Resonances and adiabatic invariance in classical and quantum scattering   theory
  We discover that the energy-integral of time-delay is an adiabatic invariant in quantum scattering theory and corresponds classically to the phase space volume. The integral thus found provides a quantization condition for resonances, explaining a series of results recently found in non-relativistic and relativistic regimes. Further, a connection between statistical quantities like quantal resonance-width and classical friction has been established with a classically deterministic quantity, the stability exponent of an adiabatically perturbed periodic orbit. This relation can be employed to estimate the rate of energy dissipation in finite quantum systems. 
Sudhir R. Jain