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Short-Time Behavior of the Exciton-Polariton Equations

Friday, March 17, 2017 - 9:00am - 9:50am
Keller 3-180
Stephen Shipman (Louisiana State University)
In the exciton-polariton (EP) 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 (NLS) equation, in which the photon field itself is nonlinear. For fixed initial data, nonlinear effects of order $\epsilon$ are observed at time $t=\epsilon^{1/5}$, as compared to NLS, for which nonlinear effects are observed at time $\epsilon$. These power laws are generalized to initial data of order $\epsilon^\alpha$ and nonlinearity power $p$. This is joint work with Cristi Guevara.
MSC Code: 
35Q55, 35B40, 35A35