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Acta Mathematicae Applicatae Sinica English Series

Solutions of Ginzburg-Landau Theory for Atomic Fermi Gases Near the BCS-BEC Crossover

Shuhong, Chen, Boling, Guo

Published Jan 1, 2015• 0 citations
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Abstract

We are concerned with a time-dependent Ginzburg-Landau equations come from the superfluid atomic Fermi-gases near the Feshbach resonance from the fermion-boson model. We obtain the global existence and uniqueness of solutions to the TDGL equations near the BCS-BEC crossover.

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We construct a time-dependent Ginzburg-Landau (TDGL) theory for the superfluid atomic Fermi-gases near the Feshbach resonance from the fermion-boson model on the basis of the functional integral formalism. We show that the GL coefficients in the TDGL equation are complex numbers except in the BEC limit. The complex TDGL equation describes both damping and propagating dynamics, which leads to very rich superfluid dynamics near the Feshbach resonance. We predict multiple plane-wave modes corresponding to the in-phase and out-of-phase like oscillations between fermionic and bosonic superfluids and a galaxylike spiral pattern for a vortex.
The present article studies the dynamic behaviour of the time-dependent Ginzburg-Landau equation, which describes the phenomenon of BCS-BEC crossover.First, the appropriate prior estimates are established by Gronwall's inequality and Gagliardo-Nirenberg interpolation inequality, etc.Then, we prove the existence of the global attractor in the time-dependent Ginzburg-Landau system.Finally, the evolution of the field and the influence of physical parameters on the dynamic behaviour are demonstrated by numerical experiments, thereby validating the theory in this article.