# Adiabatic theorem for a class of stochastic differential equations on a Hilbert space

### Martin Fraas

Albany, USA

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## Abstract

We derive an adiabatic theory for a stochastic differential equation,

$\varepsilon\, \d X(s) = L_1(s) X(s)\, \d s + \sqrt{\varepsilon} L_2(s) X(s) \, \d B_s,$

under a condition that instantaneous stationary states of $L_1(s)$ are also stationary states of $L_2(s)$. We use our results to derive the full statistics of tunneling for a driven stochastic Schrödinger equation describing a dephasing process.