Abstract
We develop a framework for investigation of asymptotic behavior of quantum Markov semigroups on C*-algebras associated with noncommutative elliptic generators. An exponential rate of convergence toward the projection onto the fixed point subalgebra has been established and, in a particular case of the semigroup selecting rotationally invariant states of a three-dimensional quantum system, the time factor of such a convergence has been estimated.
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