Time-Dependent Variational Approach to Bose-Einstein Condensation
Luca Salasnich (INFM, Univ. Milano)
TL;DR
This paper develops a time-dependent variational method using Gaussian wave-functions to analyze the dynamics, stability, and collective excitations of Bose-Einstein condensates in harmonic traps, connecting mean-field and many-body theories.
Contribution
It introduces a variational approach with time-dependent Gaussian functions to study BEC dynamics, bridging mean-field and exact many-body descriptions.
Findings
Analysis of static configurations and stability of BECs
Study of collective oscillations and vortex dynamics
Connection between mean-field and many-body theories
Abstract
We discuss the mean-field approximation for a trapped weakly-interacting Bose-Einstein condensate (BEC) and its connection with the exact many-body problem by deriving the Gross-Pitaevskii action of the condensate. The mechanics of the BEC in a harmonic potential is studied by using a variational approach with time-dependent Gaussian trial wave-functions. In particular, we analyze the static configurations, the stability and the collective oscillations for both ground-state and vortices.
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