The Stochastic Gross-Pitaevskii Equation and some Applications

Abstract

The stochastic Gross-Pitaevskii equation represents a versatile approach for studying the dynamics of trapped degenerate ultracold Bose gases in the presence of large phase and density fluctuations. Following a brief review of the original formulation of Stoof, which highlights the benefits of this approach and its relation to alternative theories, we present selected applications for the dynamics of effectively one-dimensional systems, and briefly discuss the generalization to two-dimensional systems, highlighting certain potential pitfalls in their numerical implementations.

14 pages, 9 figures. Corrected typos

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• Spontaneous vortices in the formation of Bose-Einstein condensates
• Finite Temperature Models of Bose-Einstein Condensation
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• Bose-Einstein Condensation from a Rotating Thermal Cloud: Vortex Nucleation and Lattice Formation
• The trapped two-dimensional Bose gas: from Bose-Einstein condensation to Berezinskii-Kosterlitz-Thouless physics
• Observing the Formation of Long-range Order during Bose-Einstein Condensation
• Bose-Einstein condensation and gauge symmetry breaking
• A number-conserving approach to a minimal self-consistent treatment of condensate and non-condensate dynamics in a degenerate Bose gas
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• Population and Phase Coherence during the Growth of an Elongated Bose-Einstein Condensate
• Spatial Correlation Functions of one-dimensional Bose gases at Equilibrium

Cited by in corpus (50)

• Soliton creation during a Bose-Einstein condensation
• Winding up superfluid in a torus via Bose Einstein condensation
• Decay of a quantum vortex: test of non-equilibrium theories for warm Bose-Einstein condensates
• A stochastic approach to open quantum systems
• The stochastic projected Gross-Pitaevskii equation
• A comparison between microscopic methods for finite temperature Bose gases
• Persistent current formation in a high-temperature Bose-Einstein condensate: an experimental test for c-field theory
• Dark-bright solitons in Bose-Einstein condensates at finite temperatures
• Stochastic Projected Gross-Pitaevskii equation for spinor and multi-component condensates
• Exploring Vortex Dynamics in the Presence of Dissipation: Analytical and Numerical Results
• Exploring Rigidly Rotating Vortex Configurations and their Bifurcations in Atomic Bose-Einstein Condensates
• Kibble-Zurek Dynamics in a Trapped Ultracold Bose Gas
• Ab initio methods for finite temperature two-dimensional Bose gases
• Numerical method for the stochastic projected Gross-Pitaevskii equation
• Fluctuating and dissipative dynamics of dark solitons in quasi-condensates
• Vortex formation of a Bose-Einstein condensate in a rotating deep optical lattice
• Quantitative study of quasi-one-dimensional Bose gas experiments via the stochastic Gross-Pitaevskii equation
• Low-Dimensional Stochastic Projected Gross-Pitaevskii Equation
• Second-order, number-conserving description of non-equilibrium dynamics in finite-temperature Bose-Einstein condensates
• Langevin Simulation of Scalar Fields: Additive and Multiplicative Noises and Lattice Renormalization
• Finite temperature dynamics of vortices in Bose-Einstein condensates
• Phase coherence in quasicondensate experiments: an ab initio analysis via the stochastic Gross-Pitaevskii equation
• Persistent current formation in double-ring geometries
• Quantum hydrodynamics of the spinor Bose-Einstein condensate at non-zero temperatures
• Theoretical and numerical evidence for the potential realization of the Peregrine soliton in repulsive two-component Bose-Einstein condensates
• Cross-over to quasi-condensation: mean-field theories and beyond
• Universal Vortex Statistics and Stochastic Geometry of Bose-Einstein Condensation
• Finite temperature spin dynamics of a two-dimensional Bose-Bose atomic mixture
• Evaporative cooling of cold atoms at surfaces
• Quantum fluctuation effects on the quench dynamics of thermal quasicondensates
• Non-equilibrium Atomic Condensates and Mixtures: Collective Modes, Condensate Growth and Thermalization
• The sound-ring radiation of expanding vortex clusters
• Phase transition dimensionality crossover from two to three dimensions in a trapped ultracold atomic Bose gas
• Complex Langevin approach to interacting Bose gases
• Quantum corrections to the classical field approximation for one-dimensional quantum many-body systems in equilibrium
• Metastable order protected by destructive many-body interference
• Controlling superfluid flows using dissipative impurities
• Finite temperature ferromagnetic transition in coherently coupled Bose gases
• Dynamics of Hot Bose-Einstein Condensates: stochastic Ehrenfest relations for number and energy damping
• Symplectic quantization III: Non-relativistic limit
• Finite temperature expansion dynamics of Bose-Einstein condensates
• A quantum register using collective excitations in a Bose-Einstein condensate
• Periodic quenches across the Berezinskii-Kosterlitz-Thouless phase transition
• Geometry-induced modification of fluctuation spectrum in quasi-two-dimensional condensates
• Acceleration-induced transport of quantum vortices in joined atomtronic circuits
• Coherent transfer of topological domain walls
• Simple yet Accurate Stochastic Approach to the Quantum Phase Noise of Nanolasers
• Dynamics of the order parameter in symmetry breaking phase transitions
• Deconstructing symmetry breaking dynamics
• Local Quantum Cooling for Large Fermi Systems with Pairing