On the minimization of Hamiltonians over pure Gaussian states
Mathematical Physics
2011-09-20 v2 math.MP
Abstract
A Hamiltonian defined as a polynomial in creation and annihilation operators is considered. After a minimization of its expectation value over pure Gaussian states, the Hamiltonian is Wick-ordered in creation and annihillation operators adapted to the minimizing state. It is shown that this procedure eliminates from the Hamiltonian terms of degree 1 and 2 that do not preserve the particle number, and leaves only terms that can be interpreted as quasiparticles excitations. We propose to call this fact Beliaev's Theorem, since to our knowledge it was mentioned for the first time in a paper by Beliaev from 1959.
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Cite
@article{arxiv.1102.2931,
title = {On the minimization of Hamiltonians over pure Gaussian states},
author = {Jan Dereziński and Marcin Napiórkowski and Jan Philip Solovej},
journal= {arXiv preprint arXiv:1102.2931},
year = {2011}
}
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10 pages