Low-dimensional stochastic projected Gross-Pitaevskii equation

Bradley, Ashton S.; Rooney, S. J.; McDonald, R. G.

doi:10.1103/physreva.92.033631

Cited by 17 publications

(34 citation statements)

References 65 publications

(120 reference statements)

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“…where we have derived the number-damping and energy-damping drift and diffusion constants from the effective one dimensional SPGPE [17]…”

Section: Stochastic Equationsmentioning

confidence: 99%

“…While the SPGPE can be used for quantitative modelling [16,26,27] here our aim is to test our analytic solutions of the SPGPE using the stochastic Ehrenfest relations. We choose parameters that are representative of BEC experiments, and leave a first principles treatment of reservoir interactions [17] for later work. We perform simulations of the 1D SPGPE [17] with the initial condition given by Eq.…”

Section: Analytic and Numerical Solutionsmentioning

confidence: 99%

“…We present the projector terms for the SPGPE describing a BEC in an oblate parabolic trap with only one effective C-region dimension [17]. We first consider the position and momentum terms separately, and then give the terms for the dimensionless complex variable Eq.…”

Section: B Kohn Mode Projector Termsmentioning

confidence: 99%

“…The SPGPE describes the evolution of a high-temperature partially condensed system within a classical field approximation, is valid on either side of the critical point, and has been used to quantitatively model the BEC phase transition [3], and BEC dynamics observed in high-temperature experiments [16]. The complete SPGPE includes a number-damping reservoir interaction (of Ginzburg-Landau type) described in previous works [3,16], and an additional interaction involving exchange of energy with the reservoir [2]; the latter is a number-conserving interaction that can in principle have a significant influence on dissipative evolution [8,12,17,18], yet due to technical challenges, its physical effects have thus far been largely unexplored.…”

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confidence: 99%

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Dynamics of hot Bose-Einstein condensates: stochastic Ehrenfest relations for number and energy damping

et al. 2020

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Describing high-temperature Bose gases poses a long-standing theoretical challenge. We present exact stochastic Ehrenfest relations for the stochastic projected Gross-Pitaevskii equation, including both number and energy damping mechanisms, and all projector terms that arise from the energy cutoff separating system from reservoir. Analytic solutions for the center of mass position, momentum, and their two-time correlators are in close agreement with simulations of a harmonically trapped prolate system. The formalism lays the foundation to analytically explore experimentally accessible hot Bose-Einstein condensates. Contents arXiv:1908.05809v1 [cond-mat.quant-gas] B Kohn mode projector terms 21 B.1 Position and momentum 22 B.2 Dimensionless variable z(t) 23 B.3 Numerical evaluation of projector terms 23 References 24 IntroductionA system of Bose atoms with temperature T undergoes a dramatic change in behavior at the critical temperature for the formation of a Bose-Einstein condensate (BEC), T c . Far below the BEC transition T T c , a nearly pure BEC forms, consisting of a highly occupied many-body quantum state; in this regime dilute gas BEC are renowned both for their high experimental control, and precise theoretical description [1]. At temperatures T T c thermal energy dominates, the quantum statistics are unimportant, and a Boltzman description captures the physical properties of the atoms. When T ∼ T c the quantum statistics of the atoms are decisive, despite appreciable thermal energy. In a hot BEC T T c , competition between thermal and interaction effects leads to fragmentation of the condensate, and formation of vortices, solitons, and phononic excitations. A cooling quench across the transition can inject interesting excitations into the BEC that form as remnants of the broken U(1) symmetry [2, 3], and rich turbulent dynamics develop from the competition between thermal, quantum, and interaction effects, posing a challenge for theory.At low temperatures T T c , mean field theory provides a useful description, upon which the GPE and its generalizations are based. The Zaremba-Nikuni-Griffin U(1) symmetry breaking approach has proven well suited for practical calculations in the low-temperature regime [4], having the virtue that the interactions between condensate and thermal cloud, and their respective dynamics, are all included in the dynamical description. However, it's strength for low temperatures presents a limitation at high temperatures: the symmetry-breaking ansatz cannot describe strongly fluctuating systems containing large non-condensate fraction. Fortunately, the scope of the Gross-Pitaevskii equation (GPE) upon which ZNG is based goes much further than mean-field theory: GPE-like field equations appear naturally in phase-space representations of Bose gases [5], suggesting a generalization of quantum optical open systems theory [6] for describing hot Bose gases. Indeed, various generalized Gross-Pitaevskii theories have been developed for the high temperature regime, describing many modes that...

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“…where we have derived the number-damping and energy-damping drift and diffusion constants from the effective one dimensional SPGPE [17]…”

Section: Stochastic Equationsmentioning

confidence: 99%

Section: Analytic and Numerical Solutionsmentioning

confidence: 99%

Section: B Kohn Mode Projector Termsmentioning

confidence: 99%

mentioning

confidence: 99%

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Dynamics of hot Bose-Einstein condensates: stochastic Ehrenfest relations for number and energy damping

et al. 2020

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“…For example, let us cite the modeling of random fluctuations in an optical trap [1,2,3,67,68,105] or the consideration of the interactions between a cloud of non condensed atoms and the BEC [65,66,39,110,111]. This latter model involves a space and time stochastic process that describes the fluctuations of the phase and density of the condensate.…”

Section: Origin Of Stochastic Effects In Becsmentioning

confidence: 99%

Modeling and Computation of Bose-Einstein Condensates: Stationary States, Nucleation, Dynamics, Stochasticity

Antoine

Duboscq

2015

Lecture Notes in Mathematics

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Vortex Depinning in a Two-Dimensional Superfluid

Liu,

Prasad,

Baggaley

et al. 2024

J Low Temp Phys

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We employ the Gross–Pitaevskii theory to model a quantized vortex depinning from a small obstacle in a two-dimensional superfluid due to an imposed background superfluid flow. We find that, when the flow’s velocity exceeds a critical value, the vortex drifts orthogonally to the flow before subsequently moving parallel to it away from the pinning site. The motion of the vortex around the pinning site is also accompanied by an emission of a spiral-shaped sound pulse. Through simulations, we present a phase diagram of the critical flow velocity for vortex depinning together with an empirical formula that illustrates how the critical velocity increases with the height and width of the pinning site. By employing a variety of choices of initial and boundary conditions, we are able to obtain lower and upper bounds on the critical velocity and demonstrate the robustness of these results.

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Low-dimensional stochastic projected Gross-Pitaevskii equation

Cited by 17 publications

References 65 publications

Dynamics of hot Bose-Einstein condensates: stochastic Ehrenfest relations for number and energy damping

Dynamics of hot Bose-Einstein condensates: stochastic Ehrenfest relations for number and energy damping

Modeling and Computation of Bose-Einstein Condensates: Stationary States, Nucleation, Dynamics, Stochasticity

Vortex Depinning in a Two-Dimensional Superfluid

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