Resonances and adiabatic invariance in classical and quantum scattering theory

Abstract

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.

8 pages

References in corpus (5)

• Time Delay Plots of Unflavoured Baryons
• Time delayed K+ N reactions and exotic baryon resonances
• Collision times in pi-pi and pi-K scattering and spectroscopy of meson resonances
• Open orbits and the semiclassical dwell time
• Number of quantal resonances

Cited by in corpus (4)

• Resonant Spectrum Analysis of the Conductance of Open Quantum System and Three Types of Fano Parameter
• Probabilistic Interpretation of Resonant States
• Outer Resonances and Effective Potential Analogy in Two-Dimensional Dielectric Cavities
• Qubit control using quantum Zeno effect: Action principle approach