Mean-field quantum dynamics for a mixture of Bose-Einstein condensates

Abstract

We study the effective time evolution of a large quantum system consisting of a mixture of different species of identical bosons in interaction. If the system is initially prepared so as to exhibit condensation in each component, we prove that condensation persists at later times and we show quantitatively that the many-body Schrödinger dynamics is effectively described by a system of coupled cubic non-linear Schrödinger equations, one for each component.

Updated version, published on Anal. Math. Phys. 2016

References in corpus (2)

• Sharp thresholds of blow-up and global existence for the coupled nonlinear Schrodinger system
• Derivation of Effective Evolution Equations from Microscopic Quantum Dynamics

Cited by in corpus (21)

• Higher order corrections to the mean-field description of the dynamics of interacting bosons
• Analysis of a trapped Bose-Einstein condensate in terms of position, momentum, and angular-momentum variance
• Derivation of the Maxwell-Schrödinger Equations from the Pauli-Fierz Hamiltonian
• Ground state energy of mixture of Bose gases
• Solvable model of a generic driven mixture of trapped Bose-Einstein condensates and properties of a many-boson Floquet state at the limit of an infinite number of particles
• Mean-field dynamics for mixture condensates via Fock space methods
• Mean-field limits of particles in interaction with quantized radiation fields
• Rate of convergence towards equations of Hartree type for mixture condensates with factorized initial data
• Derivation of the 2d Gross-Pitaevskii equation for strongly confined 3d bosons
• Convergence rate towards the fractional Hartree-equation with singular potentials in higher Sobolev norms
• On the characterisation of fragmented Bose-Einstein condensation and its emergent effective evolution
• Blow-Up Profile of 2D Focusing Mixture Bose Gases
• 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
• Morphology of an interacting three-dimensional trapped Bose-Einstein condensate from many-particle variance anisotropy
• Effective non-linear spinor dynamics in a spin-1 Bose-Einstein condensate
• Uniform in Time Convergence to Bose-Einstein Condensation for a Weakly Interacting Bose Gas with an External Potential
• Fragmentation of identical and distinguishable bosons' pairs and natural geminals of a trapped bosonic mixture
• Reduced fluctuations for bosons in a double well
• On the emergence of quantum Boltzmann fluctuation dynamics near a Bose-Einstein Condensate