Time-Dependent Variational Approach for Boson Systems

BEC from a time-dependent variational point of view

“…The General TDHFB equations were derived in [10] using the BV variational principle. For technical reasons, they were written in terms of the creation and annihilation operators a + and a.…”

“…In this paper, we rely on a different approach, based on the time-dependent variational principle of Balian and Vénéroni (BV) [9,10]. Not only does this method retain the essential features of the physics behind the previous approximations, but it also allows one to bypass some (if not all) of the ad-hoc assumptions.…”

Anomalous density for Bose gases at finite temperature

“…Therefore, the BV principle has been used to provide the best approximation to the generating functional for two and multi-time correlation functions of a set of bosonic and fermionic observables [49][50][51][52]. More recently, it was used to derive a set of equations governing the dynamics of trapped Bose gases [53,54]. The point is that this principle uses the notion of least biased state, which is the best ansatz compatible with the constraints imposed on the system.…”

“…But our variational theory based on the minimization of an action also with Gaussian variational ansatz. The action to minimize involves two types of variational objects one related to the observables of interest and the other akin to a density matrix [45,52,53]. This leads to a set of coupled time-dependent mean field equations for the condensate, the noncondensate and the anomalous average.…”

On the Poisson Structure of the Time-Dependent Mean-Field Equations For Systems of Bosons out of Equilibrium

“…With the same notations, we take as our variational choice [17,18] for the operator A(t) a linear plus quadratic form in the operator α:…”