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Universality classes far from equilibrium: From heavy-ion collisions to superfluid Bose systems

Kirill Boguslavski

Published Jan 1, 2016• 0 citations
Publisher

Abstract

Quantum many-body systems far from equilibrium can approach a nonthermal fixed point during their real-time evolution. One example is scalar field theory, which occurs in models \nof cosmological inflation, and similar examples are found for non-Abelian plasmas relevant for heavy-ion collisions and for ultracold Bose gases. Investigating nonthermal fixed points of different microscopic theories, we present two novel universality classes that provide links between these systems. \n \nOne of them involves nonrelativistic, N-component relativistic and expanding scalar systems. It occurs in the deep infrared regime of very high occupancies and is governed by a self-similar evolution. Its nonequilibrium dynamics leads to the formation of a Bose-Einstein condensate. The scaling properties of this region can be described by a vertex-resummed kinetic theory that is based on a systematic large-N expansion at next-to-leading order. \n \nThe other novel universality class encompasses scalar field theories and non-Abelian plasmas in a longitudinally expanding background and corresponds to an early dynamical stage of heavy-ion collisions in the high-energy limit. We show that these systems share the same self-similar scaling properties for a wide range of momenta in a limit where particles are weakly coupled but their occupancy is high. \n \nBoth universality classes are found in separate momentum regions in a longitudinally expanding N-component scalar field theory. We argue that the important role of the infrared dynamics ensures that key features of our results for scalar and gauge theories cannot be reproduced consistently in conventional kinetic theory frameworks. Moreover, the observed universality connects different physics disciplines from heavy-ion collisions to ultracold atoms, making a remarkable link between the world's hottest and coldest matter.

