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1)2 B~ 1 12

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H MO IEJIHX npOTH)I(EHHhlX 06hIltKTOB

PeQaltTOP E K AK ceHOBa MaKeT H A Kli cene uof

Ihmpa SJ1 CHO B HltypHaJl nOQmcaHO B ne4aTb 27 08 85 l lL~ ()P(~ r l-1 4eC KaA 1-1 MaTeMa Tl1yeC Ilt aR ilJ I-1 31-1Ka

~OPMaT 60x9016 O~ceTH aR ne4aTb Y 4 - ~3A n~CToB I I q T~pa 5 10 3aKa3 3662 6

H3QaTenbcK~H OTQen 06DeQ~HeHHoro ~HcT~TyTa RAepH~ X ~ ccneAO ft a H~H 19 85 ny6Ha MOCKOBCKOH 06n aC T~

sectI B B e ~ e H 11 a

B HaCTOflllle~ 180010 Mb 118CCM01PUM 3analY 0 nOC1poellJm KOBapIWH1shy

HbI)( KBWITOBO- fLOJl013llX pomellltil B MOl(B1JlX npOTJlli(GI1HUX O(YL8KTOB raRllC 10shy

nllrm upimSITO paCCM8rI1iB8Th B CBfl31 C rrpo6JIOMOii rrOCTpoelUlfl MOneJlei1

3JIeMe HTapHWI lBCTmJ K lIMN OTllOCATCfI HrurPMM8j) MO)le1lH Maumoe CTJYH I

BO1TlKOB MIJ 6yneM paCCM8TlJJl138TT KnaHTOBUe JJeJIJIfl13f1C1CKIH MOneJlJl JlJlJi

KOTOPWC COOTBeTCTByut1iIe MaCCHlOCKHe Y1lSD1JOHIiJi JOIIIJlelll1J HMel()1 HeTpUshy

BJllalThHOB T e 3aBHcsnnOe 01 nallaMe1poB IpynnlJ CmAM8TIim MOneJlJl KOHelshy

Ho-moprenf leCIWe pornelille bull

MOTOnb onopalopHoll TCOPlIJI nOJIll KOTopble rT03ROJLfl1OT IlJ)OKBaHTOBaTIgt

CHCTeMY B OqlOCTlIOCTH luracCHleCKOIO pemeHJIR IlruiTII COCTOJIHID I

ClIeKTp KBaJTOBhlX 4urYKTyauKll xopomo U3BeCTllhl 1 Ilac oyneT 1IHTepecoshy

BaTT W1I 014 acrreKT TfOPIUI ]orna OCHOBHOC BIDIMrume ynellIeTCFI nOCTposhy

ermil JlORalIhHOIO KOB8PlUUlTllOTO rrOJIR2- 4

I1pocTefllllegt MoneJThHl KOTOJ8fl B nOCTaTOtlloH Mepe HJlJIIOCTPlAPY8T Bce

B03lmlUlunHe oco6eHHOCTH I FIBJIjeTCR MOnOJrb )leilCTlHI18JrbHOro CKaJmpHOTO

leii3eu6eproBClltOTO nOM B lJBYMepHOM rrpOCTp8HCTHe-BpeMfIIM

(Igt (l) f ( J~middot )-IIV)1 IlJlOlltllaHTOBaHHOIO no 3aHOlIy

bull J ~Y-j t ~ I d o ) 0 I J

tr ( ~ bull I bull ( I ) bull - (- 0 ~ ( ) I ) ()

lpeDTIoJIo~HM iTO COOTBeTCTBYJOIIlee M 8CCHQeCKOe ypaBHeHue nBIDlteHHR

rJ l~ I (l] ) - 0 U1w1eeT HOTPI1D1HlJTbHOe peUiolUIc I HarrpllMep COJIHTOHHOro TlATI8

A1 ilt lt --(_t lt ) I -Z

xlTe~H ITJOTRlI~IIHlIH o6bowr 3aMeR1OT 3neCh Te~ COJIHTOH TJaKTyet~ B 1ID11JOKOM CMHCIle

sectI B B e ~ e H 11 a

B HaCTOflllle~ 180010 Mb 118CCM01PUM 3analY 0 nOC1poellJm KOBapIWH1shy

HbI)( KBWITOBO- fLOJl013llX pomellltil B MOl(B1JlX npOTJlli(GI1HUX O(YL8KTOB raRllC 10shy

nllrm upimSITO paCCM8rI1iB8Th B CBfl31 C rrpo6JIOMOii rrOCTpoelUlfl MOneJlei1

3JIeMe HTapHWI lBCTmJ K lIMN OTllOCATCfI HrurPMM8j) MO)le1lH Maumoe CTJYH I

BO1TlKOB MIJ 6yneM paCCM8TlJJl138TT KnaHTOBUe JJeJIJIfl13f1C1CKIH MOneJlJl JlJlJi

KOTOPWC COOTBeTCTByut1iIe MaCCHlOCKHe Y1lSD1JOHIiJi JOIIIJlelll1J HMel()1 HeTpUshy

BJllalThHOB T e 3aBHcsnnOe 01 nallaMe1poB IpynnlJ CmAM8TIim MOneJlJl KOHelshy

Ho-moprenf leCIWe pornelille bull

MOTOnb onopalopHoll TCOPlIJI nOJIll KOTopble rT03ROJLfl1OT IlJ)OKBaHTOBaTIgt

CHCTeMY B OqlOCTlIOCTH luracCHleCKOIO pemeHJIR IlruiTII COCTOJIHID I

ClIeKTp KBaJTOBhlX 4urYKTyauKll xopomo U3BeCTllhl 1 Ilac oyneT 1IHTepecoshy

BaTT W1I 014 acrreKT TfOPIUI ]orna OCHOBHOC BIDIMrume ynellIeTCFI nOCTposhy

ermil JlORalIhHOIO KOB8PlUUlTllOTO rrOJIR2- 4

I1pocTefllllegt MoneJThHl KOTOJ8fl B nOCTaTOtlloH Mepe HJlJIIOCTPlAPY8T Bce

B03lmlUlunHe oco6eHHOCTH I FIBJIjeTCR MOnOJrb )leilCTlHI18JrbHOro CKaJmpHOTO

leii3eu6eproBClltOTO nOM B lJBYMepHOM rrpOCTp8HCTHe-BpeMfIIM

(Igt (l) f ( J~middot )-IIV)1 IlJlOlltllaHTOBaHHOIO no 3aHOlIy

bull J ~Y-j t ~ I d o ) 0 I J

tr ( ~ bull I bull ( I ) bull - (- 0 ~ ( ) I ) ()

lpeDTIoJIo~HM iTO COOTBeTCTBYJOIIlee M 8CCHQeCKOe ypaBHeHue nBIDlteHHR

rJ l~ I (l] ) - 0 U1w1eeT HOTPI1D1HlJTbHOe peUiolUIc I HarrpllMep COJIHTOHHOro TlATI8

