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arXiv:2606.31406

Deviations beyond the Kibble-Zurek mechanism in a Spin-Orbit-Coupled Bose-Einstein Condensate with phenomenological damping

Jun-Hang Ren, Liu S, Yong-Sheng Zhang

Published Jun 30, 2026• 0 citations

Abstract

We investigate the quench dynamics in a one-dimensional spin-orbit-coupled Bose-Einstein condensate (SOC-BEC) across the phase transition from plane-wave (PW) to stripe (ST), incorporating phenomenological damping. In the dissipation-free case, a state stagnation phenomenon emerges during the PW-ST quench: for slow quenches, the system remains trapped in the PW phase due to the energy gap induced by critical slowing down, which prevents spontaneous relaxation to the stripe ground state. To explore this phenomenon and examine the universal scaling predicted by the Kibble-Zurek mechanism (KZM) in open systems, we introduce a dissipative Gross-Pitaevskii equation with a phenomenological damping term. Numerical simulations reveal that weak dissipation preserves the expected KZM power-law scaling for the freeze-out time and defect density, whereas strong dissipation or long quench times lead to significant deviations. Our results demonstrate that the KZM remains applicable in dissipative quantum systems under appropriate conditions, providing insights into nonequilibrium dynamics in open quantum systems.

DOI: 10.48550/arxiv.2606.31406

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Quench dynamics of first-order phase transitions in a homogeneous Bose-Einstein condensate with Raman-type spin-orbit coupling is investigated. By adjusting the coupling strength, the system can be driven across the critical point between the plane-wave phase and stripe phase in two opposite directions, and we find the scaling-law behaviors for both processes of phase transitions. This is different from previous studies, which only focus on the quench dynamics in the unidirectional transitions from a higher symmetric phase to a lower symmetric phase. Subsequently, we obtain the power law of the domain numbers (correlation length) and formation time (correlation time) of these phase transitions and extract the critical exponents. The results reveal the effect of the directionality of the phase transition on the dynamic scaling law.

The Kibble-Zurek mechanism (KZM) predicts the spontaneous formation of topological defects in a continuous phase transition driven at a finite rate. We propose the generation of spontaneous quantum turbulence (SQT) via the KZM during Bose-Einstein condensation induced by a thermal quench. Using numerical simulations of the stochastic projected Gross-Pitaevskii equation in two spatial dimensions, we describe the formation of a newborn Bose-Einstein condensate proliferated by quantum vortices. We establish the nonequilibrium universality of SQT through the Kibble-Zurek and Kolmogorov scaling of the incompressible kinetic energy.

The crossing of a continuous phase transition gives rise to the formation of topological defects described by the Kibble-Zurek mechanism (KZM) in the limit of slow quenches. The KZM predicts a universal power-law scaling of the defect density as a function of the quench time. We focus on the deviations from KZM experimentally observed in rapid quenches and establish their universality. While KZM scaling holds below a critical quench rate, for faster quenches the defect density and the freeze-out time become independent of the quench rate and exhibit a universal power-law scaling with the final value of the control parameter. These predictions are verified in several paradigmatic scenarios in both the classical and quantum domains.

Phase transitions are usually treated as equilibrium phenomena, which yields telltale universality classes with scaling behavior of relaxation time and healing length. However, in second-order phase transitions relaxation time diverges near the critical point ("critical slowing down"). Therefore, every such transition traversed at a finite rate is a non-equilibrium process. Kibble-Zurek mechanism (KZM) captures this basic physics, predicting sizes of domains - fragments of broken symmetry - and the density of topological defects, long-lived relics of symmetry breaking that can survive long after the transition. To test KZM we simulate Bose-Einstein condensation in a ring using stochastic Gross-Pitaevskii equation and show that BEC formation can spontaneously generate quantized circulation of the newborn condensate. The magnitude of the resulting winding numbers and the time-lag of BEC density growth - both experimentally measurable - follow scalings predicted by KZM. Our results may also facilitate measuring the dynamical critical exponent for the BEC transition.

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