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arXiv:cond-mat/9511058 · Physical Review A

Phase ordering kinetics of the Bose gas

Kedar Damle, Satya N. Majumdar, Subir Sachdev A

Published Dec 1, 1996• 96 citations
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Abstract

We study the approach to equilibrium of a Bose gas to a superfluid state. We point out that dynamic scaling, characteristic of far from equilibrium phase-ordering systems, should hold. We stress the importance of a nondissipative Josephson precession term in driving the system to a new universality class. A model of coarsening in dimension d=2, involving a quench between two temperatures below the equilibrium superfluid transition temperature (${\mathit{T}}_{\mathit{c}}$), is exactly solved and demonstrates the relevance of the Josephson term. Numerical results on quenches from above ${\mathit{T}}_{\mathit{c}}$ in d=2,3 provide evidence for the scaling picture postulated. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.54.5037

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We study the approach to equilibrium of a Bose gas to a superfluid state. We point out that dynamic scaling, characteristic of far from equilibrium phase-ordering systems, should hold. We stress the importance of a nondissipative Josephson precession term in driving the system to a new universality class. A model of coarsening in dimension d=2, involving a quench between two temperatures below the equilibrium superfluid transition temperature (Tc{\mathit{T}}_{\mathit{c}}Tc​), is exactly solved and demonstrates the relevance of the Josephson term. Numerical results on quenches from above Tc{\mathit{T}}_{\mathit{c}}Tc​ in d=2,3 provide evidence for the scaling picture postulated. \textcopyright{} 1996 The American Physical Society.
We study the approach to equilibrium of a Bose gas to a superfluid state. We point out that dynamic scaling, characteristic of far from equilibrium phase-ordering systems, should hold. We stress the importance of a non-dissipative Josephson precession term in driving the system to a new universality class. A model of coarsening in d=2, involving a quench between two temperatures below the equilibrium superfluid transition temperature (T_c), is exactly solved and demonstrates the relevance of the Josephson term. Numerical results on quenches from above T_c in d=2,3 provide evidence for the scaling picture postulated.
We investigate the phase ordering dynamics of a uniform two-dimensional Bose gas quenched to a finite temperature in the superfluid phase. Starting from a defect-rich, far-from-equilibrium state, we model the subsequent evolution with the projected Gross-Pitaevskii equation, which conserves both energy and particle number. By tuning the initial energy, we control the effective post-quench temperature and examine its role in the equilibration dynamics. We find that the gas exhibits universal behaviour at all temperatures, evidenced by spatio-temporal scaling of correlation functions and power-law growth of the correlation length ∼t1/z\sim t^{1/z}∼t1/z, with zzz the dynamical critical exponent. We find zzz to be temperature dependent, with z≈1.5z \approx 1.5z≈1.5 for post-quench temperatures just below the Berezinskii-Kosterlitz-Thouless (BKT) transition, and z≈1.9z \approx 1.9z≈1.9 for quenches to near-zero temperature. Analysis of the Porod tail of the momentum distribution suggests a temperature-dependent competition between vortices and sound waves in the coarsening process. The two-time correlation function also exhibits universal scaling, decaying as ∼t−λ/z\sim t^{-λ/z}∼t−λ/z, with autocorrelation exponent λλλ. Near the BKT transition we obtain λ≈2λ\approx 2λ≈2, whereas λλλ is found to diverge as the effective temperature approaches zero.
Using a non-perturbative quantum kinetic framework, we develop a unified description of the far-from-equilibrium dynamics of three-dimensional Bose gases following cooling quenches across the Bose-Einstein condensation transition. By tracking the spatio-temporal evolution of the momentum distribution, we show that the equilibrium condensation threshold simultaneously acts as a dynamical critical point, separating distinct far-from-equilibrium universality classes governed by different non-equilibrium attractors. While quenches above the transition exhibit a single-timescale relaxation toward a thermal fixed point, quenches below the transition display a crossover from a transient weak-turbulence regime to a coarsening fixed point governed by the diffusive recombination of vortex lines. Quenches directly to the condensation threshold, finally, are controlled by a previously unidentified critical fixed point characterized by the superdiffusive spreading of critical fluctuations and a distinct set of dynamical exponents. Together, these dynamical scaling laws establish a far-from-equilibrium counterpart of the condensation phase transition, in which the equilibrium critical point also organizes the long-time non-equilibrium dynamics.
Abstract Using a non-perturbative quantum kinetic framework, we develop a unified description of the far-from-equilibrium dynamics of three-dimensional Bose gases following cooling quenches across the Bose-Einstein condensation transition. By tracking the spatio-temporal evolution of the momentum distribution, we show that the equilibrium condensation threshold simultaneously acts as a dynamical critical point, separating distinct far-from-equilibrium universality classes governed by different non-equilibrium attractors. While quenches above the transition exhibit a single-timescale relaxation toward a thermal fixed point, quenches below the transition display a crossover from a transient weak-turbulence regime to a coarsening fixed point governed by the diffusive recombination of vortex lines. Quenches directly to the condensation threshold, finally, are controlled by a previously unidentified critical fixed point characterized by the superdiffusive spreading of critical fluctuations and a distinct set of dynamical exponents. Together, these dynamical scaling laws establish a far-from-equilibrium counterpart of the condensation phase transition, in which the equilibrium critical point also organizes the long-time non-equilibrium dynamics.
Coarsening of an isolated far-from-equilibrium quantum system is a paradigmatic many-body phenomenon, relevant from subnuclear to cosmological length scales and predicted to feature universal dynamic scaling. Here, we observed universal scaling in the coarsening of a homogeneous two-dimensional Bose gas, with exponents that match analytical predictions. For different initial states, we reveal universal scaling in the experimentally accessible finite-time dynamics by elucidating and accounting for the initial-state-dependent prescaling effects. The methods we introduce allow direct comparison between cold-atom experiments and nonequilibrium field theory and are applicable to any study of universality far from equilibrium.
We investigate the early coarsening dynamics of an atomic Bose gas quenched into a superfluid phase. Using a two-step quench protocol, we independently control the two cooling rates during and after passing through the critical region, respectively, and measure the number of quantum vortices spontaneously created in the system. The latter cooling rate regulates the temperature during the condensate growth, consequently controlling the early coarsening dynamics in the defect formation. We find that the defect number shows a scaling behavior with the latter cooling rate regardless of the initial cooling rate, indicating universal coarsening dynamics in the early stage of condensate growth. Our results demonstrate that early coarsening not only reduces the defect density, but also affects its scaling with the quench rate, which is beyond the Kibble-Zurek mechanism.