Subdiffusive spreading of a Bose-Einstein condensate in random potentials

Min, Bin; Li, Tiejun; Rosenkranz, Matthias; Bao, Weizhu

doi:10.1103/physreva.86.053612

Cited by 23 publications

(17 citation statements)

References 43 publications

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“…Up to now, rich and extensive research results have been obtained in experimental and theoretical understanding of ground states and dynamics of BEC. The research in this area is still very active and highly demanded due to the latest experimental and/or technological advances in BEC, such as spinor BEC [18,22,47,51], BEC with damping terms [15] or impurities [50] or random potentials [63], degenerate Fermi gas [45], Rydberg gas [53], spinorbit-coupled BEC [60], BEC at finite temperature [72], etc. These achievements have brought great challenges to AMO community, condensed matter community, and computational and applied mathematics community for modeling, simulating and understanding various interesting phenomenons related to BEC.…”

Section: Conclusion and Future Perspectivesmentioning

confidence: 99%

Mathematical theory and numerical methods for Bose-Einstein condensation

Bao¹,

Cai²

2013

Kinetic &Amp; Related Models

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470

664

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In this paper, we mainly review recent results on mathematical theory and numerical methods for Bose-Einstein condensation (BEC), based on the Gross-Pitaevskii equation (GPE). Starting from the simplest case with one-component BEC of the weakly interacting bosons, we study the reduction of GPE to lower dimensions, the ground states of BEC including the existence and uniqueness as well as nonexistence results, and the dynamics of GPE including dynamical laws, well-posedness of the Cauchy problem as well as the finite time blow-up. To compute the ground state, the gradient flow with discrete normalization (or imaginary time) method is reviewed and various full discretization methods are presented and compared. To simulate the dynamics, both finite difference methods and time splitting spectral methods are reviewed, and their error estimates are briefly outlined. When the GPE has symmetric properties, we show how to simplify the numerical methods. Then we compare two widely used scalings, i.e. physical scaling (commonly used) and semiclassical scaling, for BEC in strong repulsive interaction regime (Thomas-Fermi regime), and discuss semiclassical limits of the GPE. Extensions of these results for one-component BEC are then carried out for rotating BEC by GPE with an angular momentum rotation, dipolar BEC by GPE with long range dipole-dipole interaction, and two-component BEC by coupled GPEs. Finally, as a perspective, we show briefly the mathematical models for spin-1 BEC, Bogoliubov excitation and BEC at finite temperature.Comment: 135 pages and 10 figure

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Section: Conclusion and Future Perspectivesmentioning

confidence: 99%

Mathematical theory and numerical methods for Bose-Einstein condensation

Bao¹,

Cai²

2013

Kinetic &Amp; Related Models

Self Cite

470

664

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“…In the literatures, in some applications where the solution of the NLSE/GPE is not smooth, e.g. with random potential [10,96,140,148], then the following time-splitting finite difference (TSFD) -in which the time-splitting 6 / Computer Physics Communications 00 (2013) 1-23 7 is applied first and then the free Schrödinger equation (2.16) is discretized by the CNFD method -is used for discretizing the NLSE/GPE [29,48,49,178] as…”

Section: )mentioning

confidence: 99%

Computational methods for the dynamics of the nonlinear Schrödinger/Gross–Pitaevskii equations

Antoine

Bao

Besse

2013

Computer Physics Communications

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297

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In this paper, we begin with the nonlinear Schrödinger/Gross-Pitaevskii equation (NLSE/GPE) for modeling Bose-Einstein condensation (BEC) and nonlinear optics as well as other applications, and discuss their dynamical properties ranging from time reversible, time transverse invariant, mass and energy conservation, dispersion relation to soliton solutions. Then, we review and compare different numerical methods for solving the NLSE/GPE including finite difference time domain methods and time-splitting spectral method, and discuss different absorbing boundary conditions. In addition, these numerical methods are extended to the NLSE/GPE with damping terms and/or an angular momentum rotation term as well as coupled NLSEs/GPEs. Finally, applications to simulate a quantized vortex lattice dynamics in a rotating BEC are reported.

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“…For a theoretical analysis of global dirty boson properties, different methods have been used to describe various limits, ranging from the Bogoliubov theory [15][16][17][18][19][20][21][22][23], numerical approaches [24][25][26][27], to the Parisi replica method [28][29][30][31][32]. It turns out that long-range correlations within both the condensate and the superfluid remain, despite the presence of disorder.…”

Section: Introductionmentioning

confidence: 99%

Dipolar Bose-Einstein condensates in weak anisotropic disorder

2013

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Here we study properties of a homogeneous dipolar Bose-Einstein condensate in a weak anisotropic random potential with Lorentzian correlation at zero temperature. To this end we solve perturbatively the Gross-Pitaevskii equation to second order in the random potential strength and obtain analytic results for the disorder ensemble averages of both the condensate and the superfluid depletion, the equation of state, and the sound velocity. For a pure contact interaction and a vanishing correlation length, we reproduce the seminal results of Huang and Meng, which were originally derived within a Bogoliubov theory around a disorder-averaged background field. For dipolar interaction and isotropic Lorentzian-correlated disorder, we obtain results which are qualitatively similar to the case of an isotropic Gaussian-correlated disorder. In the case of an anisotropic disorder, the physical observables show characteristic anisotropies which arise from the formation of fragmented dipolar condensates in the local minima of the disorder potential.

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Subdiffusive spreading of a Bose-Einstein condensate in random potentials

Cited by 23 publications

References 43 publications

Mathematical theory and numerical methods for Bose-Einstein condensation

Mathematical theory and numerical methods for Bose-Einstein condensation

Computational methods for the dynamics of the nonlinear Schrödinger/Gross–Pitaevskii equations

Dipolar Bose-Einstein condensates in weak anisotropic disorder

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