dispersion law, polarization) differ significantly from those of approximate models,
such as Coulomb excitons and transverse photons. A relationship is established
between E 1 and cubic anharmonic coefficients in a normal wave system. The expressLoo
i9tained by the authors bec:omes identical to that found by other researchers
for cijl 0
if the refractive indices of all the normal waves are assumed to be close to unity
(or if the tensor tij is assumed to be a unit tensor). The new method can also be
used for calculating the nonlinear polarizablLity tensor cijl,. Orig. art. has: 38 for
mulas. ICS)
SUD.CODE:._ 20/. �UBM DATE:- 26Nov65/ ORIG REF: .014/ OTH'REF: 003/ ATD PRESS:J'0/3

MIS,
USSR,.~! ties
"Elypercom,ldec 6ystej:,,s Constructe.] in Accorl_~,~jnca idth 'L,Ihe ~Aurr -LIL)u,.-_JIIe _,qustion
or, the Y11. '1,*. 11 ~:
$ Imst of' Y~th, ',.c-, , ci Ukr :,"R
1) . . Barezanskiv
DAN Vol- 911 No 6, i,j) 1245-112.43 , 1113
Studies rings of sw:i~.ablc fwictions constructed fro,. tl,.o Stur;,-Liouville
I I
eq y' (1kt) _XY (o _6 t ~S 00) without ally Iinltatioru~; Oil the ordor of '-,I' _q13 nes 0
of q(t) -it infinit,,r, but wA.--r the~f-,sur_ption that this function is of bound.1
vur,Aion oil tho Thi.-, wis fir2t. liv A, Ya Ivzi,_,r
(Lat 'Jbor. 23 (65)) NO 1, 194-) for I(t) C(t-1-C) (u 3;00) aml V. A. LarOhk~',,'_O
in his doctoral dissertation (Tru--Iy 1,0_kov Y&A Ob-va, lol o 3, 1953). Cites
Levinson, Duke lath J. 1515, ~,'o 1, 1940 Fr:~scnted by Acal-I A. L~c-crov
27 June 53.
2_7 5'i 73

AGRANOV CH Z.S.; FOYZM. A,Ta.; IANDKOF, 11,S,, otvetetveany7 redaL-tor;
%."Swa.mm- KO, A.P., takhnicheakiy redaktor
[The application of operational methods to the solution of some
problems in mathematical physics] Primenenie operatsionnykh
metodov k reoherLiiu nekotorykh zadach mateqaticheakoi fiziki.
KharIkov, Ird-vo Miarikovskogo gos. unv. imeni A.M.GorIkogo. 1954.
53 P. (14LRA 9-.10)
(Calculus, Operational) (Mathematical physics)
.1

SUBJECT USSR/MAT#EMATICS/Differential equations CARD 1'2 PG 737
AUTHOR AGRANOVIC Z.S., MARdENKO V.A.
TITLE Determination of the potential energy with respect to the
dispersion matrix.
PERIODICAL Uspechi mat.Nauk 12, 1, 143-145 (1957)
reviewed 5/1957
Let the system of differential equations
n
Y.',~ + )~2y w v (x) Y~ _%) the asymptotic behavior of G(x, N) is described, where
3(->%) is the so-called dispersion matrix.
The authors develop a method for the determination of v(x) for given S(?~),
given 'Mk - ("\k )2 and given matrices Mk. These latter describe the
asymptotic behavior of those matrices which are formed by eigenvectors which

Uspechi mat~Nauk 12L 1, 143-145 (1957) CA.RD 2/2 PG - 737
correspond to the eigenvalue lAk. It is shown that an operator K f -
CO
n f (X) +f K(x,t)f (t)dt in exi a ting which transforms every solution z(x, X
x 2
being bounded for x -> oo, of the system Z" +*X z. - 0 c~ .1,...,n) into
Of
a solution y(x,)~-) of (i), where lim [y(x, X)-z(x,>%)] 0. Here K(x,x)
x --.> 00
f v(t)dt. It is proved that K(X,Y) satisfies the linear integral equation
2
x OD
(2) F(X+Y) + 1C(x,y) + f K(x,t)F(t+y)dt - 0,
x
+0D
where F %Iku + 1 f [Ig - S( X )] e'~ u dX
(u) XkMk e 24-
k
-00
This equation has a single solution and with the aid of the formula for
K(X,x) then v(x) can be determined.

