Beyond Bogoliubov Dynamics

Abstract

We consider a system of N interacting bosons in the mean-field scaling regime and construct corrections to the Bogoliubov dynamics that approximate the true N-body dynamics in norm to arbitrary precision. The N-independent corrections are given in terms of the solutions of the Bogoliubov and Hartree equations and satisfy a generalized form of Wick's theorem. We determine the n-point correlation functions of the excitations around the condensate, as well as the reduced densities of the N-body system, to arbitrary accuracy, given only the knowledge of the two-point functions of a quasi-free state and the solution of the Hartree equation. In this way, the complex problem of computing all n-point correlation functions for an interacting N-body system is essentially reduced to the problem of solving the Hartree equation and the PDEs for the Bogoliubov two-point functions.

51 pages; v2: revised and extended version; v3: streamlined presentation; v4: this version appeared in Pure Appl. Analysis

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Cited by in corpus (14)

• Asymptotic expansion of low-energy excitations for weakly interacting bosons
• Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron
• Large deviation estimates for weakly interacting bosons
• Quantum Fluctuations of Many-Body Dynamics around the Gross-Pitaevskii Equation
• Bogoliubov Dynamics and Higher-order Corrections for the Regularized Nelson Model
• Weak Edgeworth expansion for the mean-field interacting Bose gas
• Asymptotic analysis of the weakly interacting Bose gas: A collection of recent results and applications
• The excitation spectrum of a Bose gas with an impurity in the Gross-Pitaevskii regime
• Out-of-time-ordered correlators of mean-field bosons via Bogoliubov theory
• Beliaev damping in Bose gas
• Derivation of the Gross-Pitaevskii Dynamics through Renormalized Excitation Number Operators
• Low-energy spectrum and dynamics of the weakly interacting Bose gas
• Asymptotic series for low-energy excitations of the Fröhlich Polaron at strong coupling
• A Note on the Binding Energy for Bosons in the Mean-field Limit