Nonlinear Response Functions of Strongly Correlated Boson Fields: Bose-Einstein Condensates and Fractional Quantum Hall Systems

TL;DR

This paper calculates second order response functions of Bose-Einstein Condensates and fractional quantum Hall systems, providing insights into their nonlinear dynamics beyond linear response.

Contribution

It introduces a method to compute nonlinear response functions of BECs and FQHE systems using TDHFB equations, extending understanding beyond linear approximations.

Findings

Second order response functions for BECs at finite temperature.

Application of results to FQHE electron liquids.

Enhanced understanding of nonlinear dynamics in strongly correlated boson systems.

Abstract

The second order response functions and susceptibilities of finite temperature Bose-Einstein Condensates (BEC) in a one dimensional harmonic trap driven by an external field that couples to the particle density are calculated by solving the time-dependent Hartree-Fock-Bogoliubov (TDHFB) equations. These provide additional insight into BEC dynamics, beyond the linear response regime. The results also apply to electron liquids in the Fractional Quantum Hall Effect (FQHE) regime which can be mapped onto an effective boson system coupled to a Chern-Simons gauge field.