Strongly anomalous non-thermal fixed point in a quenched two-dimensional Bose gas

Abstract

Universal scaling behavior in the relaxation dynamics of an isolated two-dimensional Bose gas is studied by means of semi-classical stochastic simulations of the Gross-Pitaevskii model. The system is quenched far out of equilibrium by imprinting vortex defects into an otherwise phase-coherent condensate. A strongly anomalous non-thermal fixed point is identified, associated with a slowed decay of the defects in the case that the dissipative coupling to the thermal background noise is suppressed. At this fixed point, a large anomalous exponent h - 3 and, related to this, a large dynamical exponent  z 5 are identified. The corresponding power-law decay is found to be consistent with three-vortex-collision induced loss. The article discusses these aspects of non-thermal fixed points in the context of phaseordering kinetics and coarsening dynamics, thus relating phenomenological and analytical approaches to classifying far-from-equilibrium scaling dynamics with each other. In particular, a close connection between the anomalous scaling exponent η, introduced in a quantum-field theoretic approach, and conservation-law induced scaling in classical phase-ordering kinetics is revealed. Moreover, the relation to superfluid turbulence as well as to driven stationary systems is discussed. analysis as well as a comprehensive classification scheme of far-from-equilibrium universal dynamics are lacking so far.Here we consider possible universal scaling behavior of a time-evolving isolated two-dimensional (2D) quantum-degenerate Bose gas quenched far out of equilibrium. We discuss the numerically found scaling in time and in the spatial degrees of freedom in the framework of non-thermal fixed points [34][35][36][37][38]. This approach builds on a scaling analysis of non-perturbative dynamic equations for field correlation functions in the spirit of a renormalization-group approach to far-from-equilibrium dynamics [35,[39][40][41][42][43][44]. Close to a non-thermal fixed point, correlation functions show a time evolution which takes the form of a rescaling in space and time [38]. In consequence, the relaxation is critically slowed down, while correlations evolve as a power law rather than exponentially in time.We prepare far-from-equilibrium states by imprinting phase defects, i.e., quantum vortex excitations, into an otherwise strongly phase-coherent condensate. Different kinds of initial states are realized by varying the number of defects, their arrangement, and their winding numbers. Independently of the microscopic details of the initial state, such as the statistics of fluctuations, the system is attracted to one or more non-thermal fixed points where the information about these details gets lost. Close to such a fixed point the correlations exhibit and evolve according to universal power laws [45][46][47][48][49][50].More than one attractor can exist for the dynamical evolution of the system, as we will demonstrate being the case for the 2D Bose gas studied here. Consequently, different types of universal evolution wit...

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Violation of single-length-scaling dynamics via spin vortices in an isolated spin-1 Bose gas

“…Following a quench far out of equilibrium, a system can in general approach a non-thermal fixed point [10,[30][31][32][33][34][35]. Such fixed points have been discussed and experimentally observed with [35][36][37][38][39][40] and without [10,[30][31][32][33][41][42][43] reference to ordering patterns and kinetics as well as topological defects.…”

Spectral, statistical, and vertex functions in scalar quantum field theory far from equilibrium

“…5 demonstrates that the numerical data for the effective coupling collapses rather well to a common curve in the infrared momentum range when rescaled accordingly. As a check, we also determine the scaling exponents α λ and β defined by (20) directly from our numerical data without assuming the scaling relation (21), see Appendix A for details on the method. The binned data obtained for α λ in this way is plotted in Fig.…”

“…In this appendix, we present the fitting procedure employed to determine the scaling exponents α and β from the numerical data. Our method is similar to the approach put forward in [4] and [20].…”