Chaos, Fluctuations, Dissipation, Friction and Quantal-Classical Correspondence Academic Article

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• Overview
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• We make the first steps towards a theory for energy spreading and quantum dissipation. Dissipation means an irreversible systematic growth of the (average) bath energy. The bath is being driven by a classical degree of freedom. The latter is represented in the Hamiltonian by a time-dependent parameter $x (t)$. For example, $x$ may represent the position of apiston'inside a large cavity. It is assumed that $\dot {x}= V$, where $V$ is a slow velocity in the classical sense. The velocity $V$ is not necessarily slow in the quantum-mechanical case. Dissipation is associated with the stochastic spreading of energy across levels. The latter can be characterized by a transition probability kernel $P_t (n| m)$ where $n$ and $m$ are level indices. This kernel is the main object of the present study. We shall define a scaled-velocity $v_ {PR}$. Our main observation is that $v_ {PR}< 1$ is a necessary …