On the minimization of Hamiltonians over pure Gaussian states
Research output: Chapter in Book/Report/Conference proceeding › Book chapter › Research › peer-review
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
Original language | English |
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Title of host publication | Complex Quantum SystemsAnalysis of Large Coulomb Systems |
Editors | Heinz Siedentop |
Volume | 24 |
Publisher | World Scientific |
Publication date | 2013 |
ISBN (Print) | 978-981-4460-14-9 |
Publication status | Published - 2013 |
Series | National University of Singapore. Institute for Mathematical Sciences. Lecture Notes Series |
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Volume | 24 |
ISSN | 1793-0758 |
Links
- http://arxiv.org/abs/1102.2931
Accepted author manuscript
ID: 102670202