Quantum dissipation due to the interaction with chaotic degrees-of-freedom and the correspondence principle

Details Quantum dissipation due to the interaction with chaotic degrees-of-freedom and the correspondence principle Quantum dissipation due to the interaction with chaotic degrees-of-freedom and the correspondence principle

1998-10-29

arxiv.org/abs/cond-mat/9810395v3

Phys. Rev. Lett. 82, 4951-4955 (1999).

Physics

Condensed Matter

4 pages, clear presentation of the main point

Scientific paper

10.1103/PhysRevLett.82.4951

Both in atomic physics and in mesoscopic physics it is sometimes interesting to consider the energy time-dependence of a parametrically-driven chaotic system. We assume an Hamiltonian ${\cal H}(Q,P;x(t))$ where $x(t)=Vt$. The velocity $V$ is slow in the classical sense but not necessarily in the quantum-mechanical sense. The crossover (in time) from ballistic to diffusive energy-spreading is studied. The associated irreversible growth of the average energy has the meaning of dissipation. It is found that a dimensionless velocity $v_{PR}$ determines the nature of the dynamics, and controls the route towards quantal-classical correspondence (QCC). A perturbative regime and a non-perturbative semiclassical regime are distinguished.

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