Generalized inequalities for the Bogoliubov-Duhamel inner product with applications in the Approximating Hamiltonian Method

被引：6

作者：

Brankov, J. G. ^{[1
,2
]}

Tonchev, N. S. ^{[3
]}

机构：

[1] Joint Inst Nucl Res, Bogoliubov Lab Theoret Phys, Dubna 141980, Russia

[2] Bulgarian Acad Sci, Inst Mech, BU-1113 Sofia, Bulgaria

[3] Bulgarian Acad Sci, Inst Solid State Phys, BU-1784 Sofia, Bulgaria

来源：

CONDENSED MATTER PHYSICS | 2011年 / 14卷 / 01期

基金：

美国国家科学基金会;

关键词：

correlation functions; Bogoliubov-Duhamel inner product; statistical-mechanical inequalities; approximating Hamiltonian method; exactly solved models; QUANTUM STATISTICAL-MECHANICS; SUPERRADIANT PHASE-TRANSITION; QUANTIZED RADIATION-FIELD; DICKE MASER MODEL; SYSTEMS; BOUNDS;

D O I：

10.5488/CMP.14.13003

中图分类号：

O469 [凝聚态物理学];

学科分类号：

070205 ;

摘要：

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.

引用

页数：17