Effective Equations of Motion for Quantum Systems

TL;DR

This paper develops a geometric method to derive effective classical equations of motion for quantum systems, aligning with path integral results and enabling quantum corrections to classical dynamics.

Contribution

It introduces a general geometric framework for deriving effective equations of motion that incorporate quantum effects, applicable to perturbations and coherent states.

Findings

Method agrees with effective action results for harmonic oscillators

Provides a way to compute quantum corrections to classical structures

Applicable to dynamical coherent states

Abstract

In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and geometrical picture is developed and shown to agree with effective action results, commonly derived through path integration, for perturbations around a harmonic oscillator ground state. The same methods are used to describe dynamical coherent states, which in turn provide means to compute quantum corrections to the symplectic structure of an effective system.