WKB Propagation of Gaussian Wavepackets

TL;DR

This paper studies how Gaussian wavepackets evolve in chaotic systems, showing they become WKB states quickly and can be propagated using classical methods without complex trajectories, with their Wigner functions developing classical and quantum features.

Contribution

It demonstrates that Gaussian wavepackets become primitive WKB states rapidly, enabling long-time propagation with standard TDWKB without complex trajectories, and characterizes their Wigner function structure.

Findings

Gaussian wavepackets become primitive WKB states after short time

Long-time propagation can be achieved with standard TDWKB scheme

Wigner functions develop classical filament structure with quantum oscillations

Abstract

We analyze the semiclassical evolution of Gaussian wavepackets in chaotic systems. We prove that after some short time a Gaussian wavepacket becomes a primitive WKB state. From then on, the state can be propagated using the standard TDWKB scheme. Complex trajectories are not necessary to account for the long-time propagation. The Wigner function of the evolving state develops the structure of a classical filament plus quantum oscillations, with phase and amplitude being determined by geometric properties of a classical manifold.