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arXiv · 0710.3693

Exponential mixing for finite-dimensional approximations of the Schrödinger equation with multiplicative noise

Vahagn Nersesyan
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Abstract

We study the ergodicity of finite-dimensional approximations of the Schrödinger equation. The system is driven by a multiplicative scalar noise. Under general assumptions over the distribution of the noise, we show that the system has a unique stationary measure $μ$ on the unit sphere $S$ in $\C^n$, and $μ$ is absolutely continuous with respect to the Riemannian volume on $S$. Moreover, for any initial condition in $S$, the solution converges exponentially fast to the measure $μ$ in the variational norm.

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Vahagn Nersesyan. 2007-10-19. Exponential mixing for finite-dimensional approximations of the Schrödinger equation with multiplicative noise. https://arxiv.org/abs/0710.3693

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