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arXiv:1203.3651 · New Journal of Physics

Non-thermal fixed points and solitons in a one-dimensional Bose gas

Maximilian Schmidt, Sebastian Erne, Boris Nowak, Dénes Sexty, Thomas Gasenzer

Published Jul 3, 2012• 44 citations
arXivHTMLPDF

Abstract

Single-particle momentum spectra for a dynamically evolving one-dimensional Bose gas are analysed in the semi-classical wave limit. Representing one of the simplest correlation functions these give information about possible universal scaling behaviour. Motivated by the previously discovered connection between (quasi-)topological field configurations, strong wave turbulence, and nonthermal fixed points of quantum field dynamics, soliton formation is studied with respect to the appearance of transient power-law spectra. A random-soliton model is developed to describe the spectra analytically, and the analogies and difference between the appearing power laws and those found in a field theory approach to strong wave turbulence are discussed. The results open a view on solitary wave dynamics from the point of view of critical phenomena far from thermal equilibrium and on a possibility to study this dynamics in experiment without the necessity of detecting solitons in situ.

DOI
10.1088/1367-2630/14/7/075005

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Single-particle momentum spectra for a dynamically evolving one-dimensional Bose gas are analysed in the semi-classical wave limit. Representing one of the simplest correlation functions these give information about possible universal scaling behaviour. Motivated by the previously discovered connection between (quasi-)topological field configurations, strong wave turbulence, and nonthermal fixed points of quantum field dynamics, soliton formation is studied with respect to the appearance of transient power-law spectra. A random-soliton model is developed to describe the spectra analytically, and the analogies and difference between the appearing power laws and those found in a field theory approach to strong wave turbulence are discussed. The results open a view on solitary wave dynamics from the point of view of critical phenomena far from thermal equilibrium and on a possibility to study this dynamics in experiment without the necessity of detecting solitons in situ.
Abstract This chapter considers nearly coherent Bose gases brought far out of equilibrium and their behavior in the context of connections between universal properties, (quasi-)topological field configurations, and turbulent dynamics. The isolated Bose gas, on its way back to thermal equilibrium, can approach metastable nonequilibrium configurations and spend a long time in their vicinity. In such configurations, termed nonthermal fixed points, the system shows universal long-range properties manifest through scaling, i.e. self-similar correlations. The time evolution near such fixed points undergoes critical slowing down. The spatial field pattern, at the same time, is characterized by the appearance of defects and domain formation whose geometry gives rise to the particular scaling laws seen in the correlation functions. An overall picture is obtained that connects well-known concepts for describing universal dynamics such as wave turbulence, superfluid turbulence, and (quasi-)topological excitations. The extension to fermionic and gauge fields should reveal many interesting new aspects.
In these notes we discuss recent developments in the field of non-equilibrium quantum dynamics. Specifically, we consider nearly coherent Bose gases brought far out of equilibrium and study their behaviour in view of connections between universal properties, (quasi-)topological field configurations and turbulent dynamics. We demonstrate that the isolated Bose gas, on its way back to thermal equilibrium, can approach metastable non-equilibrium configurations and spend a long time in their vicinity. In such configurations, which have been termed non-thermal fixed points, the system shows universal long-range properties manifest through scaling, i.e., self-similar correlations. The spatial field pattern, at the same time, is characterized by the appearance of defects and domain formation whose geometry gives rise to the particular scaling laws seen in the correlation functions. We obtain an overall picture which connects well-known concepts for describing universal dynamics such as wave-turbulence, superfluid turbulence, and (quasi-)topological excitations. This allows to bring together a wide range of concepts and methods with a large spectrum of applications.
Quasistationary far-from-equilibrium critical states of a two-component Bose gas are studied in two spatial dimensions. After the system has undergone an initial dynamical instability it approaches a nonthermal fixed point. At this critical point the structure of the gas is characterized by ensembles of (quasi)topological defects such as vortices, skyrmions, and solitons which give rise to universal power-law behavior of momentum correlation functions. The resulting power-law spectra can be interpreted in terms of strong-wave-turbulence cascades driven by particle transport into long-wavelength excitations. Scaling exponents are determined on both sides of the miscible-immiscible transition controlled by the ratio of the intraspecies to interspecies couplings. Making use of quantum turbulence methods, we explain the specific values of the exponents from the presence of transient (quasi)topological defects.
Nonthermal fixed points of the dynamics of a dilute degenerate Bose gas far from thermal equilibrium are analyzed in two and three spatial dimensions. Universal power-law distributions, previously found within a nonperturbative quantum-field theoretical approach and recently shown to be related to vortical dynamics and superfluid turbulence [Phys. Rev. B 84, 020506(R) (2011)], are studied in detail. The results imply an interpretation of the scaling behavior in terms of independent vortex excitations of the superfluid and show that the statistics of topological excitations can be described in the framework of wave turbulence. The particular scaling exponents observed in the single-particle momentum distributions are found to be consistent with irreversibility as well as conservation laws obeyed by the wave interactions. Moreover, long-wavelength acoustic excitations of the vortex-bearing condensate, driven by vortex annihilations, are found to follow a nonthermal power law. Considering vortex correlations in a statistical model, the long-time departure from the nonthermal fixed point is related to vortex-antivortex pairing. The studied nonthermal fixed points are accessible in cold-gas experiments. The results shed light on fundamental aspects of superfluid turbulence and have strong potential implications for related phenomena, for example, in early universe inflation or quark-gluon plasma dynamics.
Critical dynamics of an ultracold Bose gas far from equilibrium is studied in two spatial dimensions. Superfluid turbulence is created by quenching the equilibrium state close to zero temperature. Instead of immediately rethermalizing, the system approaches a meta-stable transient state, characterized as a nonthermal fixed point. A focus is set on the vortex density and vortex-antivortex correlations which characterize the evolution towards the nonthermal fixed point and the departure to final (quasi-)condensation. Two distinct power-law regimes in the vortex-density decay are found and discussed in terms of a vortex unbinding process and a kinetic description of vortex scattering. A possible relation to decaying turbulence in classical fluids is pointed out. By comparing the results to equilibrium studies of a two-dimensional Bose gas, an intuitive understanding of the location of the nonthermal fixed point in a reduced phase space is developed.
Nonthermal fixed points of the dynamics of a dilute degenerate Bose gas are analyzed in two and three spatial dimensions. For such systems, universal power-law distributions, previously found within a nonperturbative quantum-field theoretic approach, are shown to be related to vortical dynamics and superfluid turbulence. The results imply an interpretation of the momentum scaling at the nonthermal fixed points in terms of independent vortex excitations of the superfluid. Long-wavelength acoustic excitations on the top of these are found to follow a nonthermal power law. The results shed light on fundamental aspects of superfluid turbulence and have strong potential implications for related phenomena, e.g., in early-universe inflation or quark-gluon plasma dynamics.