Ground state energy of mixture of Bose gases

Abstract

We consider the asymptotic behavior of a system of multi-component trapped bosons, when the total particle number $N$ becomes large. In the dilute regime, when the interaction potentials have the length scale of order $O(N^{-1})$, we show that the leading order of the ground state energy is captured correctly by the Gross-Pitaevskii energy functional and that the many-body ground state fully condensates on the Gross-Pitaevskii minimizers. In the mean-field regime, when the interaction length scale is $O(1)$, we are able to verify Bogoliubov's approximation and obtain the second order expansion of the ground state energy. While such asymptotic results have several precursors in the literature on one-component condensates, the adaption to the multi-component setting is non-trivial in various respects and the analysis will be presented in details.

arXiv commentTo appear on "Reviews in Mathematical Physics" (2018)

References in corpus (22)

• The dynamics of component separation in a binary mixture of Bose-Einstein condensates
• Measurements of Relative Phase in Binary Mixtures of Bose-Einstein Condensates
• A two atomic species superfluid
• Proof of Bose-Einstein Condensation for Dilute Trapped Gases
• Bosons in a Trap: A Rigorous Derivation of the Gross-Pitaevskii Energy Functional
• Dynamical response of a Bose-Einstein condensate to a discontinuous change in internal state
• One-and-a-half quantum de Finetti theorems
• Derivation of the Gross-Pitaevskii Equation for Rotating Bose Gases
• Observation of Heteronuclear Feshbach Molecules from a ${}^{85}$Rb - ${}^{87}$Rb gas
• The excitation spectrum for weakly interacting bosons in a trap
• Geometric methods for nonlinear many-body quantum systems
• The Excitation Spectrum for Weakly Interacting Bosons
• Ground states of large bosonic systems: The gross-pitaevskii limit revisited
• Excitation spectrum of interacting bosons in the mean-field infinite-volume limit
• Complete Bose-Einstein condensation in the Gross-Pitaevskii regime
• Ground State Energy of the Low Density Fermi Gas
• Ground State Energy of the One-Component Charged Bose Gas
• Mean-field quantum dynamics for a mixture of Bose-Einstein condensates
• Derivation of the Hartree equation for compound Bose gases in the mean field limit
• Introduction to representations of the canonical commutation and anticommutation relations
• Bose particles in a box I. A convergent expansion of the ground state of a three-modes Bogoliubov Hamiltonian
• Examples of bosonic de Finetti states over finite dimensional Hilbert spaces

Cited by in corpus (9)

• Scaling limits of bosonic ground states, from many-body to nonlinear Schr{ö}dinger
• Bogoliubov Dynamics and Higher-order Corrections for the Regularized Nelson Model
• On the characterisation of fragmented Bose-Einstein condensation and its emergent effective evolution
• Effects Beyond Center-of-Mass Separability in a Trapped Bosonic Mixture: Exact Results
• Properties of a trapped multiple-species bosonic mixture at the infinite-particle-number limit: A solvable model
• Bosons in a double well: two-mode approximation and fluctuations
• Blow-Up Profile of 2D Focusing Mixture Bose Gases
• Uniform in Time Convergence to Bose-Einstein Condensation for a Weakly Interacting Bose Gas with an External Potential
• Reduced fluctuations for bosons in a double well