The semiclassical propagator in Fock space: dynamical echo and many-body interference

TL;DR

This paper develops a semiclassical method to analyze many-body quantum dynamics in Fock space, capturing interference effects and revealing a many-body echo phenomenon through classical solutions and quantum interference.

Contribution

It introduces a non-perturbative semiclassical approach to many-body quantum propagation in Fock space, extending Gutzwiller's method to symmetrized many-body states.

Findings

Demonstrates coherent backscattering in Fock space due to interference.

Provides a framework for understanding beyond mean-field effects.

Connects classical solutions with quantum many-body interference phenomena.

Abstract

We present a semiclassical approach to many-body quantum propagation in terms of coherent sums over quantum amplitudes associated with the solutions of corresponding classical nonlinear wave equations. This approach adequately describes interference effects in the many-body space of interacting bosonic systems. The main quantity of interest, the transition amplitude between Fock states when the dynamics is driven by both single-particlecontributions and many-body interactions of similar magnitude, is non-perturbatively constructed in the spirit of Gutzwiller's derivation of the van Vleck propagator from the path integral representation of the time evolution operator, but lifted to the space of symmetrized many-body states. Effects beyond mean-field, here representing the classical limit of the theory, are semiclassically described by means of interfering amplitudes where the action and stability of the classical solutions enter. In this way, a genuinely many-body echo phenomenon, coherent backscattering in Fock space, is presented arising due to coherent quantum interference between classical solutions related by time reversal.