The role of angular momentum conservation law in statistical mechanics
Within the limits of Khinchin ideas [A.Y. Khinchin, Mathematical Foundation of Statistical Mechanics. NY, Ed. Dover, 1949] the importance of momentum and angular momentum conservation laws was analyzed for two cases: for uniform magnetic field and when magnetic field is absent. The law of momentum...
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| Видавець: | Інститут фізики конденсованих систем НАН України |
|---|---|
| Дата: | 2008 |
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут фізики конденсованих систем НАН України
2008
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| Назва видання: | Condensed Matter Physics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/119572 |
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| Цитувати: | The role of angular momentum conservation law in statistical mechanics / I.M. Dubrovskii // Condensed Matter Physics. — 2008. — Т. 11, № 4(56). — С. 585-596. — Бібліогр.: 11 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1195722017-06-08T03:06:23Z The role of angular momentum conservation law in statistical mechanics Dubrovskii, I.M. Within the limits of Khinchin ideas [A.Y. Khinchin, Mathematical Foundation of Statistical Mechanics. NY, Ed. Dover, 1949] the importance of momentum and angular momentum conservation laws was analyzed for two cases: for uniform magnetic field and when magnetic field is absent. The law of momentum conservation does not change the density of probability distribution in both cases, just as it is assumed in the conventional theory. It is shown that in systems where the kinetic energy depends only on particle momenta canonically conjugated with Cartesian coordinates being their diagonal quadric form,the angular momentum conservation law changes the density of distribution of the system only in case the full angular momentum of a system is not equal to zero. In the gas of charged particles in a uniform magnetic field the density of distribution also varies if the angular momentum is zero [see Dubrovskii I.M., Condensed Matter Physics, 2206, 9, 23]. Twodimensional gas of charged particles located within a section of an endless strip filled with gas in magnetic field is considered. Under such conditions the angular momentum is not conserved. Directional particle ows take place close to the strip boundaries, and, as a consequence, the phase trajectory of the considered set of particles does not remain within the limited volume of the phase space. In order to apply a statistical thermodynamics method, it was suggested to consider near-boundary trajectories relative to a reference system that moves uniformly. It was shown that if the diameter of an orbit having average thermal energy is much smaller than a strip width, the corrections to thermodynamic functions are small depending on magnetic field. Only the average velocity of near-boundary particles that form near-boundary electric currents creating the paramagnetic moment turn out to be essential. У рамках iдей Хiнчина [А.Я. Хинчин, Математические принципы статистической механики. ГИТТЛ, Москва-Ленинград, 1943] розглянуто закони збереження iмпульсу i кутового моменту у випадках присутностi або вiдсутностi магнiтного поля. Закон збереження iмпульсу не змiнює розподiлу густини ймовiрностi, як i передбачалося у загальноприйнятiй теорiї. Показано, що у системах, кiнетична енергiя яких залежить тiльки вiд iмпульсiв частинок, канонiчно спряжених декартовим координатам, i є дiагональною квадратичною формою, закон збереження кутового моменту змiнює розподiл густини ймовiрностi тiльки, якщо повний кутовий момент системи не дорiвнює нулю. Для газу заряджених частинок у магнiтному полi розподiл густини ймовiрностi змiнюється i у випадку нульового повного кутового моменту [Dubrovskii I.M., Condensed Matter Physics, 2206, 9, 23]. Розглянуто двовимiрний газ заряджених частинок, що знаходиться на вiдрiзку необмеженої смуги, у магнiтному полi. У цих умовах кутовий момент не зберiгається. Поблизу границь смуги iснують спрямованi потоки частинок, тому фазова траєкторiя газу, що розглядається, не залишається у обмеженiй областi фазового простору. Щоб застосувати до цього випадку метод статистичної механiки, запропоновано розглядати траєкторiї поблизу границь у системi вiдлiку, що рiвномiрно рухається. При цьому виявляється, що поправки до термодинамiчних функцiй, що залежать вiд магнiтного поля малi, якщо дiаметр орбiти з середньою термiчною енергiєю значно менший, нiж ширина смуги. Суттєва тiльки середня швидкiсть частинок, що вiдбиваються вiд границь. Цi частинки утворюють поблизу границь електричний струм, що породжує магнiтний момент. 2008 Article The role of angular momentum conservation law in statistical mechanics / I.M. Dubrovskii // Condensed Matter Physics. — 2008. — Т. 11, № 4(56). — С. 585-596. — Бібліогр.: 11 назв. — англ. 1607-324X PACS: 05.20.Gg, 75.20.-g DOI:10.5488/CMP.11.4.585 http://dspace.nbuv.gov.ua/handle/123456789/119572 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
Within the limits of Khinchin ideas [A.Y. Khinchin, Mathematical Foundation of Statistical Mechanics. NY,
Ed. Dover, 1949] the importance of momentum and angular momentum conservation laws was analyzed for
two cases: for uniform magnetic field and when magnetic field is absent. The law of momentum conservation
does not change the density of probability distribution in both cases, just as it is assumed in the conventional
theory. It is shown that in systems where the kinetic energy depends only on particle momenta canonically
conjugated with Cartesian coordinates being their diagonal quadric form,the angular momentum conservation
law changes the density of distribution of the system only in case the full angular momentum of a system is
not equal to zero. In the gas of charged particles in a uniform magnetic field the density of distribution also
varies if the angular momentum is zero [see Dubrovskii I.M., Condensed Matter Physics, 2206, 9, 23]. Twodimensional
gas of charged particles located within a section of an endless strip filled with gas in magnetic
field is considered. Under such conditions the angular momentum is not conserved. Directional particle ows
take place close to the strip boundaries, and, as a consequence, the phase trajectory of the considered set
of particles does not remain within the limited volume of the phase space. In order to apply a statistical thermodynamics
method, it was suggested to consider near-boundary trajectories relative to a reference system
that moves uniformly. It was shown that if the diameter of an orbit having average thermal energy is much
smaller than a strip width, the corrections to thermodynamic functions are small depending on magnetic field.
Only the average velocity of near-boundary particles that form near-boundary electric currents creating the
paramagnetic moment turn out to be essential. |
| format |
Article |
| author |
Dubrovskii, I.M. |
| spellingShingle |
Dubrovskii, I.M. The role of angular momentum conservation law in statistical mechanics Condensed Matter Physics |
| author_facet |
Dubrovskii, I.M. |
| author_sort |
Dubrovskii, I.M. |
| title |
The role of angular momentum conservation law in statistical mechanics |
| title_short |
The role of angular momentum conservation law in statistical mechanics |
| title_full |
The role of angular momentum conservation law in statistical mechanics |
| title_fullStr |
The role of angular momentum conservation law in statistical mechanics |
| title_full_unstemmed |
The role of angular momentum conservation law in statistical mechanics |
| title_sort |
role of angular momentum conservation law in statistical mechanics |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2008 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/119572 |
| citation_txt |
The role of angular momentum conservation law in statistical mechanics / I.M. Dubrovskii // Condensed Matter Physics. — 2008. — Т. 11, № 4(56). — С. 585-596. — Бібліогр.: 11 назв. — англ. |
| series |
Condensed Matter Physics |
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AT dubrovskiiim theroleofangularmomentumconservationlawinstatisticalmechanics AT dubrovskiiim roleofangularmomentumconservationlawinstatisticalmechanics |
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2023-10-18T20:34:53Z |
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2023-10-18T20:34:53Z |
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1796150574660452352 |