Semiclassical investigation of revival phenomena in one dimensional system

TL;DR

This paper demonstrates that semiclassical methods can effectively reproduce quantum revival phenomena in one-dimensional systems by capturing interference effects, despite classical manifolds spreading over phase space.

Contribution

The study shows that semiclassical approaches can accurately model quantum revivals in 1D systems, bridging classical and quantum descriptions of interference effects.

Findings

Semiclassical methods reproduce quantum revivals in the infinite square well.

Semiclassical amplitudes exhibit destructive and constructive interference.

Classical manifolds spread uniformly, yet interference localizes wavepackets.

Abstract

In a quantum revival, a localized wavepacket re-forms or "revives" into a compact reincarnation of itself long after it has spread in an unruly fashion over a region restricted only by the potential energy. This is a purely quantum phenomenon, which has no classical analog. Quantum revival, and Anderson localization, are members of a small class of subtle interference effects resulting in a quantum distribution radically different from the classical after long time evolution under classically nonlinear evolution. However it is not clear that semiclassical methods, which start with the classical density and add interference effects, are in fact capable of capturing the revival phenomenon. Here we investigate two different one dimensional systems, the infinite square well and Morse potential. In both cases, after a long time the underlying classical manifolds are spread rather uniformly over phase space and are correspondingly spread in coordinate space, yet the semiclassical amplitudes are able to destructively interfere over most of coordinate space and constructively interfere in a small region, correctly reproducing a quantum revival. Further implications of this ability are discussed.