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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| Published in: | Condensed Matter Physics |
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| Date: | 2011 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут фізики конденсованих систем НАН України
2011
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/119801 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862617176656052224 |
|---|---|
| author | Brankov, J.G. Tonchev, N.S. |
| author_facet | Brankov, J.G. Tonchev, N.S. |
| 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. |
| collection | DSpace DC |
| container_title | Condensed Matter Physics |
| 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 interaction of a boson field with matter.
Отримано нескiнченнi набори нерiвностей, як i 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 iтенсивної спостережуваної з гамiльтонiаном. Результати iлюструються на двох типах точно розв’язуваних моделей: однiєї з обмеженим сепарабельним притяганням та iншої, що мiстить взаємодiю бозонного поля з матерiєю.
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| first_indexed | 2025-12-07T13:11:00Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-119801 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1607-324X |
| language | English |
| last_indexed | 2025-12-07T13:11:00Z |
| publishDate | 2011 |
| publisher | Інститут фізики конденсованих систем НАН України |
| record_format | dspace |
| spelling | Brankov, J.G. Tonchev, N.S. 2017-06-09T19:15:08Z 2017-06-09T19:15:08Z 2011 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 https://nasplib.isofts.kiev.ua/handle/123456789/119801 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 interaction of a boson field with matter. Отримано нескiнченнi набори нерiвностей, як i 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 iтенсивної спостережуваної з гамiльтонiаном. Результати iлюструються на двох типах точно розв’язуваних моделей: однiєї з обмеженим сепарабельним притяганням та iншої, що мiстить взаємодiю бозонного поля з матерiєю. N.S.T. was supported by the National Science Foundation of Bulgaria
 under grant TK–X–1712/2007. en Інститут фізики конденсованих систем НАН України Condensed Matter Physics Generalized inequalities for the Bogoliubov-Duhamel inner product with applications in the Approximating Hamiltonian Method Article published earlier |
| spellingShingle | Generalized inequalities for the Bogoliubov-Duhamel inner product with applications in the Approximating Hamiltonian Method Brankov, J.G. Tonchev, N.S. |
| title | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/119801 |
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