Газодинамічна теорія бозе-квазічастинок та методи розрахунку кінетичних коефіцієнтів: Автореф. дис… канд. фіз.-мат. наук / М.Р. Бєляєв, НАН України.

IAOe?IIAEUeIA AEAAeAI?ss IAOE OE?A?IE

IAOEIAI-OAOIIEIA?*IEE EIIOeA?I

“?INOEOOO IIIIE?ENOAE?A”

?INOEOOO IIIIE?ENOAE?A

OAeE 532.132; 536.48; 537.6

A?Ess?A Ieeiea ?iiaiiae/

AACIAeEIAI?*IA OAI??ss AICA-EAAC?*ANOEIIE OA

IAOIAeE ?IC?AOOIEO E?IAOE*IEO EIAO?Oe??IO?A

01.04.02 – oai?aoe/ia o?ceea

Aaoi?aoa?ao

aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa o?ceei-iaoaiaoe/ieo iaoe

Oa?e?a — 1999

Aeena?oaoe??th ? ?oeiien.

?iaioa aeeiiaia a Oa?e?anueeiio aea?aeaaiiio oi?aa?neoao? I?i?noa?noaa
ina?oe Oe?a?ie.

Iaoeiaee ea??aiee

eaiaeeaeao o?ceei-iaoaiaoe/ieo iaoe, aeioeaio

OIAeONIA Aaea??e Aeieo?iae/, aeioeaio eaoaae?e oai?aoe/ii?
yaea?ii? o?ceee Oa?e?anueeiai aea?aeaaiiai oi?aa?neoaoo I?i?noa?noaa
ina?oe Oe?a?ie.

Io?oe?ei? iiiiaioe:

aeieoi? o?ceei-iaoaiaoe/ieo iaoe

NETHNA?AIEI TH??e A?eoi?iae/, i?ia?aeiee iaoeiaee
ni?a?ia?oiee Iaoe?iiaeueiiai iaoeiaiai oeaio?o Oa?e?anueeee
o?ceei-oaoi?/iee ?inoeooo (IIOe OOO?);

aeieoi? o?ceei-iaoaiaoe/ieo iaoe, aeioeaio

??IIEA?A Ieaenaiae? Ieoaeeiae/, caa?aeoth/ee eaoaae?ith
oai?aoe/ii? o?ceee Oa?e?anueeiai aea?aeaaiiai oi?aa?neoaoo I?i?noa?noaa
ina?oe Oe?a?ie.

I?ia?aeia onoaiiaa

?inoeooo ?aae?io?ceee ? aeaeo?ii?ee IAI Oe?a?ie, a?aeae?e
oai?aoe/ii? o?ceee

Caoeno a?aeaoaeaoueny “ 20 ” aeiaoiy 1999 ?. i 14 aiaeei? ia
can?aeaii? niaoe?ae?ciaaiii? a/aii? ?aaee Ae 64.169.01 a ?inoeooo?
iiiie?enoae?a IOE “?inoeooo iiiie?enoae?a” IAI Oe?a?ie

ca aae?anith: 310001, i. Oa?e?a, i?. Eai?ia, 60.

C aeena?oaoe??th iiaeia iciaeiieoeny o iaoeia?e a?ae?ioaoe? ?inoeoooo
iiiie?enoae?a IAI Oe?a?ie.

Aaoi?aoa?ao ?ic?neaiee “ 20 ” aa?aniy 1999 ?.

A/aiee nae?aoa?

niaoe?ae?ciaaii? a/aii? ?aaee Ae 64.169.01

eaiaeeaeao oaoi?/ieo iaoe _________________ Ao?iuaiei
E.A.

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeuei?noue oaie. Aeia?eueio eiiaeainiaaio eaaioiao nenoaio, yea
neeaaea?oueny c aaeeei? e?eueeino? /anoeiie ? i?noeoue iecueeieaaea/?
caoaeaeai? noaie, iiaeia iienaoe ca aeiiiiiaith iiaeae? eaac?/anoeiie,
ui caaeiaieueiythoue noaoenoeoe? Oa?i?–Ae??aea aai Aica–Aeiooaeia.
Aica-eaac?/anoeiee iienothoue, iai?eeeaae, oaieia? caoaeaeaiiy a
e?enoaeao oa eaaioiaeo ??aeeiao (iaaiiie, oiiiie, ?ioiie oa ?i.).

A iaeano? aeinoaoiuei iecueeeo oaiia?aoo? iiaeia iiaoaeoaaoe caaaeueio
oai??th eaac?/anoeiie, ui aeicaiey? anoaiiaeoe caeiiii??iino? iiaaae?iee
aaco eaac?/anoeiie. Oea ? a?ae?iaaciaeeiai?/ia oai??y, yea aoaeo?oueny
ia iniia? e?iaoe/ii? oai??? aeey eaac?/anoeiie. I?e oeueiio, iiaeia
aea/aoe ??ci? e?iaoe/i? yaeua a aac? eaac?/anoeiie, cie?aia, oae? yaeua
ye ?iciianthaeaeaiiy aoi?eiieo oaeeue, iiae?aieo aei oaeeue ae?oaiai
caoeo a He II.

A?ae?iaaciaeeiai?/i? ??aiyiiy aeey eaac?/anoeiie i?noyoue e?iaoe/i?
eiao?oe??ioe, ui aecia/athoue iacai?ioi? i?ioeane, ye? a?aeaoaathoueny a
aac? eaac?/anoeiie. Aea/aiiy oaeeo yaeu ye caanaiiy ia?oiai oa ae?oaiai
caoeo, neaaiia??aiiaaaeieo noai?a, ui aeieeathoue ye iane?aeie ae??
ciai?oi?o iie?a (ae?aeaeo?e/ia ?aeaenaoe?y, ?aeaenaoe?y iaai?oiiai
iiiaioo a oa?iae?aeaeo?eeao, oaieii?ia?aei?noue, aaiethoe?y oaieiaeo
?iioeuen?a, ieoaiiy caoaeaeaiiy oa ?nioaaiiy neaaicaanath/eo oaeeue oeio
oaeeue ae?oaiai caoeo, oeoeooaoe?e, ?icn?yiiy na?oea) oa ?io? e?iaoe/i?
yaeua, ui a?aeaoaathoueny a oaa?aeeo o?eao oa eaaioiaeo ??aeeiao,
iio?aaothoue ciaiiy ia o?eueee ye?nii? caeaaeiino? e?iaoe/ieo
eiao?oe??io?a a?ae oaiia?aoo?e, aonoeie oa ?ioeo ia?aiao??a, aea ? ?oi?o
/eneiaeo cia/aiue.

