On the variational description of the trajectories of averaging quantum dynamical maps

  • V. Zh. Sakbaev
Research Articles


We study the dynamics of quantum system with degenerated Hamiltonian. To this end we consider the approximating sequence of regularized Hamiltonians and corresponding sequence of dynamical semigroups acting in the space of quantum states. The limit points set of the sequence of regularized semigroups is obtained as the result of averaging by finitely additive measure on the set of regularizing parameters. We establish that the family of averaging dynamical maps does not possess the semigroup property and the injectivity property. We define the functionals on the space of maps of the time interval into the quantum states space such that the maximum points of this functionals coincide with the trajectories of the family of averaging dynamical maps.

Key words

finitely additive measure quantum state dynamical semigroup stochastic process 


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Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  1. 1.MIPTDolgoprudny, Moscow reg.Russia

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