Markov shift in non-commutative probability
نویسنده
چکیده
We consider a class of quantum dissipative semigroup on a von-Neumann algebra which admits a normal invariant state. We investigate asymptotic behavior of the dissipative dynamics and their relation to that of the canonical Markov shift. In case the normal invariant state is also faithful, we also extend the notion of ‘quantum detailed balance’ introduced by Frigerio-Gorini and prove that forward weak Markov process and backward weak Markov process are equivalent by an anti-unitary operator.
منابع مشابه
Acceptable random variables in non-commutative probability spaces
Acceptable random variables are defined in noncommutative (quantum) probability spaces and some of probability inequalities for these classes are obtained. These results are a generalization of negatively orthant dependent random variables in probability theory. Furthermore, the obtained results can be used for random matrices.
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