I?aeo?ae, ui aoaeo?oueny o?eueee ia ye?nieo ioe?ieao, ye? iaea?aeai? c
caaaeueieo i??eoaaiue, a o?ce/i?e e?iaoeoe? aeey oeueiai aaea
iaaeinoaoi?e. E?euee?nia iinoaiiaea caaea/? aeicaiey? aeine?aeeoe
ciaeaeai? ?ica’ycee, ii??aiyoe ?acoeueoaoe oai?aoe/ieo ?ic?aooie?a c
aeaieie aenia?eiaio?a ?, oei naiei, aecia/eoe, ye? ?oi? aeanoeaino? ia
caeaaeaoue a?ae c?iaeaieo i?e ioe?ieao iaaeeaeaiue oa i?eiouaiue.

Canoinoaaiiy o o?ce/i?e e?iaoeoe? ia/enethaaeueieo iaoiae?a iieaaoo?
caaea/o ?ic?aooieo oa ia/eneaiiy e?iaoe/ieo eiao?oe??io?a c
aeinoaoiueith oi/i?noth. Oiio aaaeeeaith ? ?ic?iaea iaoiae?a ?ic?aooieo
e?iaoe/ieo eiao?oe??io?a, ui aeicaieythoue caeiaooe oae? e?euee?ni?
cia/aiiy.

A e?iaoeoe? cae/aeieo aac?a ciaeoia oe?iea ?iciianthaeaeaiiy iaoiae
Aineiaa–*aiiaia ?ica’yceo e?iaoe/ieo caaea/ ca neaaiiaiaeii??aeieo oa
ianoaoe?iia?ieo oiia, yeee aeei?enoiao? eeane/i? nenoaie i?oiaiiaeueieo
iie?iii?a oa aeicaiey? caeiaooe e?euee?ni? cia/aiiy e?iaoe/ieo
eiao?oe??io?a, yeui a?aeii? eiia??iino? aca?iiae?? /anoeiie.

?icaeoeo oa canoinoaaiith iaoiaeo Aineiaa–*aiiaia a aaciaeeiai?oe?
aica-eaac?/anoeiie aeey ?ic?aooieo e?iaoe/ieo eiao?oe??io?a c
aeei?enoaiiyi niaoe?aeueii iiaoaeiaaieo nenoai i?oiaiiaeueieo iie?iii?a
oa ?ioeo iaoiae?a, iiooeo iao?e/ieo aeaiaio?a aca?iiae?? eaac?/anoeiie
i?enay/aia oey ?iaioa. Oeei ? aecia/a?oueny aeooaeuei?noue oaie
i?iaaaeaieo aeine?aeaeaiue.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie. Aeena?oaoe?eia
?iaioa iia’ycaia c aeine?aeaeaiiyie, ye? i?iaiaeyoueny a Oa?e?anueeiio
aea?aeaaiiio oi?aa?neoao? ca oaiith “Oai??y aaaaoi/anoeieiaeo nenoai”
(iiia? aea?ae?a?no?aoe?? 0197U002489), yea aeeiio?oueny ca
eii?aeeiaoe?eiei ieaiii IAe? I?iina?oe Oe?a?ie.

Iaoa ? caaea/? aeine?aeaeaiiy. Iniiaiith iaoith aeena?oaoe?eii? ?iaioe ?
oai?aoe/ia aeine?aeaeaiiy aaciaeeiai?ee eaac?/anoeiie c aeia?eueiei
caeiiii aeenia?n??, ?ic?aooiie e?iaoe/ieo eiao?oe??io?a oa ii??aiyiiy ?o
c aenia?eiaioaeueieie aeaieie. Aeey aeinyaiaiiy oe??? iaoe
?ica’ycoaaeeny oae? iniiai? caaea/?:

· aeoiaey/e c e?iaoe/iiai ??aiyiiy aeey ooieoe?? ?iciiae?eo
eaac?/anoeiie, ciaoiaeaeaiiy ??aiyiue aaciaeeiai?ee eaac?/anoeiie c
aeia?eueiei caeiiii aeenia?n??;

· ?ic?iaea iaoiaeo iiae?aiiai aei iaoiaeo Aineiaa–*aiiaia ?ic?aooieo
e?iaoe/ieo eiao?oe??io?a aaciaeeiai?ee eaac?/anoeiie c canoinoaaiiyi
niaoe?aeueii iiaoaeiaaieo nenoai i?oiaiiaeueieo iie?iii?a;

· ?icaeoie oa iiaoaeiaa iiaeae? caaaeaiiai ?cio?iiiiai e?enoaeo c
a?aooaaiiyi iiaeoe?a i?oaeiino? o?aoueiai ii?yaeeo oa ciaoiaeaeaiiy a
i?e iao?e/ieo aeaiaio?a aca?iiae?? oiiii?a;

· ?ic?aooiee e?iaoe/ieo eiao?oe??io?a oiiiiii? aaciaeeiai?ee a
e?enoae?/ieo ae?aeaeo?eeao oa aaciaeeiai?ee iaaiii?a a oa?i– ?
aioeoa?iiaaiaoeeao;

· a?aooaaiiy iai?oaeiino? ?icn?yiiy oiiii?a ia ?ioiiao a He II i?e
ia/eneaii? eiao?oe??ioa iiaeeiaiiy ia?oiai caoeo oa ia?oi? ? ae?oai?
a’yceinoae ? aiae?c aenia?eiaioaeueieo aeaieo.

Iaoeiaa iiaecia iaea?aeaieo ?acoeueoao?a.

