On the semiclassical treatment of anharmonic quantum oscillators via coherent states - The Toda chain revisited

TL;DR

This paper develops a semiclassical approach using coherent states to analyze anharmonic quantum oscillators, providing insights into quantum fluctuations, decoherence, and dynamics, exemplified by the Toda chain.

Contribution

It introduces a time-dependent variational method with coherent states for semiclassical analysis of anharmonic oscillators, including decoherence time estimation.

Findings

Square variance of Hamiltonian relates to semiclassical solutions

Method estimates decoherence times due to quantum fluctuations

Application to Toda chain demonstrates approach effectiveness

Abstract

We use coherent states as a time-dependent variational ansatz for a semiclassical treatment of the dynamics of anharmonic quantum oscillators. In this approach the square variance of the Hamiltonian within coherent states is of particular interest. This quantity turns out to have natural interpretation with respect to time-dependent solutions of the semiclassical equations of motion. Moreover, our approach allows for an estimate of the decoherence time of a classical object due to quantum fluctuations. We illustrate our findings at the example of the Toda chain.