Being the annihilation and creation operators on the space
of square integrable Bernoulli functionals, quantum Bernoulli noises (QBN) satisfy the canonical anti-commutation relation (CAR) in equal time. Let
be the Hilbert space of an open quantum system interacting with QBN (the
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Being the annihilation and creation operators on the space
of square integrable Bernoulli functionals, quantum Bernoulli noises (QBN) satisfy the canonical anti-commutation relation (CAR) in equal time. Let
be the Hilbert space of an open quantum system interacting with QBN (the environment). Then
just describes the coupled quantum system. In this paper, we introduce and investigate an interacting stochastic Schrödinger equation (SSE) in the framework
, which might play a role in describing the evolution of the open quantum system interacting with QBN (the environment). We first prove some technical propositions about operators in
. In particular, we obtain the spectral decomposition of the tensor operator
, where
means the identity operator on
and
N is the number operator in
, and give a representation of
in terms of operators
,
, where
and
are the annihilation and creation operators on
, respectively. Based on these technical propositions as well as Mora and Rebolledo’s results on a general SSE, we show that under some mild conditions, our interacting SSE has a unique solution admitting some regularity properties. Some other results are also proven.
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