· ?icaeiooi iaoiae, iiae?aiee aei iaoiaeo Aineiaa–*aiiaia ?ic?aooieo
e?iaoe/ieo eiao?oe??io?a a aaciaeeiai?oe? eaac?/anoeiie c aeei?enoaiiyi
niaoe?aeueii iiaoaeiaaieo nenoai i?oiaiiaeueieo iie?iii?a aeey
?ic?aooieo eiao?oe??io?a a’yceino? oa a?ae?iaeeiai?/ii?
oaieii?ia?aeiino? o oiiiii?e aaciaeeiai?oe? oa o iaaiiii?e
aaciaeeiai?oe? oa?i– ? aioeoa?iiaaiaoee?a ia i?eeeaae? ?cio?iiieo
oa?iae?aeaeo?ee?a oa ai-oeoa?iiaaiaoee?a oeio “eaaea ieiueia”;

· aia?oa iiaoaeiaaia iiaeaeue caaaeaiiai ?cio?iiiiai e?enoaeo noiniaii
iiaeoe?a i?oaeiino? o?aoueiai ii?yaeeo aeey e?enoae?a on?o neiaii?e;

· iiaoaeiaai? niaoe?aeuei? nenoaie i?oiaiiaeueieo iie?iii?a c aaaiaeie
ooieoe?yie, ui oa?aeoa?i? aeey noaoenoeee Aica–Aeiooaeia ? ciaeaeai?
oi?ioee aeui? aeaaa?a?/ii? oi/iino? aeey ia/eneaiiy ?ioaa?ae?a, ui
aeei?enoiaothoue oe? nenoaie i?oiaiiaeueieo iie?iii?a;

· aia?oa ca ?ic?aooieo eiao?oe??ioo ae?oai? a’yceino? oa eiao?oe??ioo
iiaeeiaiiy ia?oiai caoeo a He II a?aoiaaia iai?oaei?noue ?icn?yiiy
oiiii?a ia ?ioiiao, ui aeicaieeei caeiaooe ocaiaeaeaiiy i?ae
aenia?eiaioaeueieie aeaieie oa oai?aoe/ieie ?acoeueoaoaie.

I?aeoe/ia cia/aiiy iaea?aeaieo ?acoeueoao?a. Cai?iiiiiaaiee iaoiae
?ic?aooieo e?iaoe/ieo eiao?oe??io?a iiaeia canoinoaaoe aeey ia/eneaiiy
e?iaoe/ieo eiao?oe??io?a ia o?eueee o oiiiii?e oa iaaiiii?e
aaciaeeiai?oe?, a e a aaciaeeiai?oe? ?ioeo eaac?/anoeiie c o?aooaaiiyi
aieeao noi?iii?o iie?a (caoeiaiai, aeaeo?e/iiai, iaai?oiiai oa ?i.). Oea
aeicaieeoue ?ic?aoiaoaaoe eiao?oe??io iiaeeiaiiy aoi?eiieo oaeeue a aac?
eaac?/anoeiie ? aeyaeoe oiiae ?oiueiai ?nioaaiiy, aeaoe ?aeiiaiaeaoe?? c
?oiueiai aenia?eiaioaeueiiai niinoa?aaeaiiy, ia/enethaaoe eiao?oe??io
iiaeeiaiiy ia?oiai caoeo, aeine?aeaeoaaoe iiaeeiaiiy iecueei/anoioieo
ci?iieo noi?iii?o iie?a, aea/aoe aaiethoe?th oaieiaeo ?iioeuen?a a
??ciiiai?oieo na?aaeiaeuao.

Ciaiiy e?iaoe/ieo eiao?oe??io?a aeicaiey? aea/aoe ??ciiiai?oi? e?iaoe/i?
yaeua, ii??aithaaoe ?acoeueoaoe oai?aoe/ieo aeine?aeaeaiue c
aenia?eiaioaeueieie aeaieie ?, ia iniia? oeueiai, iaea?aeoaaoe
?ioi?iaoe?th i?i aeanoeaino? ?aaeueieo na?aaeiaeu. Canoinoaaiiy iiaeae?
caaaeaiiai ?cio?iiiiai e?enoaeo aeey aiae?co aenia?eiaioaeueieo aeaieo
aeicaieeoue aea/aoe aeanoeaino? ?aaeueieo e?enoae?a.

Iniaenoee aianie caeiaoaa/a. Iniaenoee aianie aaoi?a iieyaa? a

· ?ic?iaoe? aeai?eoi?a:

a) iiaoaeiae iaeeane/ieo nenoai i?oiaiiaeueieo iie?iii?a c ??cieie
aaaiaeie ooieoe?yie, ui oa?aeoa?i? aeey aaciaeeiai?ee
aica-eaac?/anoeiie;

a) iaaeeaeaiiai ?ica’ycaiiy iane?i/aieo iaiaeii??aeieo nenoai
e?i?eieo ??aiyiue a?aeiinii eiao?oe??io?a ?iceeaaeo ooieoe?e a ?yaee
Oo?’? ca i?oiaiiaeueieie nenoaiaie iie?iii?a c eiio?ieth?iith oi/i?noth
aeey ?ic?aooieo e?iaoe/ieo eiao?oe??io?a;

a) ia/eneaiiy cia/aiue niaoe?aeueieo ooieoe?e, ui aeei?enoiaothoueny
a aaciaeeiai?oe? eaac?/anoeiie

oa i?iaaaeaii?, ia iniia? oeeo aeai?eoi?a /eneiaeo ?ic?aooie?a
[2,3,5,7-9].

· iiaoaeia? ? canoinoaaii? oi?ioe aeui? aeaaa?a?/ii? oi/iino? oeio
oi?ioe Aaona aeey ciaeaeaieo nenoai i?oiaiiaeueieo iie?iii?a aei
iaaeeaeaiiai ia/eneaiiy ?ioaa?ae?a a aaciaeeiai?oe? eaac?/anoeiie
[2,3,5,7,8];

· ciaoiaeaeaii? iiaeoe?a i?oaeiino? o?aoueiai ii?yaeeo a iiaeae?
caaaeaiiai ?cio?iiiiai e?enoaeo aeey e?enoae?a ??cieo neiaii?e [4];

· ia/eneaii? eiao?oe??io?a a’yceino? oa a?ae?iaeeiai?/ii?
oaieii?ia?aeiino? a oiiiii?e aaciaeeiai?oe? ? iaaiiii?e aaciaeeiai?oe?
?cio?iiieo oa?iae?aeaeo?ee?a oa aioeoa?iiaaiaoee?a oeio “eaaea ieiueia”
[2, 5, 7, 8];

· i?iaaaeaii? ?ic?aooie?a eiao?oe??ioo iiaeeiaiiy ia?oiai caoeo oa
eiao?oe??io?a ia?oi? ? ae?oai? a’yceinoae a He II oa ii??aiyii?
oai?aoe/ieo ?acoeueoao?a c aeaieie aenia?eiaio?a [1, 6];

· o/ano? a iaaiai?aii? ?acoeueoao?a aeine?aeaeaiue ? iaienaii? oaeno?a
noaoae oa oac aeiiia?aeae.

