Adiabatic theorem for a class of quantum stochastic equations

Martin Fraas

Adiabatic theorem for a class of quantum stochastic equations

Mathematical Physics 2014-09-05 v2 math.MP Quantum Physics

Authors: Martin Fraas

Abstract

We derive an adiabatic theory for a stochastic differential equation, $\varepsilon\, \mathrm{d} X(s) = L_1(s) X(s)\, \mathrm{d} s + \sqrt{\varepsilon} L_2(s) X(s) \, \mathrm{d} B_s,$ 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 Schr\"{o}dinger equation describing a dephasing process.

Keywords

adiabatic quantum mechanics

Cite

@article{arxiv.1407.7127,
  title  = {Adiabatic theorem for a class of quantum stochastic equations},
  author = {Martin Fraas},
  journal= {arXiv preprint arXiv:1407.7127},
  year   = {2014}
}

Comments

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

Adiabatic theorem for a class of quantum stochastic equations

Abstract

Keywords

Cite

Comments

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