On the minimization of Hamiltonians over pure Gaussian states

Details On the minimization of Hamiltonians over pure Gaussian states On the minimization of Hamiltonians over pure Gaussian states

2011-02-15

arxiv.org/abs/1102.2931v2

Physics

Mathematical Physics

10 pages

Scientific paper

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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