Aaoi? ca ?acoeueoaoaie aeine?aeaeaiue ?iaea aeiiia?ae? ia iaoeiaeo
nai?ia?ao a OAeO, IIOe OOO?, OO?IO IAI Oe?a?ie oa ia a?o/eciyieo ?
i?aeia?iaeieo eiioa?aioe?yo.

Ai?iaaoe?y ?acoeueoao?a aeena?oaoe??. Iniiai? ?acoeueoaoe
aeena?oaoe?eii? ?iaioe aeiiia?aeaeenue ia:

· XXV Ananithci?e ia?aae? c o?ceee iecueeeo oaiia?aoo?, (25 – 27
aa?anaiue, 1989, Eai?ia?aae),

· Ananithci?e eiioa?aioe?? “No/ani? i?iaeaie noaoenoe/ii? o?ceee”, (14 –
17 o?aaaiue, 1991, Oa?e?a),

· 14 th General Conference Condensed Matter Division (March 28 – 31,
1994, Madrid),

· International Workshop of on statistical physics and condensed matter
theory (11 – 14 September, 1995, Lviv, Ukraine),

· VI international conference of mathematical methods in electromagnetic
theory (10 – 13 September, 1996, Lviv, Ukraine),

a oaeiae ia iaoeiaeo nai?ia?ao a OO?IO IAI Oe?a?ie, IIOe OOO? oa
Oa?e?anueeiio aea?aeaaiiio oi?aa?neoao?.

Ioae?eaoe??. Iniiai? ?acoeueoaoe aeena?oaoe?? iioae?eiaaii o 4 noaoyo a
oaoiaeo iaoeiaeo aeo?iaeao, 1 noaoo? a ca??oe? iaoeiaeo i?aoeue oa a 4
aeiiia?aeyo ia eiioa?aioe?yo, ye? iaae?oeiaaii a iaoa??aeao
eiioa?aioe?e.

No?oeoo?a aeena?oaoe??. Aeena?oaoe?y neeaaea?oueny c anooio, /ioe?ueio
?icae?e?a iniiaiiai oaenoo, aeniiae?a, nieneo aeei?enoaieo aeaea?ae c
116 iaeiaioaaiue oa o?ueio aeiaeaoe?a.

Ianya aeena?oaoe?? neeaaea? 150 noi??iie, ui i?noyoue 11 oaaeeoeue oa 2
?enoiee.

INIIAIEE CI?NO

O ia?oiio ?icae?e? ?icaeyiooi aaciaeeiai?/io oai??th aica-eaac?/anoeiie
c aeia?eueiei caeiiii aeenia?n??, yea a ?icae?eao 2 oa 3 canoiniao?oueny
aeey iieno oiiiiii? oa iaaiiiii? aaciaeeiai?ee eaac?/anoeiie. Iaaaaeaii
e?iaoe/ia ??aiyiiy aeey ooieoe?? ?iciiae?eo aica-eaac?/anoeiie c
o?aooaaiiyi ae?? ia aac eaac?/anoeiie iia?eueiici?iieo eieaeueieo
ciai?oi?o iie?a, ye?, ye aia?oa aoei iieacaii Ao??ca?ii A.?.,
iiaeoeththoue aia?a?th eaac?/anoeiie. ?ioaa?ae c?oeiaiue a e?iaoe/iiio
??aiyii? a?aoiao? o?e– oa /ioe?e/anoeieia? i?ioeane aca?iiae??.

O aeiaaeeo, eiee i?ioeane aca?iiae?? eaac?/anoeiie c? caa?aaeaiiyi
?iioeueno ? aecia/ath/eie, caeiaooi eaac???aiiaaaeiee ?ica’ycie oeueiai
??aiyiiy, yeee aecia/a?oueny oa?iiaeeiai?/ieie aaee/eiaie: ae?aeoiaith
oaeaee?noth, eieaeueiith oaiia?aoo?ith oa o?i?/iei iioaioe?aeii.
Iiaoaeiaaii oa?iiaeeiai?eo oeueiai eaac???aiiaaaeiiai noaio. Ia iniia?
e?iaoe/iiai ??aiyiiy ciaeaeai? aaciaeeiai?/i? ??aiyiiy
aica-eaac?/anoeiie c o?aooaaiiyi aeeneiaoeaieo iioie?a, ye? o aeiaaeeo
iaeeo a?aae??io?a oaiia?aoo?e, o?i?/iiai iioaioe?aeo oa ae?aeoiai?
oaeaeeino? ? e?i?eieie ooieoe?yie oeeo a?aae??io?a ? aecia/athoue
e?iaoe/i? eiao?oe??ioe. Iieacaii, ui eiee caeii aeenia?n?? eaac?/anoeiie
wmetafile8? ??O????????????
???????????yyy????.????1?????? ???????
?A???&??yyyy?????AyyyAyyy???A?? ???&?
?MathType??P????u?th???????icaeiooi iaoiae ?ic?aooieo e?iaoe/ieo
eiao?oe??io?a ca aeiiiiiaith niaoe?aeueii iiaoaeiaaieo nenoai
iaeeane/ieo i?oiaiiaeueieo iie?iii?a ia iniia? aaaiai? ooieoe??, ui
oa?aeoa?ia aeey noaoenoeee Aica–Aeiooaeia aeey eaac?/anoeiie c
aeia?eueiei caeiiii aeenia?n??. Ia iniia? ocaaaeueiaii? I-oai?aie
Aieueoeiaia aeacai? ieaei? ioe?iee aeey eiao?oe??io?a ia?aiino. Aeey
iaaeeaeaiiai ia/eneaiiy ?ioaa?ae?a, ui cono??/athoueny a ?ic?aooieao
e?iaoe/ieo eiao?oe??io?a, cai?iiiiiaaii iineoaiaoaaoeny oi?ioeaie aeui?
aeaaa?a?/ii? oi/iino? oeio oi?ioe Aaona. Aiae?c aaaiaeo iiiaeiee?a a
oi?ioeao oeio Aaona ? cia/aiue i?ae?ioaa?aeueii? ooieoe?? aeicaiey? o
iaaeanieo ?ioaa?aeao ia iane?i/aieo i?ii?aeeao ?icoiiei /eiii cai?noue
iane?i/aiiai i?ii?aeeo aeae?aoe ne?i/aiee.

