Evaluation of the semiclassical coherent state propagator in the presence of phase space caustics

TL;DR

This paper reviews a uniform approximation for the coherent state propagator near phase space caustics, applying it to model systems to demonstrate its effectiveness in complex quantum dynamics.

Contribution

It presents a detailed derivation of a uniform approximation for the coherent state propagator and applies it to both integrable and chaotic systems.

Findings

Effective approximation near phase space caustics

Application to quartic oscillator and chaotic system

Demonstrates accuracy in complex quantum systems

Abstract

A uniform approximation for the coherent state propagator, valid in the vicinity of phase space caustics, was recently obtained using the Maslov method combined with a dual representation for coherent states. In this paper we review the derivation of this formula and apply it to two model systems: the one-dimensional quartic oscillator and a two-dimensional chaotic system.