Short-Time Nonlinear Effects in the Exciton-Polariton System

Authors

Cristi D. Guevara, Louisiana State University
Stephen P. Shipman, Louisiana State University

Document Type

Article

Publication Date

4-1-2018

Abstract

In the exciton-polariton system, a linear dispersive photon field is coupled to a nonlinear exciton field. Short-time analysis of the lossless system shows that, when the photon field is excited, the time required for that field to exhibit nonlinear effects is longer than the time required for the nonlinear Schrödinger equation, in which the photon field itself is nonlinear. When the initial condition is scaled by ϵ^α, it is found that the relative error committed by omitting the nonlinear term in the exciton-polariton system remains within ϵ for all times up to t= Cϵ^β, where β= (1 - α(p- 1 )) / (p+ 2). This is in contrast to β= 1 - α(p- 1) for the nonlinear Schrödinger equation. The result is proved for solutions in H^s(Rⁿ) for sCloseSPigtSPi n/2. Numerical computations indicate that the results are sharp and also hold in L²(Rⁿ).

Publication Source (Journal or Book title)

Journal of Nonlinear Science

First Page

579

Last Page

597

Recommended Citation

Guevara, C., & Shipman, S. (2018). Short-Time Nonlinear Effects in the Exciton-Polariton System. Journal of Nonlinear Science, 28 (2), 579-597. https://doi.org/10.1007/s00332-017-9419-9