O ae?oaiio ?icae?e? aeey ?aae?caoe?? caaaeueieo iaoiae?a,
cai?iiiiiaaieo a ?icae?e? 1, iiaoaeiaaii iiaeaeue caaaeaiiai
?cio?iiiiai e?enoaeo noiniaii iiaeoe?a i?oaeiino? o?aoueiai ii?yaeeo,
yea ca nai?ie i?oaeieie aeanoeainoyie iaei a?ae??ciy?oueny a?ae
?aaeueieo e?enoae?a. O iiaeae? caaaeaiiai ?cio?iiiiai e?enoaeo ciaeaeaii
iao?e/i? aeaiaioe aca?iiae?? oiiii?a, ye? aecia/athoueny iiaeoeyie
i?oaeiino? ae?oaiai oa o?aoueiai ii?yaeeo. A caaaeaiiio ?cio?iiiiio
e?enoae? eiao?oe??ioe oiiiiii? a’yceino? oa a?ae?iaeeiai?/ii?
oaieii?ia?aeiino? iathoue aeaeyae: wmetafile8? ??“???????????
???????????yyy????.????1?????? ??????? 
????&??yyyy?????Ayyy?yyy@??E?? ???&? ?MathType??A?
???u?????????»????-?????@¦???@7???u?th??????O o?aoueiio
?icae?e? aeey ?ic?aooieo oa?iiaeeiai?/ieo aaee/ei, ui oa?aeoa?ecothoue
oa?iiaeeiai?/io ??aiiaaao, oa aeey ia/eneaiiy iiiaio?a, ui aecia/athoue
i?oiaiiaeuei? iie?iiie, canoiniaaii niaoe?aeuei? ooieoe?? wmetafile8?
????????????? ???????????yyy????.????1??????
???????   ???&??yyyy?????AyyyYyyy`??A?? ???&?
?MathType??P????u tha?????Iiaoaeiaai? nenoaie i?oiaiiaeueieo iie?iii?a
oa oi?ioee aeui? aeaaa?a?/ii? oi/iino? iiaeooue aooe aeei?enoai? ia
o?eueee a iaaiiii?e aaciaeeiai?oe?, a ? i?e aea/aii? aeanoeainoae aaco
aica-eaac?/anoeiie c eaaae?aoe/iei caeiiii aeenia?n?? oa aaco
?aeyoea?nonueeeo aica-/anoeiie. C aeei?enoaiiyi niaoe?aeueii? ooieoe??
wmetafile8? ?????????????
???????????yyy????.????1?????? ??????? 
 ???&??yyyy?????AyyyYyyy`??A?? ???&? ?MathType??P????u
tha?????Aeey aioeoa?iiaaiaoee?a c iaai?oiith ai?cio?ii??th oeio “eaaea
ieiueia”, a yeeo ?niothoue iecueei/anoioi? wmetafile8?
??I???????????? ???????????yyy????.????1??????
???????  A???&??yyyy?????AyyyYyyy???A?? ???&?
?MathType??P????u tha?????Ciaeaeaii eiao?oe??io caanaiiy aoi?eiieo
oaeeue a iaaiiii?e aaciaeeiai?oe?. *enei, iiae?aia aei /enea
I?aiaeoey, a iaaiiii?e aaciaeeiai?oe? aeey a?eueoino? oa?iae?aeaeo?ee?a
noaiiaeoue aaee/eio ii?yaeeo iaeeieoe?. Oea na?ae/eoue, ui yaeua
a’yceino? oa a?ae?iaeeiai?/ii? oaieii?ia?aeiino? aeathoue aianee iaeiiai
ii?yaeeo aaee/eie a aeeneiaoeai? i?ioeane.

A aioeoa?iiaaiaoeeao oeio “eaaea ieiueia”, yeui nei?enoaoeny iaaeeaeaiei
caeiiii aeenia?n?? iaaiii?awmetafile8? ??a???????????
???????????yyy????.????1?????? ???????
?????&??yyyy?????Ayyy¦yyy@??¦?? ???&?
?MathType???????uYth??????O /aoaa?oiio ?icae?e?, iineoaiaoth/enue
iaoiaeeeith, ?ic?iaeaiith a ?iaioao Aaeaiaiea ?.I. ? Oeeaaiea A.?., ui
a?oioo?oueny ia aeei?enoaii? iia?aoi??a-i?iaeoi??a ia ?iaa??aioi?
i?aei?inoi?e e?iaa?eciaaiiai iia?aoi?o c?oeiaiue oa aeoiaey/e c
e?iaoe/ieo ??aiyiue aeey oiiii?a ? ?ioii?a, ciaeaeaii eiao?oe??io
iiaeeiaiiy ia?oiai caoeo. ?ic?aoiaai? eiao?oe??ioe ia?oi? oa ae?oai?
a’yceinoae ? eiao?oe??io iiaeeiaiiy ia?oiai caoeo a He II ca ??cieo
oene?a o oe?ieiio ae?aiacii? oaiia?aoo?, ui i?noeoue oiiii–?ioiiio ?
/enoi oiiiiio iaeano? c o?aooaaiiyi aeenia?n?? oiiiiiiai niaeo?o ?
iai?oaeiiai ?icn?yiiy oiiii?a ia ?ioiiao.

