On the characterisation of fragmented Bose-Einstein condensation and its emergent effective evolution
arXiv:2211.07133 · doi:10.1088/1361-6544/ad027a
Abstract
Fragmented Bose-Einstein condensates are large systems of identical bosons displaying \emph{multiple} macroscopic occupations of one-body states, in a suitable sense. The quest for an effective dynamics of the fragmented condensate at the leading order in the number of particles, in analogy to the much more controlled scenario for complete condensation in one single state, is deceptive both because characterising fragmentation solely in terms of reduced density matrices is unsatisfactory and ambiguous, and because as soon as the time evolution starts the rank of the reduced marginals generically passes from finite to infinite, which is a signature of a transfer of occupations on infinitely many more one-body states. In this work we review these difficulties, we refine previous characterisations of fragmented condensates in terms of marginals, and we provide a quantitative rate of convergence to the leading effective dynamics in the double limit of infinitely many particles and infinite energy gap.
References in corpus (34)
- Proof of Bose-Einstein Condensation for Dilute Trapped Gases
- The multi-configurational time-dependent Hartree method for bosons: Many-body dynamics of bosonic systems
- Derivation of the Cubic Non-linear Schrödinger Equation from Quantum Dynamics of Many-Body Systems
- Fragmentation of Bose-Einstein Condensates
- Spatial fragmentation of a Bose-Einstein condensate in a double-well potential
- Mean-Field Dynamics: Singular Potentials and Rate of Convergence
- Reduced density matrices and coherence of trapped interacting bosons
- Exact quantum dynamics of bosons with finite-range time-dependent interactions of harmonic type
- Rigorous Derivation of the Gross-Pitaevskii Equation with a Large Interaction Potential
- Rate of Convergence Towards Hartree Dynamics
- The multiconfigurational time-dependent Hartree method for bosons with internal degrees of freedom: Theory and composite fragmentation of multi-component Bose-Einstein condensates
- Quantitative Derivation of the Gross-Pitaevskii Equation
- Fragmented many-body ground states for scalar bosons in a single trap
- Condensate fragmentation as a sensitive measure of the quantum many-body behavior of bosons with long-range interactions
- Derivation of the time dependent Gross-Pitaevskii equation without positivity condition on the interaction
- Quantum many-body fluctuations around nonlinear Schrödinger dynamics
- On the criterion for Bose-Einstein condensation for particles in traps
- Derivation of the nonlinear Schrödinger equation from a many body Coulomb system
- Time-dependent multi-orbital mean-field for fragmented Bose-Einstein condensates
- Revealing single-trap condensate fragmentation by measuring density-density correlations after time of flight
- Interacting trapped bosons yield fragmented condensate states in low dimensions
- Rate of Convergence in Nonlinear Hartree Dynamics with Factorized Initial Data
- 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
- Higher order corrections to the mean-field description of the dynamics of interacting bosons
- Generalized Bose-Einstein Condensation
- Ground state energy of mixture of Bose gases
- Rate of Convergence towards Hartree Dynamics with Singular Interaction Potential
- On a fragmented condensate in a uniform Bose system
- Dynamics of Ultracold Bosons in Artificial Gauge Fields: Angular Momentum, Fragmentation, and the Variance of Entropy
- Mean-field dynamics for mixture condensates via Fock space methods
- Rate of convergence towards equations of Hartree type for mixture condensates with factorized initial data
- On the time dependence of the rate of convergence towards Hartree dynamics for interacting Bosons
- Effective non-linear spinor dynamics in a spin-1 Bose-Einstein condensate
Cited by in corpus (4)
- Condensates Breaking Up Under Rotation
- Interference of longitudinal and transversal fragmentations in the Josephson tunneling dynamics of Bose-Einstein condensates
- Fragmentation of a trapped multiple-species bosonic mixture
- Uniform in Time Convergence to Bose-Einstein Condensation for a Weakly Interacting Bose Gas with an External Potential