Higher Order Corrections to the Mean-Field Description of the Dynamics of Interacting Bosons

Lea Boßmann, Nataša Pavlović, Peter Pickl, Avy Soffer

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

In this paper, we introduce a novel method for deriving higher order corrections to the mean-field description of the dynamics of interacting bosons. More precisely, we consider the dynamics of Nd-dimensional bosons for large N. The bosons initially form a Bose–Einstein condensate and interact with each other via a pair potential of the form (N- 1) - 1Nd βv(Nβ·) for β∈[0,14d). We derive a sequence of N-body functions which approximate the true many-body dynamics in L2(RdN) -norm to arbitrary precision in powers of N- 1. The approximating functions are constructed as Duhamel expansions of finite order in terms of the first quantised analogue of a Bogoliubov time evolution.

Original languageEnglish (US)
Pages (from-to)1362-1396
Number of pages35
JournalJournal of Statistical Physics
Volume178
Issue number6
DOIs
StatePublished - Mar 1 2020

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Keywords

  • Bose-Einstein condensation
  • Many-body quantum dynamics
  • Mean-field scaling
  • Norm approximation

Fingerprint

Dive into the research topics of 'Higher Order Corrections to the Mean-Field Description of the Dynamics of Interacting Bosons'. Together they form a unique fingerprint.

Cite this