Taming the entanglement in the dynamical theory of weakly interacting Bose gases

TL;DR

This paper introduces a modified Bogoliubov theory for weakly interacting Bose gases that incorporates decoherence steps, reducing entanglement complexity and enabling a classical stochastic description of quantum dynamics.

Contribution

It presents a novel approach to simplify quantum dynamics by transforming entanglement into classical entropy, applicable to a broad class of quantum systems.

Findings

Reduces entanglement in Bose gas dynamics

Achieves exponential accuracy in the mean field limit

Extends to general quantum systems with variational ground states

Abstract

I show that the dynamics of the weakly interacting bose gas can be described by a modified time dependent Bogoliubov theory. The novelty of the approach is to include decoherence steps that gradually transform the entanglement entropy of the pure state into the von Neumann entropy of a statistical mixture. This approximation drastically reduces the entanglement that is needed in order to represent the system's state while becoming exponentially accurate in the mean field limit. I argue that this scheme can be extended to all quantum systems whose ground state can be well approximated by a variational wave function. The upshot is that the dynamics of almost all quantum systems can be reduced to stochastic classical motion supplemented with small quantum fluctuations.