Proof of the Variational Principle for a Pair Hamiltonian Boson Model
Valentin Zagrebnov, Joseph V. Pul\'e
TL;DR
This paper establishes a rigorous variational formula for the grand-canonical pressure of a Pair Boson Hamiltonian model using the Approximating Hamiltonian Method, advancing theoretical understanding of such quantum systems.
Contribution
It provides the first rigorous proof of the variational principle for the Pair Boson Hamiltonian model.
Findings
Derived a two-parameter variational formula for the model's pressure.
Applied the Approximating Hamiltonian Method to prove the formula rigorously.
Enhanced theoretical framework for analyzing bosonic quantum systems.
Abstract
We give a two parameter variational formula for the grand-canonical pressure of the Pair Boson Hamiltonian model. By using the Approximating Hamiltonian Method we provide a rigorous proof of this variational principle.
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Taxonomy
TopicsBlack Holes and Theoretical Physics · Cosmology and Gravitation Theories · Nonlinear Waves and Solitons