A1 ilt lt --(_t lt ) I -Z

xlTe~H ITJOTRlI~IIHlIH o6bowr 3aMeR1OT 3neCh Te~ COJIHTOH TJaKTyet~ B 1ID11JOKOM CMHCIle

PeweHle J ~eTCR TUlBCClflaCKOH COCTaBJUlJOIIleM nOJleBOli

lJyHKllJlI l onpeneJlRer npOCTpaHCTBelUlNe cBOilCTBa OCHOBHOro COC-

TOflHHfl CymecTByeT deCKOHe~Oe ~~nno pa~ KnaCc~eCKHX pemo~ xapaJToplI3yeMliX napBM9TTIOM TIJaJiCJIJlUill l J RMeDIIIU OnEO il TO lK9 SH8shy

leHKe 3HeprIDI I bull rne i1 j 1( LYU)l- TalUIM 06pa30M OCHOBH08 COCTOIDUlO BIIPOJKn6110 OTHOCJlTeJThHO npe06pasoBashy

HlIil TpaHCJUIlUli a KJlaCCIflOCltO(gt pewemte HapymaeT TpaHCJJUlKOHHJ1O CHMshy

MTpmo poundm lQ)YJIJ fllnOh jlUiIOUKii ypaBHelflrii JiuIepa B03MOJilHO H8pyme1fi1e

II WYnlX CaMM8rpII CBilloHlI~X C rpynnoli nBHE9IDli 3qqeKTHBHblM MeTonOM

nUJIIiJ1lffiOIlKM paCCM8TpimaTh CKCT9MH C BIlPO~9reM bull RBJIR9TCfl M9rOll K8J10shy

1IleCKlIX npe06p1iOpoundlPHn~ HlI lorOm06oB8 5-7

OCHoBnoii l1lll)l)1 1~IJTona igtorom06ona JlaJUleTCfl nepexon 1lt HOBbIM mmashyMIIWC KHM ne peMtl 11111 1M C1IJIJJ KO 10plH HMeJOTCil )lOnOJI1llTElJI1gtHlie nepeMoHiffie

nBJIIDOlIHCCfl napaMl IlBMM rpYTmu (IMMU11I1J I1x npllllIiTo HaSliBaTL KOJIJIBKshy

1aHIIIlMH Koop)JHHaTaMK tl CJly48 lpy l1ltH MlDK9IDrn KIIOMO TpaHCJIJIDltO~UlJD(

lltOo plUfHaT w B aB~ICiMOC Tll 01 ItWil1lOCKO~i c KTy8URK MO)l(HO BBeCTll TaKshy

w yrJlO BWe rrepsMemme K COOTBOTCT3YJOOIHeurol UlCTO JlopeHlJeBCKHM Bpa-

UGlliU1M nepeM8HHHe ~~ bull BBe)1eHKe KOJIJICI(TKBHIlX lOOPMH8T n03BOJIJleT peshy

~30BaTh Ha nOJIeBHX nepeM9ltHHX lleKOTOpoe TlJl9nCT8BIIJiIfI19 rpymw IIyaHK8shy

pc 4 lLnR 3TO ro C pDRTCil KHBapHaHTIill8 OTIlOCHTeJJbHO npeo6pa30 BaHHH

FgtynI1H IIyaHl8pe ~YHKIJIDI OT npDcTp81CTB9HHO-BpeMOHHJD( KOop)UUlaT

l KOJlJleKTIIBHblX lltOOp)lIDl8T (y H RBJIOHHleCKH corrpmKeHshy

HlX 1m Be1llfmH B KJIaCCIPl eC1ltOM ITp9ne1l8 ipyluuum ~ xspaKTepH3YllT no-

JIOlKeHJl e 11 o JReHTal(l11O npOTRlIWHlIOro OObeKT8 B npoCTpaHCTBe

0600weHMe JIBYMepHOM Mone~ C~HOI~ nORfl BKnD~aeT B ceOH H3y shy

~eHHe MHOIOCOJIlTOHHOrO c e opa 48 pacIIIlfPeHHa l1ICJla H3MepeHIDi rrpoc shylTpaHCTBa MHlIKOBcoro 9 IO bull rroJIei1 60JIe e CJIOJllHOh 1 c~ JIopeHUeshy

Boi1 CTPYKTypII pemoffile npod1leMbl rrepeHopMlfpOBOI I2 If T bull n

UanL naHHOH p aOO TIl COCTOHT B nocTpoeHHK B leTupe XMepHoM rrpOCTshy

paHCTBe KBa 3HIUIaCCHeCKoro rrpH~effilfl AHR ceKTopa TeopKH conepMashy

mero orum npoTIDKeHlIWt OObeKT OCHOBHOl-i 3anae~ RBJlReTCH H3yqeshy

HIIe B03MOXHOCTH pacCMOTpeHKR ne~pMKPOa8HHllX ( cqepKqeCKH HeCI~eTshy

lil HllX ) OObeKTOB B leTup9XMepHoM rrpOCTp aHCTBe-BpeMeRlJ

fuaH H8illerO 3iOyeHliil CJIenYJOllllR B sect 2 omlcuaaeTCR M8TOll IUlHOH1shy

tteClillX rrpeoop a30Erumi HE borom060Ba lI)IR rpymm ITYaHKaje B sect 3 peshy

waeTCR sanal8 0 il O llfl I-IHBapHBlITHUX qJyHKIUtiI ~(L ) B le TupeuroXMOp shy

HOM rrpoCTpaHCTBC ( ( = middot1) i3 sect 4 B KBa3HKJIaCClfleCKOM rrpl6JrDemm

CrpOIlTCfl KOBapvaHTlioe JlOY-aJIbHOe nOJIe JIJIR MoneID ITpOTroKeHHoro 06beKTa

YlTOnl PI HUBOr IT) BnlHII UDle-ULI sect 5)

