Dynamics of Sound Waves in an Interacting Bose Gas
Skip to main content
eScholarship
Open Access Publications from the University of California

Dynamics of Sound Waves in an Interacting Bose Gas

  • Author(s): Deckert, D. -A.
  • Fröhlich, J.
  • Pickl, P.
  • Pizzo, A.
  • et al.

Published Web Location

https://arxiv.org/pdf/1406.1590.pdf
No data is associated with this publication.
Abstract

We consider a non-relativistic quantum gas of $N$ bosonic atoms confined to a box of volume $\Lambda$ in physical space. The atoms interact with each other through a pair potential whose strength is inversely proportional to the density, $\rho=\frac{N}{\Lambda}$, of the gas. We study the time evolution of coherent excitations above the ground state of the gas in a regime of large volume $\Lambda$ and small ratio $\frac{\Lambda}{\rho}$. The initial state of the gas is assumed to be close to a \textit{product state} of one-particle wave functions that are approximately constant throughout the box. The initial one-particle wave function of an excitation is assumed to have a compact support independent of $\Lambda$. We derive an effective non-linear equation for the time evolution of the one-particle wave function of an excitation and establish an explicit error bound tracking the accuracy of the effective non-linear dynamics in terms of the ratio $\frac{\Lambda}{\rho}$. We conclude with a discussion of the dispersion law of low-energy excitations, recovering Bogolyubov's well-known formula for the speed of sound in the gas, and a dynamical instability for attractive two-body potentials.

Item not freely available? Link broken?
Report a problem accessing this item