On the Hartree-Fock-Bogoliubov equations
Volker Bach, S\'ebastien Breteaux, Thomas Chen, J\"urg Fr\"ohlich,, Israel Michael Sigal
TL;DR
This paper reviews the derivation and analysis of the time-dependent Hartree-Fock-Bogoliubov equations as an approximation for quantum fluctuations in Bose gases, based on a nonlinear quasifree approach.
Contribution
It introduces a nonlinear quasifree approximation to derive and analyze the time-dependent HFB equations for Bose gases.
Findings
Derivation of the time-dependent Hartree-Fock-Bogoliubov equations.
Analysis of properties of the HFB equations.
Approximate description of quantum fluctuations around Bose-Einstein condensates.
Abstract
We review some results of our paper arXiv:1602.05171v2 on the "nonlinear quasifree approximation" to the many-body Schr\"odinger dynamics of Bose gases. In that paper, we derive, with the help of this approximation, the time-dependent Hartree-Fock-Bogoliubov (HFB) equations, providing an approximate description of the dynamics of quantum fluctuations around a Bose-Einstein condensate and study properties of these equations.
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Taxonomy
TopicsCold Atom Physics and Bose-Einstein Condensates · Quantum Information and Cryptography · Quantum many-body systems