l

sect 2 Ilp eo6pasoBamlo HH EoroJIJ06oBa

B STOM pasneJIe MIJ paCCMOTpIDiI nonxon K pemeHlflO 3analH KB3HTOBashy

HRR rrOHR B OKpBCTHOCTH KJlaCCH~ecKoro pemeHKR C TIOMO~~ MeTOna KaHOshy

lmleCKHX rrpeo6paSOBElHldt H H EoroJl1060Ba BUIJeJT9lme KO1leKTJlBHIIX KOshy

opIHHaT n03BOJlReT nopenncaTlgt KCXOJlHlle ypaBHeHRil lepe3 nepeMellHue RHshy

BapH8HTHbl9 OTHOCHTeJllgtHO npe06pa30BllIiKf1 rpyrrIJ] CllMMerpRH It CTPOro

Yl9CTL COOTBeTCTBYJOutI9 38KOHbI COXpaHeHl1R B JOOC50M nOpR)tKC l eOplH BO~gtshy

MYIIeHlfR TauaR npouenypa YJFe B HYJIe130M nOpfllIRe TeOplrn BO 3MymeHru1

yltUJTllBa9T H9TpHBli8lThHYJO CrpyKTYJlY peweHHR CIlfI38HJljO co cnOHTaJIIIllM

HapyruelfHeM OID1MeTpl1Jl

HaJmUe B CHCTpoundJMe npOrf11tCHIlOro OOM I(T8 OOR3areJTbllO npHBOIUIl I

HapywelllOO TpaHCIUIIrOHHOH H JlopeHlleooii CaMMeTpl1i1 TO ooycJlODJIellO TeM

ITO B JUI8cclPlecKOiI MexazrnKe MarOpH8JThHOi TOUltH OOH3aTenJHO CJlenYCT

y-Ka3aTlgt B K81ltoki TOUte ITpOCTpaHCTBa II C I(Bl()ji CKopocn1O JIBI1liBTCR laCshy

TKl(a ECJm rrpoTfIlI(eHHhtii 06b9J1 crpeplfleCIJI HeCllMMelpI1l9H TO llOllO1lH1shy

reJlbHO CJIenyeT YKa3aTb ero 01l19J1r8UR1O B lI]10CTpaHCTBe

IIepelineM KAicCMOTpelUfJO rJxgtlUympOBlltH KOBapHBHTHoro aHaJI01a M9shy

Tona Eoromo60Ba Ha npHMepe nOJIeBoi1 MOlleJrn CaMoneiiCTBYJOI1ero CI(8]RJr-

Horo nOM c--t) B ( - MepHOM npOCTPaHCTIl8

Bu6epeM 1larpaHRaaH eopIDf B cpo~e

I( lA -= - J lt-~ ) Lmiddot ( ~ I)

r ne rJ = Jt bull = D I d - I ll C (W -CKaJlJJpHaRI ~ -

IPYHKl(HR orpaHWleHHM cIDI3y llonYCTlIM ITO cymccrByeT ReTplfBllaJILHOO

pemeHl19 JI~ ()) ( He OORSaT8JThHO CTaTllleCRoe) C KOHellloll 3Heprliel1

J~aCCHqeCKOrO ypaBHeHRR A~emlR

I - ( - i-~ t r ( () ~ 0 (2 2 amp

npraquo K8HOilllfJCKOM KBaHTOBaHIDl cPY1i~ IX) C1aJIOBHTCR onepashy

TopH03Hawoil CIUlUIpHoi JlOJltalIbHOn nOJleBOJt dlY1UUIKel YJlOBlIeTBOpmlUIol

ypaJ3HeH1flO ( 2 ) 1 ltaH01UfleCKKM tOMM-yTauHOHHHM COOTTIOllleHIDlM

1 1 l [J J i f~) - ~ i A 7

1= 0 (23 )$ I c) ~ (~o)

3neCh Cf - pOpMamHIDi napaMeTp TeOpKH B03MYll1eillili bull

~

TeopHH OrrpeDCJIeHHaR JIarpaOOaHOM (2 1) 0 tl9BHRO mmapRaHTHa

OTHOCBTcmHO rrpo06pa30Bamm rpyrrrnl IIYBJiKape lTO o 3 HaWeT bull lTO BllA

ypanlleHlfil (n H CooTHowelUlM ( 23) He M9liffeTCR 1Iplf rrpe06pa30BlHlffiX

nOJIR

T ~ ~ i -l ) L -1 bull 1 J I J ) ( v I K ( N4)~ 1 I L = +( X I 1ltmiddotl v -==

reHepaTOpaMll OTRX rrpeo6pa30aaHHil RBJIRlOTCR onepaTopbl

v I I middot I bull l J J )j C - J t L - )JlI) ~ l ~ ~ ) r U (~ Ii J

_ - L ( u

I I C ~ ~) ( -= - ) J

I J l L l ~ J=

- (25)1 I I ) I f ~ ) J f

1 J middot Z J j

J

nOCTPOeHHbl9 lIO TeopeMe HeTOp H3 (2I)

KnaCCi1leCKOe pelUelUfe ypaIlH9Hldi (2 2 ) B006mo roBOPiI HellRBapUshy

aJlTHO OTHOCllTeJIbHO npc06p a30Brumi (21) Ii cIH3lfleCKaR CHCT8Ma ORa3Hshy

BUSTCR Bupo~eHHo~ TpYnHOCTK CBR3aHHHe C ~eM B~~eBRfl B

CHCTeMe CHIDllaJOTCfl 8CM BUllomUTb npeo6pa30BaIDe BoroJl06oBa K HOshy

BUM nepeMeHHhIM

ITYCTb apmTOBli Ol1ep aTopll 1-13 MHO~e(rBa 5 1Pl J 1 bullbull 1 YDOBJIeT-

BOpmoT COOTHOIlJeIUUlM aJlrc6pu ITyaHKape I

1 10 0) 1- 0 [ l) II I - J ( 1

~ rI urLo I r ~ j ) - - lor id~ I

i 1 ~ 1 - I t ~ -- (t f middot1 L 1 I I I ~ j - l ltJI tmiddot I ~ - ~ 7 1_ bull 1 v I 7 j J J i I J ~

PaCCMOTpHM rrODCTaHOBKY

On-) = ~lS())) jJ i ~pl t lts~lx) l til-f) ( 2 6)

rne t lt -lllfC]lOBHe nepSMeHHIl8 IiHTerpepoBClHIDl a orrepaTopno 3HatJHHa

i[lYH~ C (1) fIBJIJlj)rCfi tlJYH~ ti=l MJ fi t bull IIpeIJJl0JI8rae1cJI

iTO BTOPIflliO KBaJ-ITOBDFIHClC 110ne i Ll) ]OMMYTHpyeT C onopaTOprum 113

aJIreOpli P a rrpoClP8HCTBO rrpCDCT8DJeHlUI rrOJIJ C(~) HBiLIleTCR 1Tp1lshy

MIlM npDM3BonelliHlM npoCTprulC IB ITpenCTaMeami rurre6pH P If rrOJIJ qLX)

ITepeMellHhle C ltl) OIlJ)eneJIeHH CBOHCTBOM

LJ ( - ) 4- bull I

~~ h t~ t- l L lor ~ 1- ( tr r l j

r e ~~~ 1-0 (- amp- - ~~ ( 2 7))

