On a dissipative Gross-Pitaevskii-type model for exciton-polariton condensates

TL;DR

This paper investigates a generalized dissipative Gross-Pitaevskii model for exciton-polariton condensates, establishing existence, analyzing long-term behavior, and exploring convergence to simpler regimes through numerical simulations.

Contribution

It provides the first global existence results and detailed long-time analysis for this specific dissipative model, including convergence to adiabatic regimes.

Findings

Global in-time existence established

Long-time behavior characterized for homogeneous solutions

Numerical simulations illustrate dynamics and convergence

Abstract

We study a generalized dissipative Gross-Pitaevskii-type model arising in the description of exciton-polariton condensates. We derive global in-time existence results and various a-priori estimates for this model posed on the one-dimensional torus. Moreover, we analyze in detail the long-time behavior of spatially homogenous solutions and their respective steady states and present numerical simulations in the case of more general initial data. We also study the convergence to the corresponding adiabatic regime, which results in a single damped-driven Gross-Pitaveskii equation.