Large Deviations for Nonlinear Stochastic Schrodinger Equation

TL;DR

This paper establishes a large deviation principle for the one-dimensional stochastic nonlinear Schrödinger equation using the weak convergence approach and explores the exit problem as an application.

Contribution

It introduces a novel application of the weak convergence approach to large deviations in stochastic nonlinear Schrödinger equations.

Findings

Large deviation principle proven for the 1D stochastic nonlinear Schrödinger equation.

Application to exit problem demonstrates practical implications.

Method extends large deviation analysis to nonlinear stochastic PDEs.

Abstract

Large deviation principle by the weak convergence approach is established for the stochastic nonlinear Schrodinger equation in one-dimension and as an application the exit problem is investigated.