Quantum Dynamics, Coherent States and Bogoliubov Transformations

TL;DR

This paper discusses how coherent states and Bogoliubov transformations can be used to approximate the dynamics of interacting bosons in the Gross-Pitaevskii regime, aiding the understanding of non-equilibrium behavior.

Contribution

It introduces a method using coherent states and Bogoliubov transformations to approximate many-body dynamics of bosons in the Gross-Pitaevskii regime.

Findings

Effective approximation of many-body dynamics

Application of Bogoliubov transformations in non-equilibrium systems

Enhanced understanding of bosonic systems in the Gross-Pitaevskii regime

Abstract

Systems of interest in physics are usually composed by a very large number of interacting particles. At equilibrium, these systems are described by stationary states of the many-body Hamiltonian (at zero temperature, by the ground state). The reaction to perturbations, for example to a change of the external fields, is governed by the time-dependent many-body Schroedinger equation. Since it is typically very difficult to extract useful information from the Schroedinger equation, one of the main goals of non-equilibrium statistical mechanics is the derivation of effective evolution equations which can be used to predict the macroscopic behavior of the system. In these notes, we are going to consider systems of interacting bosons in the so called Gross-Pitaevskii regime, and we are going to show how coherent states and Bogoliubov transformations can be used to approximate the many body dynamics.