Fractional generalization of the quantum Markovian master equation

V. E. Tarasov

Teoretičeskaâ i matematičeskaâ fizika, Tome 158 (2009) no. 2, pp. 214-233

Résumé

We propose a generalization of the quantum Markovian equation for observables. In this generalized equation, we use superoperators that are fractional powers of completely dissipative superoperators. We prove that the suggested superoperators are infinitesimal generators of completely positive semigroups and describe the properties of this semigroup. We solve the proposed fractional quantum Markovian equation for the harmonic oscillator with linear friction. A fractional power of the Markovian superoperator can be considered a parameter describing a measure of "screening" of the environment of the quantum system: the environmental influence on the system is absent for $\alpha=0$, the environment completely influences the system for $\alpha=1$, and we have a powerlike environmental influence for $0<\alpha<1$.

Détail

Keywords: fractional power of an operator, non-Hamiltonian quantum system, completely positive semigroup.
Mots-clés : quantum Markovian equation

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