Anoaiiaeaii, ui ia?oa a’yce?noue aei??aith? noi? /enoi oiiiiii? oa /enoi
?ioiiii? a’yceinoae. I?e oaiia?aoo?ao wmetafile8? ??????????????
???????????yyy????.????1?????? ???????
? ???&??yyyy?????Ayyyayyy`??e?? ???&? ?MathType??
????u?th??????Aeey oaiia?aoo? wmetafile8? ??????????????
???????????yyy????.????1?????? ???????
? ???&??yyyy?????Ayyyayyy`??e?? ???&? ?MathType??
????u?th??????Eiee oaiia?aoo?a wmetafile8? ??????????????
???????????yyy????.????1?????? ???????
? ???&??yyyy?????Ayyyayyy`??e?? ???&? ?MathType??
????u?th??????I?iaaaeaii ii??aiyiiy ?ic?aooieiaeo cia/aiue
eiao?oe??ioo iiaeeiaiiy ia?oiai caoeo c aeaieie aenia?eiaio?a, ye ca
oene?a iane/aii? ia?e oae ? ca aenieeo oene?a. Niinoa??aa?oueny
ocaiaeaeai?noue oai??? c aenia?eiaioaie. Aeayea ?ica?aei?noue a
?ioa?aae? aeoaea iecueeeo oaiia?aoo? iaoiiaeaia ii?ooaiiyi
a?ae?iaeeiai?/iiai ?aaeeio ca aenieeo /anoio.

O aeiaeaoeo A aeeeaaeaii iaoiaeeeo iiaoaeiae nenoai i?oiaiiaeueieo
iie?iii?a ia caaeaiiio i?ii?aeeo c caaeaiith aaaiaith ooieoe??th.

O aeiaeaoeo A ?icaeyiooi iaoiaeeeo iiaoaeiae eaaae?aoo?ieo oi?ioe aeui?
aeaaa?a?/ii? oi/iino? oeio oi?ioe Aaona, ye? aeei?enoiaothoue
iiaoaeiaai? nenoaie i?oiaiiaeueieo iie?iii?a.

O aeiaeaoeo A aecia/athoueny niaoe?aeuei? ooieoe?? wmetafile8?
????????????? ???????????yyy????.????1??????
???????  `???&??yyyy?????AyyyYyyy ??A?? ???&?
?MathType??P????utha?????

AENIIAEE

O aeena?oaoe?ei?e ?iaio? caeiaooi oae? ?acoeueoaoe:

· ?icaeiooi iaoiae ?ic?aooieo e?iaoe/ieo eiao?oe??io?a o aaciaeeiai?oe?
eaac?/anoeiie, iiae?aiee aei iaoiaeo Aineiaa – *aiiaia, ui a?oioo?oueny
ia aeei?enoaii? iaeeane/ieo i?oiaiiaeueieo iie?iii?a;

· iiaoaeiaaii nenoaie i?oiaiiaeueieo iie?iii?a c aaaiaeie ooieoe?yie, ui
oa?aeoa?i? aeey aica-eaac?/anoeiie ??ciiai oeio (oiiii?a, iaaiii?a o
oa?i– ? aioeoa?iiaaiaoeeao);

· canoiniaoth/e iiaoaeiaai? nenoaie i?oiaiiaeueieo iie?iii?a, ciaeaeaii
oi?ioee aeui? aeaaa?a?/ii? oi/iino? aeey iaaeeaeaiiai ia/eneaiiy
?ioaa?ae?a, ui cono??/athoueny a aaciaeeiai?oe? aica-eaac?/anoeiie;

· aeey ?ic?aooieo oa?iiaeeiai?/ieo aaee/ei, ui oa?aeoa?ecothoue
oa?iiaeeiai?/io oa eaac?eieaeueio oa?iiaeeiai?/io ??aiiaaao, oa aeey
ia/eneaiiy iiiaio?a, ui aecia/athoue i?oiaiiaeuei? iie?iiie canoiniaaii
niaoe?aeuei? ooieoe?? wmetafile8? ?????????????
???????????yyy????.????1?????? ??????? 
????&??yyyy?????AyyyYyyy@??A?? ???&? ?MathType??P????u
tha?????· ?icaeiooi iiaeaeue caaaeaiiai ?cio?iiiiai e?enoaeo noiniaii
iiaeoe?a i?oaeiino? ae?oaiai oa o?aoueiai ii?yaee?a, aeiaaaeaii ??
aoaeoeai?noue ia i?eeeaae? e?enoae?a eoa?/ii? neiaii??, ia/eneaii
oaaeeoeth iiaeoe?a i?oaeiino? a iiaeae? caaaeaiiai ?cio?iiiiai e?enoaeo
aeey ??cieo e?enoaeia?ao?/ieo eean?a on?o neiaii?e;

· ciaeaeaii e?iaoe/i? eiao?oe??ioe a’yceino?, a?ae?iaeeiai?/ii?
oaieii?ia?aeiino?, caanaiiy ae?oaiai caoeo o aac? oiiii?a a e?enoae?/ieo
ae?aeaeo?eeao oa a aac? iaaiii?a o ?cio?iiieo oa?iae?aeaeo?eeao ?
aioeoa?iiaaiaoeeao oeio “eaaea ieiueia” c oi/i?noth aei /eneiaeo
cia/aiue eiao?oe??io?a.

· ciaeaeaii eiao?oe??ioe ia?oi? oa ae?oai? a’yceino? ? eiao?oe??io
iiaeeiaiiy ia?oiai caoeo a He II c a?aooaaiiyi iai?oaeiino? ?icn?yiiy
oiiii?a ia ?ioiiao oa aeenia?n?? oiiiiiiai niaeo?o, i?iaaaeaii
ii??aiyiiy ?ic?aoiaaieo aaee/ei c aenia?eiaioaeueieie aeaieie.

NIENIE IIOAE?EIAAIEO AAOI?II I?AOeUe

CA OAIITH AeENA?OAOe??

1. Aaeaiaiei E.I., Aaeyaa I.?., Oeuaaiie A.E. Iiaeiuaiea ia?aiai caoea e
aeenneiaoeaiua eiyooeoeeaiou He II. / / OIO – 1988. – O. 14, ? 9 – N.
899 – 905.

2. Aeaenei A.O., Aaeyaa I.?., Oiaeonia A.Ae. Eiyooeoeeaiou ia?aiina a
aaca oiiiiia a e?enoaee/aneeo aeeyeaeo?eeao. / / AAIO – 1992. – O. 24,
Aui. 3 – N. 9 – 13.

3. Aeaenei A.O., Aaeyaa I.?., Oiaeonia A.Ae. Eaaae?aoo?iua oi?ioeu oeia
Aaonna a aaciaeeiaieea eaace/anoeoe. / / Aanoiee OAO, na?ey oece/aneay
“ssae?a, /anoeoeu, iiey”. – 1998. — ? 421 – N. 62 – 67.