DOI
10.11588/heidok.00021780

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Quantum many-body systems far from equilibrium can approach a nonthermal fixed point during their real-time evolution. One example is scalar field theory, which occurs in models \nof cosmological inflation, and similar examples are found for non-Abelian plasmas relevant for heavy-ion collisions and for ultracold Bose gases. Investigating nonthermal fixed points of different microscopic theories, we present two novel universality classes that provide links between these systems. \n \nOne of them involves nonrelativistic, N-component relativistic and expanding scalar systems. It occurs in the deep infrared regime of very high occupancies and is governed by a self-similar evolution. Its nonequilibrium dynamics leads to the formation of a Bose-Einstein condensate. The scaling properties of this region can be described by a vertex-resummed kinetic theory that is based on a systematic large-N expansion at next-to-leading order. \n \nThe other novel universality class encompasses scalar field theories and non-Abelian plasmas in a longitudinally expanding background and corresponds to an early dynamical stage of heavy-ion collisions in the high-energy limit. We show that these systems share the same self-similar scaling properties for a wide range of momenta in a limit where particles are weakly coupled but their occupancy is high. \n \nBoth universality classes are found in separate momentum regions in a longitudinally expanding N-component scalar field theory. We argue that the important role of the infrared dynamics ensures that key features of our results for scalar and gauge theories cannot be reproduced consistently in conventional kinetic theory frameworks. Moreover, the observed universality connects different physics disciplines from heavy-ion collisions to ultracold atoms, making a remarkable link between the world's hottest and coldest matter.
We investigate universal behavior of isolated many-body systems far from equilibrium, which is relevant for a wide range of applications from ultracold quantum gases to high-energy particle physics. The universality is based on the existence of nonthermal fixed points, which represent nonequilibrium attractor solutions with self-similar scaling behavior. The corresponding dynamic universality classes turn out to be remarkably large, encompassing both relativistic as well as nonrelativistic quantum and classical systems. For the examples of nonrelativistic (Gross-Pitaevskii) and relativistic scalar field theory with quartic self-interactions, we demonstrate that infrared scaling exponents as well as scaling functions agree. We perform two independent nonperturbative calculations, first by using classical-statistical lattice simulation techniques and second by applying a vertex-resummed kinetic theory. The latter extends kinetic descriptions to the nonperturbative regime of overoccupied modes. Our results open new perspectives to learn from experiments with cold atoms aspects about the dynamics during the early stages of our universe.
In recent years, there have been important advances in understanding the far-from-equilibrium dynamics in different physical systems. In ultra-relativistic heavy-ion collisions, the combination of different methods led to the development of a weak-coupling description of the early-time dynamics. The numerical observation of a classical universal attractor played a crucial role for this. Such attractors, also known as non-thermal fixed points (NTFPs), have been now predicted for different scalar and gauge theories. An important universal NTFP emerges in scalar theories modeling ultra-cold atoms, inflation or dark matter, and its scaling properties have been recently observed in an ultra-cold atom experiment. In this proceeding, recent progress in selected topics of the far-from-equilibrium evolution in these systems will be discussed. A new method to extract the spectral function numerically is a particularly promising tool to better understand their microscopic properties.
We map the infrared dynamics of a relativistic single-component (N=1N=1N=1) interacting scalar field theory to that of nonrelativistic complex scalar fields. The Gross-Pitaevskii (GP) equation, describing the real-time dynamics of single-component ultracold Bose gases, is obtained at first nontrivial order in an expansion proportional to the powers of $\ensuremath{\lambda}{\ensuremath{\phi}}^{2}/{m}^{2}$ where $\ensuremath{\lambda}$, $\ensuremath{\phi}$, and mmm are the coupling constant, the scalar field, and the particle mass respectively. Our analytical studies are corroborated by numerical simulations of the spatial and momentum structure of overoccupied scalar fields in (2+1)-dimensions. Universal scaling of infrared modes, vortex-antivortex superfluid dynamics, and the off-equilibrium formation of a Bose-Einstein condensate are observed. Our results for the universal scaling exponents are in agreement with those extracted in the numerical simulations of the GP equation. As in these simulations, we observe coarsening phase kinetics in the Bose superfluid with strongly anomalous scaling exponents relative to that of vertex resummed kinetic theory. Our relativistic field theory framework further allows one to study more closely the coupling between superfluid and normal fluid modes, specifically the turbulent momentum and spatial structure of the coupling between a quasiparticle cascade to the infrared and an energy cascade to the ultraviolet. We outline possible applications of the formalism to the dynamics of vortex-antivortex formation and to the off-equilibrium dynamics of the strongly interacting matter formed in heavy-ion collisions.
Abstract Predicting the dynamics of quantum systems far from equilibrium represents one of the most challenging problems in theoretical many-body physics1, 2. While the evolution of a many-body system is in general intractable in all its details, relevant observables can become insensitive to microscopic system parameters and initial conditions. This is the basis of the phenomenon of universality. Far from equilibrium, universality is identified through the scaling of the spatio-temporal evolution of the system, captured by universal exponents and functions. Theoretically, this has been studied in examples as different as the reheating process in inflationary Universe cosmology3, 4, the dynamics of nuclear collision experiments described by quantum chromodynamics5, 6, and the post-quench dynamics in dilute quantum gases in non-relativistic quantum field theory7–11. However, an experimental demonstration of such scaling evolution in space and time in a quantum many-body system has been lacking. Here we observe the emergence of universal dynamics by evaluating spatially resolved spin correlations in a quasi-one-dimensional spinor Bose–Einstein condensate12–16. For long evolution times we extract the scaling properties from the spatial correlations of the spin excitations. From this we find the dynamics to be governed by an emergent conserved quantity and the transport of spin excitations towards low momentum scales. Our results establish an important class of non-stationary systems whose dynamics is encoded in time-independent scaling exponents and functions, signalling the existence of non-thermal fixed points10, 17, 18. We confirm that the non-thermal scaling phenomenon involves no fine-tuning of parameters, by preparing different initial conditions and observing the same scaling behaviour. Our analogue quantum simulation approach provides the basis with which to reveal the underlying mechanisms and characteristics of non-thermal universality classes. One may use this universality to learn, from experiments with ultracold gases, about fundamental aspects of dynamics studied in cosmology and quantum chromodynamics.
Abstract Closed quantum systems far from thermal equilibrium can show universal dynamics near attractor solutions, known as non-thermal fixed points, generically in the form of scaling behaviour in space and time. A systematic classification and comprehensive understanding of such scaling solutions are tasks of future developments in non-equilibrium quantum many-body theory. In this tutorial review, we outline several analytical approaches to non-thermal fixed points and summarise corresponding numerical and experimental results. The analytic methods include a non-perturbative kinetic theory derived within the two-particle irreducible effective action formalism, as well as a low-energy effective field theory framework. As one of the driving forces of this research field are numerical simulations, we summarise the main results of exemplary cases of universal dynamics in ultracold Bose gases. This encompasses quantum vortex ensembles in turbulent superfluids as well as recently observed real-time instanton solutions in one-dimensional spinor condensates.