Integrable dynamics of coupled Fermi-Bose condensates

TL;DR

This paper provides an exact analytical solution for the integrable dynamics of coupled Fermi-Bose condensates, revealing their evolution through a variable separation method and connecting to the BCS model.

Contribution

It introduces a comprehensive analytical approach to solve the mean-field dynamics of coupled Fermi-Bose systems, extending previous BCS model studies.

Findings

Derived the general solution for coupled Fermi-Bose condensates.

Identified a full set of integrals of motion for the system.

Established a connection between the generalized Dicke model and the BCS problem.

Abstract

We study the mean-field dynamics of a fermionic condensate interacting with a single bosonic mode (a generalized Dicke model). This problem is integrable and can be mapped onto a corresponding BCS problem. We derive the general solution and a full set of integrals of motion for the time evolution of coupled Fermi-Bose condensates. The present paper complements our earlier study of the dynamics of the BCS model (cond-mat/0407501 and cond-mat/0505493). Here we provide a self-contained introduction to the variable separation method, which enables a complete analytical description of the evolution of the generalized Dicke, BCS, and other similar models.