4. Aeaenei A.O., Aaeyaa I.?., Oiaeonia A.Ae. Iiaeaeue i?eaaaeaiiiai
ecio?iiiiai e?enoaeea ioiineoaeueii iiaeoeae oi?oainoe. / / Aanoiee OAO,
na?ey oece/aneay “ssae?a, /anoeoeu, iiey”. – 1999. – ? 438, Aui. 1/ 5 /
– N. 39 – 42.

5. Aeaenei A.O., Aaeyaa I.?., Oiaeonia A.Ae. Eiyooeoeeaiou ia?aiina a
aaca oiiiiia a e?enoaeee/aneeo aeeyeaeo?eeao. / / I?iaeaiu oai?aoe/aneie
oeceee: Na. iao/. o?.– E.: Iaoeiaa aeoiea, 1991. – N. 15 – 25.

6. Aaeaiaiei E.I., Aaeyaa I.?., Iai/aiei E.Y., Oeuaaiie A.E.
Aeenneiaoeaiua eiyooeoeeaiou e caoe a o?aoeiiiiiaioiii aaca eaace/anoeoe
o naa?oaeo/eo ?anoai?ia 3He – 4He. / / Oacenu aeieeaaeia “XXV
Ananithciia niaauaiea ii oeceea ieceeo oaiia?aoo?”. – *anoue 2. – 25 –
27 naio., 1988, Eaieia?aae – N. 90 – 91.

7. Aeaenei A.O., Aaeyaa I.?., Oiaeonia A.Ae. Eiyooeoeeaiou ia?aiina a
aaca oiiiiia a e?enoaeee/aneeo aeeyeaeo?eeao. / / Na. aiiioaoeee
Ananithciie eiioa?aioeee “Nia?aiaiiua i?iaeaiu noaoenoe/aneie oeceee”,
14 – 17 iay, 1991, Oa?ueeia – N. 3 – 4.

8. Aleksin V.F., Belyaev N.R., Khodusov V.D. Transport coefficients in
magnon gas in antiferromagnetics. / / Abstracts International Workshop
on statis-tical physics and condensed matter theory, 11 – 14 September,
1995, Lviv, Ukraine – C. 70.

9. Aleksin V.F., Belyaev N.R., Belyaeva T. N., Khodusov V.D.
Construction and application of ortogonal polinomials in kinetic of
quasi–particls. / / Proc. VI International conference of mathematical
methods in electromagnetic theory, 10 – 13 September, 1996, Lviv,
Ukraine – P. 61 – 64.

A?ey?a I.?. Aaciaeeiai?/ia oai??y aica-eaac?/anoeiie oa iaoiaee
?ic?aooieo e?iaoe/ieo eiao?oe??io?a. – ?oeiien.

Aeena?oaoe?y ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa
o?ceei–iaoaiaoe/ieo iaoe ca niaoe?aeuei?noth 01.04.02. – oai?aoe/ia
o?ceea – ?inoeooo Iiiie?enoae?a IAI Oe?a?ie, Oa?e?a, 1999.

Aeena?oaoe?y i?enay/aia ieoaiiyi aea/aiiy aaciaeeiai?ee
aica-eaac?/anoeiie a /enoeo iiiie?enoaeao oa a He II. A ?iaio?, ia
iniia? e?iaoe/ieo ??aiyiue aeey aica-eaac?/anoeiie c aeia?eueiei caeiiii
aeenia?n??, caeiaooi ??aiyiiy aaciaeeiai?ee aica-eaac?/anoeiie.
Cai?iiiiiaaii iaoiae, iiae?aiee aei iaoiaeo Aineiaa–*aiiaia, ?ic?aooieo
e?iaoe/ieo eiao?oe??io?a, ui a?oioo?oueny ia niaoe?aeueii iiaoaeiaaieo
nenoaiao i?oiaiiaeueieo iie?iii?a. Caeiaooi oi?ioee aeui? aeaaa?a?/ii?
oi/iino? oeio Aaona aeey iaaeeaeaieo ia/eneaiue ?ioaa?ae?a, ui
aeei?enoiaothoue iiaoaeiaai? nenoaie i?oiaiiaeueieo iie?iii?a.
Iiaoaeiaaii iiaeaeue caaaeaiiai ?cio?iiiiai e?enoaeo noiniaii iiaeoe?a
i?oaeiino? ae?oaiai oa o?aoueiai ii?yaee?a aeey e?enoae?a on?o neiaii?e.
?ic?aoiaaii e?iaoe/i? eiao?oe??ioe a oiiiii?e aaciaeeiai?oe? a
e?enoae?/ieo ae?aeaeo?eeao oa iaaiiii?e aaciaeeiai?oe? ?cio?iiieo
oa?iae?aeaeo?ee?a oa aioeoa?iiaaiaoee?a oeio “eaaea ieiueia” c
o?aooaaiiyi ii?yaeeo /eneiaeo eiao?oe??io?a. Ia/eneaii eiao?oe??ioe
caanaiiy aoi?eiieo oaeeue oeio oaeeue ae?oaiai caoeo a aaciaeeiai?oe?
eaac?/anoeiie.

O oiiiii?e aaciaeeiai?oe?, aeei?enoiaoth/e caeiaoo? cia/aiiy e?iaoe/ieo
eiao?oe??io?a, aeey e?enoaeo NaF ia/eneaii ?ioa?aae ?nioaaiiy ae?oaiai
caoeo, yeee ni?aiaaea? c ?ioa?aaeii eiai aenia?eiaioaeueiiai
niinoa?aaeaiiy. Aeey He II ?ic?aoiaaii ia?oo oa ae?oao a’yceino?,
eiao?oe??io caanaiiy ia?oiai caoeo c o?aooaaiiyi iai?oaeiino? ?icn?yiiy
oiiii?a ia ?ioiiao a oe?ieiio ae?aiacii? oaiia?aoo? oa oene?a.
I?iaaaeaii ii??aiyiiy ciaeaeaieo oai?aoe/ieo ?acoeueoao?a c
aenia?eiaioaeueieie aeaieie.

Eeth/ia? neiaa: aaciaeeiai?ea eaac?/anoeiie, oiiiie, iaaiiie, ?ioiie,
e?iaoe/i? eiao?oe??ioe, i?oiaiiaeuei? iie?iiie.