V
Ali HOR
AgRANOVICH Z.Sj MARCHENKO V.-k.-
TV~IE The Setting Up of the Potential of the Soattering Matrix For a SystG2
of Differential Equations.
'(Vosstanovleniye potentsiala po matritse raeseyaniya dlya sistemy
differentsialinykh uravneniy -Russian)
PERIODICAL DoVady Akademii Nauk SSSR,1957,Vol 113,Nr 5,PP 951-954 (U.S.S.R.)
Received 6/1957, ' Reviewed 7/1957
ABSTRLCT The present paper deals with the inverse problem of the scattering
theory for a system of differential equations of the form
Y" + ;~2y n V Wye, 0 0 there exists
F11(t) and we have OD t F1 (t) Idt 4 oo (- EZ9 < Z). Besides
0
S(O)P - P.
In a further theorem the authors give four necessary and
sufficient conditions that a given unitary matrix S(-,,\), the
numbers 'A 240 and the Hermitean. matrices Rk are the data of
k
dispersion of a boundary value problem (1)-(2) with the
Hermitean potential V(x) which satisfies (A ):I American, 1 Engli
There are 3 references, 1 of which is Soviet oh.
PRESENTEDs October 9, 1957, by S.N.Bernshteyn, Academician
SUBMITTEDs October 9, 1957
Card 3/3

FHASE I BOOK EXiLOITATION SOV/5164
Agranovich, Zalman Samoylovich, and Vladimir Aleksandrovich Marchenko
Obx*'nay,% zadacha teorii rasseyaniya (Inverse Problem of the Scatter Theory)
Khs2kov, Izd-vo, Khar1kovskogo univ., 1960. 267 P. 4,000 copies printed.
Reap. Ed.: N.S. Landkof, Docent; Ed.: A.N. Tretlyakova; Tech. Ed.: A.S. Trofimenko.
PURPOSE: This book is intended for scientists working in the field of mathematics
and theoretical physics; it may also be useful to advanced students interested in
the spectral theory of differential equations.
COVERAGE: The book deals with one of the new problems in the spectral theory of
differential equations - the so-called inverse problem of the quantum theory
of scatter. This problem., which has its origin in theoretical physics, is,
in the simplest case,, reduced to the formation of the differential operator, based
on the asymptotic behavior of its nomed eigenfunctions at infinity. The book
contains a rigorous investigation and solution of'the above-mentioned problem.
The mathematical apparatus developed for this may also find application in other
related problems. Conventionally, problems that indicate which spectral data
Card-1/6

Inverse Problem of the Scatter Theory SOV/51641
unequivocally determine the differential operator-, and present methods for re-
ducing the operator according to these data, have beeaca" ed "inverse spectral-
analysis" problems. The following personalities are mentioned: V.A.
Ambartsumyan, V.A. Marchenko, M.G. &eyn, I.M. Gellfand, and B.M. Levitan.
There are 14 references: 10 Soviet ~.nd 4 English.
TABLE OF CONTENTS:
Preface
Introduction
PART I. BOUNDARY PROBLEM WITHOUT SINGULARITIES
3
5
Ch. I. Particular Solutions of a System Without Singularities 13
1. Preliminary information and symbols 13
2. Fundamental system of solutions with given behavior near zero 14
Card-,"~

59040
S/()44/60/000/009/010/021
C1 11 C222
AUTHORi Agranovioh, Z.S.
TITLEt On the Transfo-iii`Udn Operator Generated by a Differential Equation
of BeoQnd Order and a C9ndition in Infi
PERIODICAM Referativnyy zhurnal. Matematika, IW'y, No-9, P-73,
Abstract No.102889 Uohozapogoe.ped.in-ta, 1957, VoI.21,PP-3-8
MM tgroves the following theorem which strengthens a theorem
M Mt The author
of D.Ya.Levin on e transformation operator (R.zh.Mat, 1957, 423). Lot
(1) Y11 -V (x)y + h2y _ 0
and let hold the condition 00 xlv(x)ldxN a finite set of equations:
Card 3/5

S/057/62/032/004/001/017
Diffraction of electroma,r--netic ... B125/B108
bo= NA ; b. =_ ~L'- -i i-D(") , (21 ) -with
i%A -+- D n n
A=A0-+-IA,B,_F .7-4 AijedFj -I- I Aijk8jF1,t -4-
i i