Coherent Quantum Dynamics: What Fluctuations Can Tell

TL;DR

This paper develops systematic expansions for expectation values in coherent states, revealing that energy fluctuations are primarily driven by classical variable dynamics, with applications to various quantum models and Loop Quantum Gravity.

Contribution

It introduces general expansions for operator expectation values in coherent states and links energy fluctuations to classical variable dynamics, extending understanding across multiple quantum systems.

Findings

Energy fluctuations are mainly due to classical variable time dependence.

Derived systematic expansions for expectation values in coherent states.

Applied results to models like Lipkin-Meshkov-Glick, Dicke, and spin networks.

Abstract

Coherent states provide a natural connection of quantum systems to their classical limit and are employed in various fields of physics. Here we derive general systematic expansions, with respect to quantum parameters, of expectation values of products of arbitrary operators within both oscillator coherent states and SU(2) coherent states. In particular, we generally prove that the energy fluctuations of an arbitrary Hamiltonian are in leading order entirely due to the time dependence of the classical variables. These results add to the list of wellknown properties of coherent states and are applied here to the Lipkin-Meshkov-Glick model, the Dicke model, and to coherent intertwiners in spin networks as considered in Loop Quantum Gravity.