~ - JI ~ iL~) ( ) f ttf v shy yOlopoe r apaHTHpyeT COBMeCTHOC1h npe0 6pn30BaHlUI (~ 7) C Tjl8JICT1loprlttshy

llJfOHIillMH CBol1CTBaMH nOAA qgt( x ) _

IIoMe BbIllOJTHeHlU 3aMeHbI ( 26) ( 27) onopa T0lgtu ) bull I~I r v C1ashy

llOBilTCR reuepaTOpaMM rrpocrp8HcTueHHo- DlJeMeHlillx IlpI)06Ja~OBam[li OTOlKshy

neCTBJlCHH8 3TgtlX orrepaTopoB C DblpaKC lmHmiddot~ 1 COOTIleICTIJyY1Uij1X r eH9[JaTopoB

(2 5) nocTpoellliillC no rroJllO lJLl ) C nOMOll1hlO TeoperllJ leTep lae T one shy

paTOpHIle CBSl3H KOTopue 11 06eCrrelJffiaOT COXpaJlCHJ1e amp101lt1 H93llillCJLUIX

nep9MeHlillX llO 11 IlOCJIe npeo6pa 30BaHJl[R ( 2 6 ) II Clffi311 paCCMrlTpgtIB8JilTCR

Ha ReMTope COC1OflHlllil )~) M ID-leJOT mUI

bull j shy

) 0 I -- C iI M ) - l L r - [ l raquo) J l r - [ [ - I 4 _ ~ I bull I y- I - bull (2 8) I

ITpe0 6pa30B8JlIIe (2 6 ) C YCJIonPlfMJl c Efl3eJi (~o C ) Jo ]OMMYTaI(J10HIl1lMl1

COO THoweH1HIMVI DJIR nOM C x ) bull neperrncaHHbJM B HOBUX nepeMe HHblx pound -t)

bull ~ ) ~ j ) f ) ~ JL -Su h~ J - I cgt (2 9)

H83UBaeTCil IltaHOlUflleCKHM rrpe OOpS30BallliCM IJoroJT1OCio Ba DJIjl pPyntlH lIYaHlltashy

pc1 1 n03BOJIRCf fi lUlHOM BVIDe peaJlJl30B8Th np0)1CTaBJIelUf8 lTOti rpymrn

JJnR TOlO 1m6b1 HDHUM 0 6pa30M BHITOmUfTb npeoops 30Bamre BaroJTI(-OBa CJJc nyeT IlIll1TH I1lIBaplIaHTHHe nepeMelllible ( J ) VI rrpoK3se CTK 3aMeshy

By nOlJeMeHHJiX B COOTIlOlUeHl1JlX ( 0) ( 9) lTO VI 6YJ16T CJ1eJI8HO B sect 3

II sect 1 COOTBllTC TIJeHIO

~ J 1 0ClpoeHliu P11lllapHaJfTIIIIX nepeMOIU11IX

$lUUUeM c VlcTeMY YPaBlIOHlHI ( ~ ) onpeneJlR1OOllofx iJJyHKUKJol C J)

B IHrMHllTeJHMaJIbHO~i 11-OpMe -

1 ~

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AMee n TOM pa3J1eJre H8M 0 YDeT YllOOHO nOJIOJKlllTlgt I) 1

Cymec TBOBaHHe pelllemrn ypaBHeFlliH (3 I) H FIX mgtmm BlUl 3aBHClIT 0 T

Budopa KOHKpeTHoro rrpe~cTaaneFllilI anredpu rpyrrnu llyaHKape jO B Tepshy

MHHax KaHOmrqeCKFlX orrepaTopoB ( y p I 0 Po ) Budop lKe rrpencTaaneshy

IDlI orrpe~eIDeTClI lM3FIleCKIDIIlI CO 0 clpalKeFlliHMH bull l1epeMeHHHs S (X)

FlMeIDT CMHC~ ododmeHHHx KBaHTOBHX Koop~aT KOTopue B COCTOJIHHH rroshy

KOlI od~eKTa rrepexo~JlT B ~CCHieCKOM rrpen~e B rrpocTpaRCTBeHHO-Bpeshy

MeHHlle KOopmmaTu rrpoCTpaHCTBa MmlliOBCKOro 2- bull OTMeTflM lTO t gt

~O~ dUTb de3pa3MepHHMH Be~HBMH TaR RaK rrpeodpa30BaHHe ( 2 6)

He co~epJKHT lliC~OBOro pa3MspHoro rrapaM9Tpa IIpH 3TlIX ~orrO~Te~HHX

ifJH 3HlSCKFlX rrpenrrO~OlKelmRX ypaBHeFlliJI (3 I ) rrO~OCTbID orrpene~T d (cIshy-pa3MepHocTb rrpoCTPaHCTBa-BPSM8HFl ) H93aBHCRMllX HHBaPllaRTHliX OTHOCHshy

TenHO rrpeodpa30B8IUlli rpymm n yrurnape rrepeMSIDillX S-lt RaK lPyHKIUm aprYMeHToB X ~ bull J bull () bull tJ B WHRILHRX S rrpenrro~araeTClI orrpe~e~eHHoe yrropRUOleHHe H8JltOMMYTHPynttHX rrap orrepaTopOB Ii bull ~ H

I () () - HarrpgtIMep ( II Jj c D J)

I L~ I l l

PaCCMOTpgtIM Terrspb rrpOCTei1wee rrpenCTaBJISIDe aJIIsdpu F lepe3 Kashy

HOHWleCKH8 orrepaTOpu I il KOTOpoe peaIDl3ye TcH B rrpOCTpaHCTBe

QJyHKlUfi1 1 ) H 3MaIIO C rrOMOIllMl Coo TBolDemrli

p~== r ( 1v1r = ((~ J P - l( G Pf) (32)

Lp l~ ( shyI I ) L (1

B rrpOCTpaHCTBenBYX H3M8peHlll1 ( j = 2) ypaBHeFlliH (31) B rrpeJ]shy

CT~eHHH (32) gtlMeIDT CBOFlM pellleFllieM ~Ba ~HejiHllX rro 2 orrepaTopHo-

3HalHHX pemeHKH

toUJ~2~1 +f~Ir T-Y))~ JI r~ (33)

~ _ -ltv ) t~l(lf= cl (X7~r -= u ~ L v r flo1

B BHpaJKeHm ( 3 3 ) oIIepaTop JIOpeHIJeBCKIX BpameHJ-fi1 OL c ~ a orrepashy

TOp j)= lIc l 11 P pr(1 ~) gtlMSeT TaIDle lKe KOMMYTamlOHHue CBol-icTBa C

anre6poJ C2 IlTO H ohepaTOp pacTJIlKeHIDi

I1HBapHaHTHUe rrepeMeHllile S - (v-G = 0 I) ItOMMyrnpylOT MaJKny COshy

dOll FI rrOJIHOCTbID y~OBJIeTBOpHIDT BceM TpedOBaHllHMHeodxo)lHMHM ~ HCshy

IIOn30BaHHff 3THX ifurmami1 RaK apryMeHToB B rrpaBofI laCTH rrpeodpa30BaIllilI

(26) B nByMepHllX MO~eJIRX OrraCliBaIDmKX KBaHTOBOe peIDTllBHCTcKoe nBHshy

llleFllie OlJHoro rrpoTJIlKeHHoro od~eKTa2 4

KoMMyrHPyromne KOBapHaHTHe Koop~HaTu qrBHp8lKeHHl1e lSpe3 orrepa-

TOpH H3 aJIIedpH t(f2 ) D 1 6

l-iL ~Cl_~J il(~ - 2 D M ~ 2 L Me 1- M2 J j

i -=1 r pi l i if I ~ 2 lD tj 2 J -2 LMOL Mo J I

(34)

