Semiclassical quantization with a quantum adiabatic phase

Frank R. Johnston, Philip Pechukas

Jonathan M. Robbins

Tasko P. Grozdanov, Subhash Saini, Howard S. Taylor

The semiclassical method based on the Einstein-Brillouin-Keller quantization of invariant phase-space tori and the hypothesis of adiabatic invariance of classical action variables is applied in the calculation of highly excited energy levels of two-dimensional coupled oscillator systems. The results obtained are in good agreement with quantum-mechanical calculations even in the regions where the corresponding classical dynamics becomes apparently irregular. General limitations of the method are discussed.

Hiroshi Kuratsuji, Shinji Iida

A dynamical meaning is given for the phase $\ensuremath{\Gamma}$ recently found in a quantum adiabatic process. A noncanonical system, specifically a spin system coupled with a proper intrinsic system, is considered by use of a path integral in a SU (2) coherent-state representation. It is shown that $\ensuremath{\Gamma}$ appears as an addition of topological nature to the conventional action function, which leads to a novel form of the semiclassical quantization rule including the phase $\ensuremath{\Gamma}$.

Paul Houle

Luis Gottdiener