Semiclassical Ehrenfest Paths

TL;DR

This paper introduces a method to determine semiclassical paths directly from classical trajectories, providing insights into quantum-classical transition for short times without complex calculations.

Contribution

It offers a new approach to approximate quantum averages in phase space using classical trajectories and the Heller semiclassical approximation, avoiding complex intermediate steps.

Findings

Valid for short propagation times

Provides non-trivial quantum-classical transition insights

Simplifies semiclassical path determination

Abstract

Trajectories are a central concept in our understanding of classical phenomena and also in rationalizing quantum mechanical effects. In this work we provide a way to determine semiclassical paths, approximations to quantum averages in phase space, directly from classical trajectories. We avoid the need of intermediate steps, like particular solutions to the Schroedinger equation or numerical integration in phase space by considering the system to be initially in a coherent state and by assuming that its early dynamics is governed by the Heller semiclassical approximation. Our result is valid for short propagation times only, but gives non-trivial information on the quantum-classical transition.