Title: Generalized inequalities for the Bogoliubov-Duhamel inner product with applications in the Approximating Hamiltonian Method
Author(s):

	J.G. Brankov (Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russian Federation) ,
	N.S. Tonchev (Institute of Solid State Physics, Bulgarian Academy of Science, 72 Tzarigradsko Chaussee Blvd., 1784 Sofia, Bulgaria)

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.

Key words: correlation functions, Bogoliubov-Duhamel inner product, statistical-mechanical inequalities, approximating Hamiltonian method, exactly solved models
PACS: 05.30.Rt, 64.60.-i, 64.60.De, 64.70.Tg
Comments: Refs. 37

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