2014/06/06 by Dirk-André Deckert, Jürg Fröhlich, Deckert, D. -A. +5
Physics and Astronomy · #Atomic and Subatomic Physics Research #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Quantum optics and atomic interactions
paper · pdf · doi:10.48550/arxiv.1406.1590
openalex publication_date 2014/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a non-relativistic quantum gas of N bosonic atoms confined to a box of volume Λ in physical space. The atoms interact with each other through a pair potential whose strength is inversely proportional to the density, ρ=\fracNΛ, of the gas. We study the time evolution of coherent excitations above the ground state of the gas in a regime of large volume Λ and small ratio \fracΛρ. The initial state of the gas is assumed to be close to a 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 Λ. 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 \fracΛρ. 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.