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arXiv:1601.06623 · Journal of Computational Mathematics

Exponential Integrators for Stochastic Schrödinger Equations Driven by Itô Noise

Rikard Anton, David Cohen

Published Feb 11, 2018• 30 citations
arXivHTMLPDF

Abstract

We study an explicit exponential scheme for the time discretisation of stochastic Schrödinger Equations Driven by additive or Multiplicative Itô Noise. The numerical scheme is shown to converge with strong order 1 if the noise is additive and with strong order 1/2 for multiplicative noise. In addition, if the noise is additive, we show that the exact solutions of the linear stochastic Schrödinger equations satisfy trace formulas for the expected mass, energy, and momentum (i. e., linear drifts in these quantities). Furthermore, we inspect the behaviour of the numerical solutions with respect to these trace formulas. Several numerical simulations are presented and confirm our theoretical results.

DOI
10.4208/jcm.1701-m2016-0525

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