Higher order terms for the quantum evolution of a Wick observable within the Hepp method

TL;DR

This paper develops a comprehensive expansion for the quantum evolution of Wick observables under a quadratic Hamiltonian using the Hepp method, applicable in both infinite and finite dimensions.

Contribution

It introduces a complete higher-order expansion for the evolution of Wick observables, extending the Hepp method to include higher order terms in the small parameter.

Findings

Provides a rigorous asymptotic expansion in  for Wick observables.

Bridges finite and infinite-dimensional frameworks.

Enhances understanding of semiclassical and mean field dynamics.

Abstract

The Hepp method is the coherent state approach to the mean field dynamics for bosons or to the semiclassical propagation. A key point is the asymptotic evolution of Wick observables under the evolution given by a time-dependent quadratic Hamiltonian. This article provides a complete expansion with respect to the small parameter \epsilon > 0 which makes sense within the infinite-dimensional setting and fits with finite-dimensional formulae.