Belyaev N.R. The gasdynamical theory of Bose quasi-particles and the
methods of calculating the kinetic coefficients. – Manuscript.

Thses for a Candidate of Sciences Degree in Phisics and Mathematics,
speciality 01.04.02 – Theoretical Physics, Institute for Single Crystal
Academy of Sciences of Ukraine, Kharkov, 1999.

This thesis deals with the theory of gas dynamics of Bose
quasi-particles in pure single crystals and in He II. Equations of
gasdynamics for Bose quasi-particles have been obtained on the basis of
the kinetic equations with an arbitrary low of dispersion.

To calculate the kinetic coefficients a method similar to the
Enskog-Chapman is used. This method uses specially constructed
orthogonal system of polynomials.

Formuli of the highest algebraic accuracy of the Gauss type have been
obtained. This formuls use the constructed orthogonal system of
polynomials.

A model of reduced isotropic crystal with respect to second- and
third-order elastic moduli is presented, which allows us to find the
main regularities of various nonlinear effects and to estimate the order
of magnitude of quantities characterizing them.

With the account of numerical coefficients the kinetic coefficients in
the phonon gasdynamics in isotropicals ferromagnets type and
antiferromagnets type of “easy plane” have been calculated.

The damping factor of secondary waves of the second sound wave type is
calculated in gasdynamics of quasi- particles.

By using the calculated values of the kinetic coefficients the interval
of the existens for second sound waves is obtained for NaF crystals.
This interval coincides with that observed in experiments.

The coefficients of the first and second viscosity and the damping
factor for first sound are calculated with the account of inelastic
scattering of phonons and rotons in wide of temperature and pressure
ranges. Theoretical and experimental are compared.

Key words: gasdynamics of quasi-particles, phonons, magnons, rotons,
kinetic coefficients, orthogonal polinomials.

Aaeyaa I.?. Aaciaeeiaie/aneay oai?ey aica-eaace/anoeoe e iaoiaeu ?an/aoa
eeiaoe/aneeo eiyooeoeeaioia. – ?oeiienue.

Aeenna?oaoeey ia nieneaiea o/aiie noaiaie eaiaeeaeaoa
oeceei–iaoaiaoe/aneeo iaoe ii niaoeeaeueiinoe 01.04.02 –
oai?aoe/aneay oeceea – Einoeooo Iiiie?enoaeeia IAI Oe?aeiu, Oa?ueeia,
1999.

Aeenna?oaoeey iinayuaia aii?inai eco/aiey aaciaeeiaieee
aica-eaace/anoeoe a /enouo iiiie?enoaeeao e a He II. A ?aaioa, ia iniiaa
eeiaoe/aneeo o?aaiaiee aeey aica-eaace/anoeoe n i?iecaieueiui caeiiii
aeenia?nee, iieo/aiu o?aaiaiey aaciaeeiaieee aica-eaace/anoeoe. ?acaeo
iaoiae, aiaeiae/iue iaoiaeo Yineiaa–*aiiaia, ?an/aoa eeiaoe/aneeo
eiyooeoeeaioia, eniieuecothuee niaoeeaeueii iino?iaiiua nenoaiu
i?oiaiiaeueiuo iieeiiiia. Iieo/aiu oi?ioeu aunoae aeaaa?ae/aneie
oi/iinoe, oeia oi?ioe Aaonna, aeey i?eaeeaeaiiiai au/eneaiey eioaa?aeia,
eniieuecothuea iino?iaiiua nenoaiu i?oiaiiaeueiuo iieeiiiia. Iino?iaia
iiaeaeue i?eaaaeaiiiai ecio?iiiiai e?enoaeea ioiineoaeueii iiaeoeae
oi?oainoe aoi?iai e o?aoueaai ii?yaeea aeey e?enoaeeia anao neiaiiee.
?an/eoaiu eeiaoe/aneea eiyooeoeeaiou a oiiiiiie aaciaeeiaieea, n
eniieueciaaieai iiaeaee i?eaaaeaiiiai ecio?iiiiai e?enoaeea, e iaaiiiiie
aaciaeeiaieea ecio?iiiuo oa??iaeeyeaeo?eeia e aioeoa??iiaaiaoeeia oeia
“eaaeay ieineinoue” n o/aoii ii?yaeea /eneaiiuo eiyooeoeeaioia.

Au/eneaiu eiyooeoeeaiou caoooaiey aoi?e/iuo aiei, oeia aiei aoi?iai
caoea, a aaciaeeiaieea eaace/anoeoe.

A oiiiiiie aaciaeeiaieea, eniieuecoy iaeaeaiiua cia/aiey eeiaoe/aneeo
eiyooeoeeaioia, aeey e?enoaeea NaF ii?aaeaeaia iaeanoue nouanoaiaaiey
aoi?iai caoea, eioi?ay niaiaaeaao n iaeanoueth aai yenia?eiaioaeueiiai
iaaethaeaiey.

?an/eoaiiia /enei, aiaeiae/iia /eneo I?aiaeoey a oai?ee aacia,
iieacuaaao, /oi a oiiiiiie aaciaeeiaieea e?enoaeeia, ii?aaeaeythueie a
aeenneiaoeaiuo i?ioeannao yaeyaony oiiiiiay ayceinoue, a a iaaiiiiie
aaciaeeiaieea oa??iiaaiaoeeia ayceinoue e aeae?iaeeiaie/aneay
oaieii?iaiaeiinoue aeatho n?aaieiua aeeaaeu.

Aeey He II ?an/eoaiu ia?aay e aoi?ay ayceinoe, eiyooeoeeaio caoooaiey
ia?aiai caoea n o/aoii iaoi?oainoe ?annayiey oiiiiia ia ?ioiiao a
oe?ieii aeeaiaciia oaiia?aoo? e aeaaeaiee. Onoaiiaeaii, /oi a iaeanoe
oaiia?aoo? wmetafile8? ??????????????
???????????yyy????.????1?????? ???????
? ???&??yyyy?????Ayyyayyy`??e?? ???&? ?MathType??
????u?th??????Eeth/aaua neiaa: aaciaeeiaieea eaace/anoeoe, oiiiiu,
iaaiiiu, ?ioiiu, eeiaoe/aneea eiyooeoeeaiou, i?oiaiiaeueiua iieeiiiu.

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