Semiclassical Description of Wavepacket Revival

TL;DR

This paper evaluates semiclassical methods, specifically WKB and Van Vleck propagation, for accurately describing long-time quantum wavepacket revivals in a one-dimensional quartic oscillator, demonstrating impressive agreement with quantum results.

Contribution

It provides a detailed comparison of semiclassical theories, showing their effectiveness in modeling wavepacket revivals over extended timescales, including analytical insights for Van Vleck propagation.

Findings

Both semiclassical methods accurately reproduce the autocorrelation function.

The agreement between theory and quantum results persists beyond the revival time.

Van Vleck approach's validity extends to arbitrarily long times, as shown analytically.

Abstract

We test the ability of semiclassical theory to describe quantitatively the revival of quantum wavepackets --a long time phenomena-- in the one dimensional quartic oscillator (a Kerr type Hamiltonian). Two semiclassical theories are considered: time-dependent WKB and Van Vleck propagation. We show that both approaches describe with impressive accuracy the autocorrelation function and wavefunction up to times longer than the revival time. Moreover, in the Van Vleck approach, we can show analytically that the range of agreement extends to arbitrary long times.