Time-dependent Gross-Pitaevskii equation for composite bosons as the strong-coupling limit of the fermionic BCS-RPA approximation

TL;DR

This paper demonstrates that the linear response of dilute composite bosons, described by the time-dependent Gross-Pitaevskii equation, aligns with the strong-coupling limit of the fermionic BCS-RPA approximation, linking bosonic and fermionic excited-state properties.

Contribution

It establishes a connection between the time-dependent Gross-Pitaevskii equation and the strong-coupling limit of the fermionic BCS-RPA approximation, providing a unified perspective on excited states.

Findings

Linear response of composite bosons matches the strong-coupling limit of fermionic BCS-RPA.

The Gross-Pitaevskii equation can be derived from fermionic approximations in the strong-coupling regime.

Unified description of bosonic and fermionic excited-state properties achieved.

Abstract

The linear response to a space- and time-dependent external disturbance of a system of dilute condensed composite bosons at zero temperature, as obtained from the linearized version of the time-dependent Gross-Pitaevskii equation, is shown to result also from the strong-coupling limit of the time-dependent BCS (or broken-symmetry RPA) approximation for the constituent fermions subject to the same external disturbance. In this way, it is possible to connect excited-state properties of the bosonic and fermionic systems by placing the Gross-Pitaevskii equation in perspective with the corresponding fermionic approximations