Generalized inequalities for the Bogoliubov-Duhamel inner product with applications in the Approximating Hamiltonian Method
Infinite sets of inequalities which generalize all the known inequalities that can be used in the majorization step of the Approximating Hamiltonian method are derived. They provide upper bounds on the difference between the quadratic fluctuations of intensive observables of a N -particle system and...
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| Видавець: | Інститут фізики конденсованих систем НАН України |
|---|---|
| Дата: | 2011 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут фізики конденсованих систем НАН України
2011
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| Назва видання: | Condensed Matter Physics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/119901 |
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| Цитувати: | Generalized inequalities for the Bogoliubov-Duhamel inner product with applications in the Approximating Hamiltonian Method / J.G. Brankov, N.S. Tonchev // Condensed Matter Physics. — 2011. — Т. 14, № 1. — С. 13003: 1-17. — Бібліогр.: 37 назв. — англ. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1199012017-06-11T03:03:53Z Generalized inequalities for the Bogoliubov-Duhamel inner product with applications in the Approximating Hamiltonian Method Brankov, J.G. Tonchev, N.S. Infinite sets of inequalities which generalize all the known inequalities that can be used in the majorization step of the Approximating Hamiltonian method are derived. They provide upper bounds on the difference between the quadratic fluctuations of intensive observables of a N -particle system and the corresponding Bogoliubov-Duhamel inner product. The novel feature is that, under sufficiently mild conditions, the upper bounds have the same form and order of magnitude with respect to N for all the quantities derived by a finite number of commutations of an original intensive observable with the Hamiltonian. The results are illustrated on two types of exactly solvable model systems: one with bounded separable attraction and the other containing interactionof a boson field with matter. Отримано нескiнченнi набори нерiвностей, якi узагальнюють всi вiдомi нерiвностi, що можуть бути використанi на етапi мажорування методу апроксимуючого гамiльтонiану Вони забезпечують верхнi границi на рiзницю мiж квадратичними флуктуацiями iнтенсивних спостережуваних N-частинкової системи i вiдповiдного внутрiшнього добутку Боголюбова-Дюамеля. Новою рисою є те, що при достатньо м’яких умовах верхнi границi мають однакову форму i порядок величини по вiдношенню до N для всiх величин, отриманих шляхом скiнченного числа перестановок початкової iнтенсивої спостережуваної з гамiльтонiаном. Результати iлюструються на двох типахточно розв’язуваних моделей: однi є iз обмеженим сепарабельним притяганням та iншої, що мiстить взаємодiю бозонного поля з матерiєю. 2011 Article Generalized inequalities for the Bogoliubov-Duhamel inner product with applications in the Approximating Hamiltonian Method / J.G. Brankov, N.S. Tonchev // Condensed Matter Physics. — 2011. — Т. 14, № 1. — С. 13003: 1-17. — Бібліогр.: 37 назв. — англ. 1607-324X PACS: 05.30.Rt, 64.60.-i, 64.60.De, 64.70.Tg DOI:10.5488/CMP.14.13003 arXiv:1101.2882 http://dspace.nbuv.gov.ua/handle/123456789/119901 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 |
Infinite sets of inequalities which generalize all the known inequalities that can be used in the majorization step of the Approximating Hamiltonian method are derived. They provide upper bounds on the difference between the quadratic fluctuations of intensive observables of a N -particle system and the corresponding Bogoliubov-Duhamel inner product. The novel feature is that, under sufficiently mild conditions, the upper bounds have the same form and order of magnitude with respect to N for all the quantities derived by a finite number of commutations of an original intensive observable with the Hamiltonian. The results are illustrated on two types of exactly solvable model systems: one with bounded separable attraction and the other containing interactionof a boson field with matter. |
| format |
Article |
| author |
Brankov, J.G. Tonchev, N.S. |
| spellingShingle |
Brankov, J.G. Tonchev, N.S. Generalized inequalities for the Bogoliubov-Duhamel inner product with applications in the Approximating Hamiltonian Method Condensed Matter Physics |
| author_facet |
Brankov, J.G. Tonchev, N.S. |
| author_sort |
Brankov, J.G. |
| title |
Generalized inequalities for the Bogoliubov-Duhamel inner product with applications in the Approximating Hamiltonian Method |
| title_short |
Generalized inequalities for the Bogoliubov-Duhamel inner product with applications in the Approximating Hamiltonian Method |
| title_full |
Generalized inequalities for the Bogoliubov-Duhamel inner product with applications in the Approximating Hamiltonian Method |
| title_fullStr |
Generalized inequalities for the Bogoliubov-Duhamel inner product with applications in the Approximating Hamiltonian Method |
| title_full_unstemmed |
Generalized inequalities for the Bogoliubov-Duhamel inner product with applications in the Approximating Hamiltonian Method |
| title_sort |
generalized inequalities for the bogoliubov-duhamel inner product with applications in the approximating hamiltonian method |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/119901 |
| citation_txt |
Generalized inequalities for the Bogoliubov-Duhamel inner product with applications in the Approximating Hamiltonian Method / J.G. Brankov, N.S. Tonchev // Condensed Matter Physics. — 2011. — Т. 14, № 1. — С. 13003: 1-17. — Бібліогр.: 37 назв. — англ. |
| series |
Condensed Matter Physics |
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2023-10-18T20:35:41Z |
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