BooksecrCollected Volumepp. 223–243

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

  • Martin Fraas

    Albany, USA
Adiabatic theorem for a class of stochastic differential equations on a Hilbert space cover
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Abstract

We derive an adiabatic theory for a stochastic differential equation,

ε\dX(s)=L1(s)X(s)\ds+εL2(s)X(s)\dBs,\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 L1(s)L_1(s) are also stationary states of L2(s)L_2(s). We use our results to derive the full statistics of tunneling for a driven stochastic Schrödinger equation describing a dephasing process.