1v)=P -P~ C l )

JIBiIRKlTCR aHaJlorBMI1 KOopmmaT fu IOToHa--BITHepa B ~YMepHOM iIpOCTPaH-

CTBe

OleBHJHO lTO B rrpoC TpaHCTBe d raquo 2 H3Mep eHllM cywecTByeT Tonshy

KO OIHO JIlIHelHo e rro X pelliorme (31) Sf2) = 2~~j) 1I03Toshy

MY B 06mSM cnyqae rrpelLCTaBJI8flHe (32) HerrpIDoIlRO II)IR OIIHCaHHH peJlRshy

THBHCTCKOro IIpOTHlKeIDloro Od1eKTal1 CJI8Iye T paclllFlpHT1 KO lqmrypaIJHOHshy

Hoe rrpoCTPaBC TBO rrpe~CT~ermlI ~OrrOrrHffB ero YTJIOBHMH rrepeMeHHYMH

OlLHaKO eCJIB rrpoTHlKeHHilll od~eKT 06~aJLaeT CBO~CTBOM c~p~eCKOH

CI1MMeTplm TO OKa3UBaeTClI ~OCTaTOiHO nOCTpoHTb ~e IDmapHaHTHllX KOshy

opIJffiaTu BpeMeHHyIO H paJJlfanHyro

Sc()c) = (ctr~)rpr) l~ x)l coo LJlql() (35)

~TO HaxO~TCR B COOTBeTCTBllH C pe3YJIbTaTaMll pa60T9

KaK j~e OTMelaJIOCb Bume paCCMOTpeHH8 dOJIee od~ero CJIYiaJI MOshy

ue1IH cifgtepWleCKI1 HeCHMMe TpHlHoro od~eKTa TpedyeT rrepexoua K dOJIse

C~CraquoUUlM npelLCT~eH1UlM lJJm OrmCaHMH CTaTHleCKoro ~eiJoPMrrpOBaHHOrO

06beKra MH BH6epeM rrpe~CT~8ID8 anredpu lIyaHKape 13 iPJPMe

J C l e lL r I f f11S P = Igt IV) = (i f - ~I ) shyJ ) ) ( (J 1)

)-) K1 -- (C( pd - ~r~ ~ ~ - c - J

1) fj =t ~ )(36) j ~ - J

1 r~ [S ) f ~1 Li ( y) 7 ( - ( r 1 1= (C Coil S~

~ro npSuCT8BJI8HH8 peam3yeTcH B rrpoC Tp aHCTBe IWH1QWlli If yJ ~ r~e X - yrJill rrpoCTpaIlCTBCHHHX BpamellmL TIo ifJH3H1eCKOMY CMliCJIy KO[shy

JIeKTIlBHlle KOOPlUrnaTH r HI ol1IJe~eJIRlOT rrMOlKefDlle ~8txlpMllpOBaHHOshyr o od~eKTa 1lt1 ero opHeraquoTaIJJm B rrpo CTpaHCTB MaTp~ vl lre( YJ B (35 )

3aJLaIDT BHn r eHepaTopoB rpymru Bpame~ S t I l) pyt

~ c (l) (( ~) OleBHlUlO YOBJIeTBOPReT ClCr eMe

ypaBHermii (31) Hai1l1eM Te n epb TJlH IlPyrRX HHB8PHaHTHWC peIDeHRH cncshyTeMil yenPaBHeHHil (3 I) IIBJIHI[lllHXC$l JIHHeiiHliMll no -t H RIlHO 3aBffCRlItltX

0 1 yrJIOBbIX nepeMeHHIDC llruJ 3TO IleJIJ MbI paCCMOTpHM CHa~ ypaBHeHHH

orrpe~e~e TpaHC~OH~ HHBapnaHTHOCTb KCROMHX pemeHR~

J l1 () c ~ (T S (37)

0611HM perueHKeM ypaalieHIDl (37) OqeBlmHO HBJIReTCSl ltPYtultmm ~ u I( J I ) y S) == c (I 1 ) J ~ ) C YleTOM IIOryq9HHOIO pemsmm

CMCTeMa ypaTmelllHl rapaHTIIPYfOIllWl mrnafiHaHTHOCTlgt pemeHlUl OT80ClIlTe7IbHO

rrpoCTp aHCTBeHHhIX Bpa1I9HHii BJJIJlR)tllr C19I(ylOlllIDgtl 06pa30M

- (t lt r amp _~ Ij ~ L~ i 1 I c ) SJ~LL ) 1 I 11 ip rJ r ~P p ~ (18)

JlilHeilHhle no _t peweHKc1 yprumelDfH (3l ) HMelOT IDlll

So (J J ( fl f ~) = I (J) j(J( l bull J ~)pe ) U t ) - MaTpoUB TPeXMePHHX 13P8U(OHlol11 3am1CalUlaJT illllTpl1Mep B napaMeTpif31lltIDl ~JIe-pa

I i

U ) - l

( )1 ) ~ ~ll I t)

l~ UIIJr 1 1 dk

( P)middot -

( P) pound y~ p ) ~

j l ( J II 1J I I) ( l II) ) ) j ) ) 1( P) a lljJ) Fr jJ) I r)) 111 11 ) - npol~ 3BOJIbHble PYJiRltlm SIBJIftlOOUI8Cf CIUlshy

nfYpflMH OTIlOCHTeJIhHO npoCTVaIiCTBeHIiliX BpamellJiJi nepeMeHRl1X p

~ 1 t r 11 OTIICllCJl1IM 113 p8Ul8HM OCTaBIDKXCR

ypaBHeHIlli CHCTeMIi (3 I) KOToplie BupalKaKlT c060H c BOkicTBO HmapHaHTshyHOC TH IfCROMliX ltWH~I OTHOCIITeJIbHO [ZCTO JlOpeaneBClltJ1X Bpauterurlt )

t it pJs ~ r tl i f 12 F i- pJY ld f _

( rIt ) PtI ( 11 )l r () rf-f~fjij ~ (39

= LaC 1 T (1 ~L 1 i) L I )1( 1 J( J11 Jp ~

TIOCJIe nOllCTaHOBKPI B ypaBHeHIHl (39) pemeHlUi (38) 1I0JIyltmM ypaB-

HeHHH Ha HeH3BeCTHJle JiYHKl(KJI ~ L ZF U ~ Hal1neM HX peweHH8

iz~ l-I (Ill I ll( P) -I - _ p - =- Ili r f )

