Adiabatic theorem for a class of quantum stochastic equations

Abstract

We derive an adiabatic theory for a stochastic differential equation, $\epsilon \mathrm{d}X(s)=L_1(s)X(s)\mathrm{d}s+\sqrt{\epsilon }{L}_2(s)X(s)\mathrm{d}{B}_s,$ 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.

Correction of a mistake in Lemma 2, several other minor changes

References in corpus (2)

• Adiabatic approximation in open quantum systems
• General Adiabatic Evolution with a Gap Condition