Journal of Mathematical Physics

Linear stochastic Schrödinger equations in terms of quantum Bernoulli noises

Jinshu Chen, Caishi Wang

Published May 1, 2017• 11 citations

Abstract

Quantum Bernoulli noises (QBN) are the family of annihilation and creation operators acting on Bernoulli functionals, which satisfy a canonical anti-commutation relation. In this paper, we study linear stochastic Schrödinger equations (LSSEs) associated with QBN in the space of square integrable complex-valued Bernoulli functionals. We first rigorously prove a formula concerning the number operator N on Bernoulli functionals. And then, by using this formula as well as Mora and Rebolledo’s results on a general LSSE [C. M. Mora and R. Rebolledo, Infinite. Dimens. Anal. Quantum Probab. Relat. Top. 10, 237–259 (2007)], we obtain an easily checking condition for a LSSE associated with QBN to have a unique Nr-strong solution of mean square norm conservation for given r≥0. Finally, as an application of this condition, we examine a special class of LSSEs associated with QBN and some further results are proven.

DOI: 10.1063/1.4983660

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