T8KHM 06pa30M MH n ORa3aJrJt ~TO B IpellCTarureHID (36) mmapH8BTshylWMH OTHOCHT8J1bllO npeo6pa30Ba~ rpynnh IlyaHK8pe (3 I) P9JIJITlrIBIICTCll1shyMIl ROOpItHHa TaMll JIBJtIllOTCH nepeM9HHlle BIfJJB

raquo

Scmiddot

p o) = (1 rJl c () ) = A) j) X t ) (31u) J

eP) r f n fgt n oS rlXdt) =- [( X ri)k _ (L rq -g 1 ik r lle -- f-r p j

LlJklP) = (a Jk -T p~ rgt( _ ) M Mt ~h r )

HanOMRHM ITO no 111lBalHaHTHOCrM1 n epeMeHHlLX (3 ro) nOllpa3YMoshy

BaeTCR CJI8~ee CBOtlCTnO nycTb T(l = fJl ) ( 1 c1 [raquo 1-1 Lf = c~ (L ~f) eCTb YHHTapHble onepaTopu TpaHCJImm0 H JlOpeHUeBcIGJX Bpamemrn COO 1shy

BeTCTB9HHO TOrna

U T --ltgt) T Umiddot L -= S(I(4~)( fa)) i() tl lJ R LL)

OlemIJrfIO 110

LS degC)J S ( )c ) ]=Ugt (3 1I )

TaR KaK S~ lt

(x) 6eSpa3MepHl1

KOMMYT8UHOHlrue COOTHomellIDl Meany S ~Y) HMeJOT BHn

l c 0) l tI~~-J1 =- c ~fS~_ P Ilaquo l~~5) ( 3 L 7 (fl-r Pj

TrurnM o6pasoM B rrpecTaBJI81ID1 anre6pu r8liepaTopoB rpymru TIyaushyKape 3aAaHHOM COOTHOWeHHRMI1 (3 6) cymecTByeT 4 KHBapHaHTHUe ve~~-

1rnWCTCKlW KOo]1JlHHaTIi ~(( 2 ) (3 IO ) AAHeiltlHl1e no t ll IDIIeJOmHe

MellnY eo60M KOMMYTattHOHHhle COOTHomemm (3 II) ReKoMMYTaIyenBHOCTb

BeJmllJfJ l 4U) (3 TI) orpatlHllffiaeT B031JlOlKHOCTh IIOCT]XlSHo$l pery-

JISJpHoi TeOplrn B03Mymelllfi no J lIlUi nOJIR 0(X) (2 6) TI03TOMY B

CJIenllUleM p a3llOJle Te MlJ zCIloJlbyeM nepCtvleHHll8 IJ1IR lJOCTshyS- (2) poeHHH UOJUI B Moneml CTamqeCKoro ]J9cJxlpmpOBalUlOIO 06b9KTa Bce Beshy

JmtUrnbi eoprul paCC~mTpltBamplTCR TOJIhKO B lByx nepBux fIeI1C~e3amplnnrr noshy

pJInK8X IlX pa3JI01leHIDI B IM no napaM8 -r1Y 17 (ItIm lleROTOpoii CTeneHR

J ) ilepSMeHH18 71 (3 10) JllIJI1IM o6pa30M Bup~alOTCJ tIepea reHepa-

TOphi lpyYlIlH PI L~ fr )

reHcparop paCTRllteHKi1 j) v bull i I I

iC ~ =- L 112 i ] 111

I)

q = _L ~k ii~Jk T Do ~ ~

~ ~

LV t- W-) p M r ue ~L -_ L T CC Ik P I

Vd1 S

3TH ~eTHpeXMepHHe KOOp~TU ~TCH aHanoroM KOOp~T HbDTOHashyBKrHepa B ~eT~eXMepHOM rrpoCTp8HCTBe EnH HKX BUDo~eHH COOTHomeHKH

L l~ rt( J I -0 0 ) L l1 r pJ 1~ - ~~

B 3aRJIJOleHl1e SToro pa3lleJIa MIl paCCMOTpIDJ C~ oCimIDi CJIYiaH MOshylle~ HepaBHOMepHo llBHEyme rocR ~eqopMKpOBaHHoro oCi~eKTa

~ STOro BuCiepeM rrpellCTaBH8HHe rpynnH ITYaHKape lle ttcTB~ee B

MaKCHMarrbHO pacIDHPeHHoM ICOHqiHrypauHOHHOM rrpoCTpaHCTBe napaMeTpoB

rpyrrrru I ( L f 0) ~

f I ( V 4 ltv (3 12 )I ~ i r M = j 1 ( pi Sl )~ -tshy

rlle [ r () LI h LGj rv LC r J 0 r J = L fl t (l~)( r j)

[ S( ) sf J ~ ( fj fS J1 -f IY ))1 VsJJ

B STOM rrpellCTaMBHIDI iPYlnuurn

AgtLl) () ~ ) V (I))r ( ()Pl )middot lt 1 (3 13)

oCipa3yroT TIM M HaCiop mrnapHaHTHRX peweHJtii ypaBHC~ (3 I) B Bupashylte HIDI (3 13) t~ C-) een MaTpHua npco6pa30BaHIiH JIopeI-n18 ~CKOMye peJIRTlmllCTClrne Koopmrn3ThI BIgt Ci epeM B BlUle

)S ( J ) = II I _ fl 1 ~ ) 11 ( 3 14 )

ITepeMeHHHe (3 14) o6Jla)l8JOT cBOilCTB8MH

LJ T C (X) Tt i L1 pound -t

-= S( _1 J ) 80gt

10

rlle ~r

-= it II(()] II

R LSr(~)) SJ(r) J = j [(lj)r1jJ) J_ UIf)(f Y IJ

MTaK HaMH nOKa3aHO ITO C nOMomom BuCiopa pa3~ux rrpellCTaaneshyHHH anreCipu ITyaHKape lepe3 KaHOHHleCKHe KOOpllHHaTU (32 ) (36) (312) MorYT CiUTb nocTpoeHN ouepaTopH03HalHHe fiHBapHaHTHUe nepeMeHshyHUe C oX O- (33) (35) (310) (314) 3TH ltpyHKIlID BXOJfjT KaK

apryMeHTU B rrpaByro laCTb rrpeoCipa30BaHHR (16)

