On the minimization of Hamiltonians over pure Gaussian states

TY - CHAP

T1 - On the minimization of Hamiltonians over pure Gaussian states

AU - Derezinski, Jan

AU - Napiorkowski, Marcin

AU - Solovej, Jan Philip

PY - 2013

Y1 - 2013

N2 - 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

AB - 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

M3 - Book chapter

SN - 978-981-4460-14-9

VL - 24

T3 - National University of Singapore. Institute for Mathematical Sciences. Lecture Notes Series

BT - Complex Quantum SystemsAnalysis of Large Coulomb Systems

A2 - Siedentop, Heinz

PB - World Scientific

ER -