Finite dimensional global and exponential attractors for a coupled time-dependent Ginzburg-Landau equations for atomic Fermi gases near the BCS-BEC crossover

TL;DR

This paper proves the existence of finite-dimensional global and exponential attractors for a coupled Ginzburg-Landau system modeling atomic Fermi gases near the BCS-BEC crossover, demonstrating long-term stability and finite complexity.

Contribution

It establishes the existence of global and exponential attractors with finite fractal dimension for the coupled Ginzburg-Landau equations in this physical context.

Findings

Existence of a strongly continuous semigroup for the system.

Presence of a finite-dimensional global attractor.

Existence of an exponential attractor with finite fractal dimension.

Abstract

We study a coupled nonlinear evolution system arising from the Ginzburg-Landau theory for atomic Fermi gases near the BCS-BEC crossover. First, we prove that the initial boundary value problem generates a strongly continuous semigroup on a suitable phase-space which possesses the global attractor. Then we establish the existence of an exponential attractor. As a consequence, we show that the global attractor is of finite fractal dimension.