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


  • 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 …

publication date

  • January 1, 2000