From a nonlinear string to a weakly interacting Bose gas

TL;DR

This paper demonstrates how a classical nonlinear wave equation can effectively describe a quantum many-boson system by introducing a universal action and a carefully chosen frequency cut-off, linking classical and quantum descriptions.

Contribution

It establishes a method to model quantum interacting bosons using classical nonlinear wave dynamics with a specific action and frequency cut-off.

Findings

Classical nonlinear wave equations can approximate quantum boson systems.

A universal action equal to Planck's constant is essential for particle number definition.

Proper cut-off selection ensures macroscopic occupation of low-frequency modes.

Abstract

We investigate a real scalar field whose dynamics is governed by a nonlinear wave equation. We show that classical description can be applied to a quantum system of many interacting bosons provided that some quantum ingredients are included. An universal action has to be introduced in order to define particle number. The value of this action should be equal to the Planck constant. This constrain can be imposed by removing high frequency modes from the dynamics by introducing a cut-off. We show that the position of the cut-off has to be carefully adjusted. Finally, we show the proper choice of the cut-off ensures that all low frequency eigenenmodes which are taken into account are macroscopically occupied.