B c~euyromeM naparpaWe MIl Bocno~3yeMcR pa3BHTliM B sect 2 B

qoPM~~noM ~ nocTpoeHMR TeopHH B03MYmeliHH B oKpecTHOcTH ~aCCHshyleCKoro pellle ImR XapaKTepH3YlJl11ero CTaTliJ1lec KIrl lleqopMHpOBaHHlill rrposhyTRlIIeffilm oCi~eKT

sect 4 3aMeHa nepeMeHHux

BepHeMCR K nOCTpoel-Urn B MOll8Jrn (21) nOM cfJ ( t) bull rrpOKBaHshy

TOBaHHOrO C nOMOmhm KaHO~eCKKX KOMMYTauHOHHUX CooTHollleHHM (23) TpYllHOCTH CBR3aHHUe C pa3lle~eImeM onepaTopoB R nOM 0rx) a TaKlKe HeKOMMYTaTRBHOCTbm C - (2) (3 II) lleJIaJOT 3aKOHHllM UOIiaK peshyllieHHR KHllih B KBa3H~aCCHleCKOM rrpH~eHHH

(4 1)ocs) = ~laquo) Vf q L Cs) ~ 0(d)t-

3lleCb 0 (~) COlleplKHT oCTaTolHl1i1 ~eH paMOlKeHMR nOJiR C1JCS) H Heshy

onpeue~eHHOCTb OCiyc~OMeHHy1O npoCiJeMoll ynopRllOleHMR onepa1opoB Clt KaK BI1llHO H3 llaJIbHeilIlJero B ITpHCiJIIDKeHHH (4 I) nepeMeHl-ilie MOlKHO pac-CMaTpHBaTb KaK C -llic~a a BUp1lleIDIR (28) (29) orrpell8JIIDJllU1e CBR3H H KOMMyTauHoHHHe COOTHomeHKH llOCTaTOlHO C~TaTb orrepaTOpHliMR COOTHOmeHRIDm

PaCCMOTpHM 38MeHY nepeMeHHblX B ypaBHeIDIRX lUllIlKeaaa KOTopue B oCiDleM BRlle llMem fllopMy

w llIJgt Cj) - U(Q)) ( f) l X)) 14J gt= 0 (42)

BoCIT0JU30BaBIlIKCh RlIIillIM lJH]lOM nepeM811HllX C ( 3 12 ) H cIoPMY~8MR

II

3

-lt ) APd c j

( [) 1 J)

) A (

HM80M j L J shy

)(4 )I I I 4 --) bullbull L UJ I~ )

~j ~ (4 3)

llIlCJ iL - nepB~l-i I1IeH B pa3JIOllteHlfR

s )~l co ~ ( -0- V I ~ I 1 ( ~1 L ( ( d

~ middot1

( [Ii i = U B clUJ) BlIllOm 8ID1R yCJloJmii CBR 311 CM liIDPie ) TaKHM 0 6pa 30M

nonyqaeM ITO ypaRHeHI1Jl IIBIDK8Hlltf11 B HYJle1l0M 11 nepOOM nOPMRO oa3JIOllleshy 1

IIlHi no D HOBblX n epSMOH1lUX 11j ilUiHMl1OT Dlfn

1

I

I L I (1 L (( L ) ( (44)L

j (4 5 )lJ ((1 l bull ( ur middot )1 t

iteJlJHegtiHOo y paJ3H0JllIe (44 ) IlpencT8BJUIeT codol KJIaCCI1eCKoe ypaBlletme

nB1U8HlIH COOTSOTCTBYOlueo MO)JeJH ( l ) 0110 no npeJIJlOJ[OlKeHIfIO MeeT

HeTpHBlfaJID HOe peOJllrne 1 (t ) xapAKrepI1 3YXlIllec CTallllCClillii Jl(shy

~OPMHllOBaHHWi OOheKT i3 TpeoyeMoM nj ll1(IJIWIWHHI1 Yl)aBHBlllIe (45) onJl8Jleshy

J1ReT BTOPllUlO KBaHTOBaJlHoe n ore n i I )

TIepei-inUM TeneJb K Rli110JlY TPX oJJ aHl1PHHii K IOTOPHM nplHlOlll1T

lIaJTOlgtlCltI1P YCJJOBlIP CBR311 ( i) Ha nolll q J) OTM P THM ITO KOBAlI11shy

aJITlIOCTb nonxona ooucneI1Ba8T rrpaalVTMIJjO ~laBHCJlMOC r h iOHCIaHT JlBIIJlte shy~HHH 01 JIlIHeliHoil 11 yrJlOBO ffOpOc nd1 nO ~lTOMY yCJlOHlIR CnRal1

IJ8CCMO TPJIM Hrl Atlno C()CTOIlHHJI coo rHuTC InYlI1li1 1I0 KOlweMYCJl OOmiddotH KlY

~~ ( bull l )

c )H Ij n i 1 I () ( 6)

~ )l i )1 rT ) 1) 111

jfl1 COOTIOUlelllR I ypan BlIUlR (44 ) Ilol11(CJ11JYJOT jO ~~i(lJ1W1e IlTU ra3ll0JWHlUI

orrcpAToF3 ~

12

M ~ -ll l U 1 (1 c -= t x ( (J ((L ) Mi - gt

AHaJI01l-flJIO 13 CBR3efi Clt) C~1 ( r1 noJIYlKM COOTlle[CT I VL l

BSHHO YCIOH1f

~ I ~ )CPl XJ _ 0II -_ ( lB )3t TA gt

JCD~ Q Cshy~d) d X 1 -~ ) (4 ttj)

~ I ~ III( l (X JJ - J) ) G-I ~ = D I u ) x ( 1 ( u ) I L

ITPU)JCT8BI1M IToJIe ([II C ) R13Jrmomeecp lBWeHveM (4 5 ) H Blfne Pamp3JlomiddotshyteHJUl no nOJllioll CHCTeMe pem8H1f~ YP8BHSHIfl

J f f )- ) oJ U ((j)~ ) I = it) t t )

(4 9)~ C~lt) fJA

(C) ( (() = ~ltr

YCJWBI1H (4 8a) (4 8d) flCIltJ1X)laroT fl p a ilIoJtEilTllil J(OMIIOHGIITLI COOTlef shy

cTRYlOUU-Ie IIYJleBIJM MOnBM

J 11~j J ~(j - ((lt ) r I _( J de middot lt)

111 Cf8Jl110HapHUX KJlaCClfleCKlIX UWulIlll1 C ( YCJJ(lBII ( L IIJ) IUiloIIIlI shy

UTC CCII1 yCJlOUI18 ( 488) YJtOHll lIlOJf Il O Tr ]IJl NUl lion ( HIrI~

IIIElnCll 18W(IlIWM YjlEllIllt llIlfl (1r) ~I 1I0)I IIIWIIlrj O yoqOllllHM (middotI tmiddot) I lIonyshyIJiM lU~fWlltf l lIll

