Classical field records of a quantum system: their internal consistency and accuracy

Abstract

We determine the regime where the widespread classical field description for quantum Bose gases is quantitatively accurate in 1d, 2d, and 3d by a careful study of the ideal gas limit. Numerical benchmarking in 1d shows that the ideal gas results carry over unchanged into the weakly interacting gas. The optimum high energy cutoff is in general shown to depend strongly on the observable in question (e.g. energy, density fluctuations, phase coherence length, condensate fraction). This explains the wide spread of past results. A consistent classical field representation with less than 10% deviation in all typical observables can be given for systems at temperatures below 0.0064 degeneracy temperature in 1d, and 0.49 critical temperature in 3d. Surprisingly, this is not possible for the 2d ideal gas even at zero temperature because mean density, density fluctuations and energy cannot be simultaneously matched to the quantum results.

10 pages, 6 figures

References in corpus (18)

• Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose condensate
• Spontaneous vortices in the formation of Bose-Einstein condensates
• Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques
• Critical Dynamics of Spontaneous Symmetry Breaking in a Homogeneous Bose gas
• Emergence of coherence in a uniform quasi-two-dimensional Bose gas
• Finite Temperature Models of Bose-Einstein Condensation
• Observation of Solitonic Vortices in Bose-Einstein Condensates
• A Stochastic Mean-Field Approach For Nuclear Dynamics
• Emergence of order from turbulence in an isolated planar superfluid
• Stochastic classical field model for polariton condensates
• Quantum turbulence and correlations in Bose-Einstein condensate collisions
• Dynamics and interaction of vortex lines in an elongated Bose-Einstein condensate
• Prethermalization in one-dimensional Bose gases: description by a stochastic Ornstein-Uhlenbeck process
• A quantum Langevin model for non-equilibrium condensation
• Nonthermal fixed points and solitons in a one-dimensional Bose gas
• Numerical method for evolving the Projected Gross-Pitaevskii equation
• Many-body physics in the classical-field description of a degenerate Bose gas
• Thermal fluctuations and quantum phase transition in antiferromagnetic Bose-Einstein condensates

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• Dynamics of thermalization of two tunnel-coupled one-dimensional quasicondensates
• Frequency beating and damping of breathing oscillations of a harmonically trapped one-dimensional quasicondensate
• Benchmarks of Generalized Hydrodynamics for 1D Bose Gases
• A tractable prescription for large-scale free flight expansion of wavefunctions
• Complex wave fields in the interacting one-dimensional Bose gas
• Viability of rotation sensing using phonon interferometry in Bose-Einstein condensates
• On the fluctuations of the number of atoms in the condensate
• Berezinskii-Kosterlitz-Thouless phase induced by dissipating quasisolitons
• Equilibrium, Relaxation and Fluctuations in homogeneous Bose-Einstein Condensates: Linearized Classical Field Analysis
• Spin distillation cooling of ultracold Bose gases