Classical Limit of Quantum Dissipative Systems

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We discuss the Lindblad equation for the density matrix where the dissipation is linear in the position operator. We consider a potential which is a bounded perturbation of the harmonic oscillator. We show that the perturbation of the potential leads to an analytic perturbation of the Wigner distribution. Then the Wigner distribution of the quantum dissipative system tends (uniformly in time) to the classical phase space distribution of the classical dissipative system (if the initial distribution converges when ħ → 0).

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