1 laquo) (I) (4 Ill)I ( ~

HrullleM fII 1(lMMY1lHlIICI II II II

11

-lt ) APd c j

( [) 1 J)

) A (

HM80M j L J shy

)(4 )I I I 4 --) bullbull L UJ I~ )

~j ~ (4 3)

llIlCJ iL - nepB~l-i I1IeH B pa3JIOllteHlfR

s )~l co ~ ( -0- V I ~ I 1 ( ~1 L ( ( d

~ middot1

( [Ii i = U B clUJ) BlIllOm 8ID1R yCJloJmii CBR 311 CM liIDPie ) TaKHM 0 6pa 30M

nonyqaeM ITO ypaRHeHI1Jl IIBIDK8Hlltf11 B HYJle1l0M 11 nepOOM nOPMRO oa3JIOllleshy 1

IIlHi no D HOBblX n epSMOH1lUX 11j ilUiHMl1OT Dlfn

1

I

I L I (1 L (( L ) ( (44)L

j (4 5 )lJ ((1 l bull ( ur middot )1 t

iteJlJHegtiHOo y paJ3H0JllIe (44 ) IlpencT8BJUIeT codol KJIaCCI1eCKoe ypaBlletme

nB1U8HlIH COOTSOTCTBYOlueo MO)JeJH ( l ) 0110 no npeJIJlOJ[OlKeHIfIO MeeT

HeTpHBlfaJID HOe peOJllrne 1 (t ) xapAKrepI1 3YXlIllec CTallllCClillii Jl(shy

~OPMHllOBaHHWi OOheKT i3 TpeoyeMoM nj ll1(IJIWIWHHI1 Yl)aBHBlllIe (45) onJl8Jleshy

J1ReT BTOPllUlO KBaHTOBaJlHoe n ore n i I )

TIepei-inUM TeneJb K Rli110JlY TPX oJJ aHl1PHHii K IOTOPHM nplHlOlll1T

lIaJTOlgtlCltI1P YCJJOBlIP CBR311 ( i) Ha nolll q J) OTM P THM ITO KOBAlI11shy

aJITlIOCTb nonxona ooucneI1Ba8T rrpaalVTMIJjO ~laBHCJlMOC r h iOHCIaHT JlBIIJlte shy~HHH 01 JIlIHeliHoil 11 yrJlOBO ffOpOc nd1 nO ~lTOMY yCJlOHlIR CnRal1

IJ8CCMO TPJIM Hrl Atlno C()CTOIlHHJI coo rHuTC InYlI1li1 1I0 KOlweMYCJl OOmiddotH KlY

~~ ( bull l )

c )H Ij n i 1 I () ( 6)

~ )l i )1 rT ) 1) 111

jfl1 COOTIOUlelllR I ypan BlIUlR (44 ) Ilol11(CJ11JYJOT jO ~~i(lJ1W1e IlTU ra3ll0JWHlUI

orrcpAToF3 ~

12

M ~ -ll l U 1 (1 c -= t x ( (J ((L ) Mi - gt

AHaJI01l-flJIO 13 CBR3efi Clt) C~1 ( r1 noJIYlKM COOTlle[CT I VL l

BSHHO YCIOH1f

~ I ~ )CPl XJ _ 0II -_ ( lB )3t TA gt

JCD~ Q Cshy~d) d X 1 -~ ) (4 ttj)

~ I ~ III( l (X JJ - J) ) G-I ~ = D I u ) x ( 1 ( u ) I L

ITPU)JCT8BI1M IToJIe ([II C ) R13Jrmomeecp lBWeHveM (4 5 ) H Blfne Pamp3JlomiddotshyteHJUl no nOJllioll CHCTeMe pem8H1f~ YP8BHSHIfl

J f f )- ) oJ U ((j)~ ) I = it) t t )

(4 9)~ C~lt) fJA

(C) ( (() = ~ltr

YCJWBI1H (4 8a) (4 8d) flCIltJ1X)laroT fl p a ilIoJtEilTllil J(OMIIOHGIITLI COOTlef shy

cTRYlOUU-Ie IIYJleBIJM MOnBM

J 11~j J ~(j - ((lt ) r I _( J de middot lt)

111 Cf8Jl110HapHUX KJlaCClfleCKlIX UWulIlll1 C ( YCJJ(lBII ( L IIJ) IUiloIIIlI shy

UTC CCII1 yCJlOUI18 ( 488) YJtOHll lIlOJf Il O Tr ]IJl NUl lion ( HIrI~

IIIElnCll 18W(IlIWM YjlEllIllt llIlfl (1r) ~I 1I0)I IIIWIIlrj O yoqOllllHM (middotI tmiddot) I lIonyshyIJiM lU~fWlltf l lIll

1 laquo) (I) (4 Ill)I ( ~

HrullleM fII 1(lMMY1lHlIICI II II II

11

11 YCJIOBI1R KBaHTOOOHHR BMTlJIIfTyn ex C IIOMOUlhlO rrpe odpa30BaHlUl

(2 6) rrpli yllCpl8IiID B pa3Jolle lUIR BI1pall81ildi (2 3) CJIara ElMHX He Bhllll8

nepsoro I10PRIlKa no ~ noJIYUIM

[ (jl(T) (] i l ~I) ( -()1 - LA lJ(t~ ~7) =C )

[G1((rrd () ] 11 t 8(((~)=tfr((()- I1(((~

tr -)T I r- J J P ) jJ 1 I ( - ) I - _ (4II)L 1( J 1 ) I ) r l F ~~ ~ laquo r- ~- 1 -~ It b( t $lt) = a

1 IJ )

(h 0gt( 7) = r)- + ) f7(t~ g(s~F) = L 0 (Jdl l - t l 1 ~

- [ 6 Ip) R l~) lt t) I -COafeCrHOCTb pa3JOlfeIDIR (410) H COOTHOm8HHA (4 n) rrpImOllwr K rrpashyBwry KBaHTOBalliUl

-[ [1 ~ (t 1 ~ ( T

L1i ~

I () -J L( I l ll-- (I T~ I ~ c ~ (4 12 )

ITO JIeIKO npOBepRCTCR Ha aelltTOpe COCTORI-UiR JOKOR ( = 0)

TaKHM o dpa30M B lCKOMOM rropU)(e T80Pruf B03MymCHHIl nOJIe ctshynpellCTaBHMO B ~e

1lh J ) 0 4 1 (~ ) ~ (J l ( ~ S-) -c=

(413)- J ~ J) i - r

[ T t r l L I 11 u ) 1 ~ i ) )

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P2-85-632 in MtI l s of Ext e n d e d Objects

The invest i ga L 1011 Iw o hl~O Il lir f middot11l(middotd ~ j l Ihc Laorilt o ry

of T h e o retical Physics J INH Prprint of the Joint Institute InJ NIII I ~u f iI IIH h Dllbna 1985

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