Quantum statistical mechanics of electron gas in magnetic field
Electron eigenstates in a magnetic field are considered. Density of the electrical current and an averaged magnetic moment are obtained. Density of states is investigated for two-dimensional electron in a circle that is bounded by the infinite potential barrier. The present study shows that the co...
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| Дата: | 2006 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут фізики конденсованих систем НАН України
2006
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| Назва видання: | Condensed Matter Physics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/121376 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Quantum statistical mechanics of electron gas in magnetic field / I.M. Dubrovskii // Condensed Matter Physics. — 2006. — Т. 9, № 4(48). — С. 645–658. — Бібліогр.: 13 назв. — англ. |
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irk-123456789-1213762017-06-15T03:03:32Z Quantum statistical mechanics of electron gas in magnetic field Dubrovskii, I.M. Electron eigenstates in a magnetic field are considered. Density of the electrical current and an averaged magnetic moment are obtained. Density of states is investigated for two-dimensional electron in a circle that is bounded by the infinite potential barrier. The present study shows that the common quantum statistical mechanics of electron gas in a magnetic field leads to incorrect results. The magnetic moment of electron gas can be computed as the sum of averaged moments of the occupied states. The computations lead to the results that differ from the ones obtained as the derivative of the thermodynamical potential with respect to the magnetic field. Other contradictions in common statistical thermodynamics of electron gas in a magnetic field are pointed out. The conclusion is done that these contradictions arise from using the incorrect statistical operator. A new quantum function of distribution is derived from the basic principles, taking into account the law of conservation of an angular momentum. These results are in accord with the theory that has been obtained within the framework of classical statistical thermodynamics in the previous work. Розглянуто власнi стани електрону в магнiтному полi. Одержано густину електричного струму i середнiй магнiтний момент. Дослiджено густину станiв для двовимiрного електрону в колi обмеженому нескiнченним потенцiальним бар’єром. З використанням цих результатiв показано, що загальноприйнята квантова статистична механiка електронного газу в магнiтному полi приводить до помилкових результатiв. Магнiтний момент електронного газу може бути обчислений як сумма середнiх моментiв заповнених станiв. Таке обчислення приводить до результату, що вiдрiзняється вiд того, який одержується як похiдна термодинамiчного потенцiалу по магнiтному полю. Наведено й iншi протирiччя у загальноприйнятiй статистичнiй термодинамiцi електронного газу в магнiтному полi. Зроблено висновок, що цi протирiччя виникають внаслiдок використання неправильного статистичного оператора. Нова квантова функцiя розподiлу виведена з основних принципiв, беручи до уваги закон збереження кутового моменту. Цi результати узгоджуються з теорiєю, яка була виведена у рамках класичної статистичної термодинамiки у попереднiй роботi 2006 Article Quantum statistical mechanics of electron gas in magnetic field / I.M. Dubrovskii // Condensed Matter Physics. — 2006. — Т. 9, № 4(48). — С. 645–658. — Бібліогр.: 13 назв. — англ. 1607-324X PACS: 05.30.Ch, 75.20.-g DOI:10.5488/CMP.9.4.645 http://dspace.nbuv.gov.ua/handle/123456789/121376 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 |
Electron eigenstates in a magnetic field are considered. Density of the electrical current and an averaged
magnetic moment are obtained. Density of states is investigated for two-dimensional electron in a circle that
is bounded by the infinite potential barrier. The present study shows that the common quantum statistical
mechanics of electron gas in a magnetic field leads to incorrect results. The magnetic moment of electron
gas can be computed as the sum of averaged moments of the occupied states. The computations lead to the
results that differ from the ones obtained as the derivative of the thermodynamical potential with respect to
the magnetic field. Other contradictions in common statistical thermodynamics of electron gas in a magnetic
field are pointed out. The conclusion is done that these contradictions arise from using the incorrect statistical
operator. A new quantum function of distribution is derived from the basic principles, taking into account the
law of conservation of an angular momentum. These results are in accord with the theory that has been
obtained within the framework of classical statistical thermodynamics in the previous work. |
| format |
Article |
| author |
Dubrovskii, I.M. |
| spellingShingle |
Dubrovskii, I.M. Quantum statistical mechanics of electron gas in magnetic field Condensed Matter Physics |
| author_facet |
Dubrovskii, I.M. |
| author_sort |
Dubrovskii, I.M. |
| title |
Quantum statistical mechanics of electron gas in magnetic field |
| title_short |
Quantum statistical mechanics of electron gas in magnetic field |
| title_full |
Quantum statistical mechanics of electron gas in magnetic field |
| title_fullStr |
Quantum statistical mechanics of electron gas in magnetic field |
| title_full_unstemmed |
Quantum statistical mechanics of electron gas in magnetic field |
| title_sort |
quantum statistical mechanics of electron gas in magnetic field |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2006 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/121376 |
| citation_txt |
Quantum statistical mechanics of electron gas in magnetic field / I.M. Dubrovskii // Condensed Matter Physics. — 2006. — Т. 9, № 4(48). — С. 645–658. — Бібліогр.: 13 назв. — англ. |
| series |
Condensed Matter Physics |
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AT dubrovskiiim quantumstatisticalmechanicsofelectrongasinmagneticfield |
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2023-10-18T20:39:18Z |
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2023-10-18T20:39:18Z |
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1796150766033960960 |