Universal self-similar dynamics of relativistic and nonrelativistic field theories near nonthermal fixed points

Orioli, Asier Piñeiro; Boguslavski, Kirill; Berges, Jürgen

doi:10.1103/physrevd.92.025041

Cited by 102 publications

(294 citation statements)

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“…We discuss the universal dynamics near the non-thermal fixed points in the framework of the classical theory of phase-ordering kinetics. The anomalous scaling exponent η of the field-theoretic approach [34][35][36]38] can be related to the scaling exponent μ which characterizes the coarsening dynamics of a conserved order parameter as compared to a non-conserved one [11]. Our results are consistent with m  4.…”

supporting

confidence: 82%

“…3.1. Non-thermal fixed points in a superfluid The formation of turbulent ensembles of vortices in an isolated, dilute, superfluid Bose gas [45,46,48] can be associated with the system approaching a non-thermal fixed point [34][35][36] where the time evolution is critically slowed down before the vortices have mutually annihilated and the system eventually thermalizes [38,47]. Turbulent behavior and critical slowing down are signaled by characteristic scaling properties of correlation functions such as the angle-averaged single-particle momentum spectrum defined in equation (4) 5 .…”

Section: Universal Time Evolutionmentioning

confidence: 99%

“…6 0 0 0 At the same time, energy conservation forces a few particles to scatter into higher momentum modes, eventually forming an incoherent thermalized fraction of the gas. The scaling exponents α and β in equation (6) have been calculated for the nonlinear Schrödinger model [38]. The predictions are derived by means of a scaling analysis of Dyson-type field dynamic equations obtained with 2-particle-irreducible effective-action techniques [76].…”

Section: Universal Time Evolutionmentioning

confidence: 99%

“…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].…”

mentioning

confidence: 99%

“…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.…”

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confidence: 99%

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

2017

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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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supporting

confidence: 82%

Section: Universal Time Evolutionmentioning

confidence: 99%

Section: Universal Time Evolutionmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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

2017

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Feynman rules for forced wave turbulence

Rosenhaus

Smolkin

2023

J. High Energ. Phys.

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It has long been known that weakly nonlinear field theories can have a late-time stationary state that is not the thermal state, but a wave turbulent state with a far-from-equilibrium cascade of energy. We go beyond the existence of the wave turbulent state, studying fluctuations about the wave turbulent state. Specifically, we take a classical field theory with an arbitrary quartic interaction and add dissipation and Gaussian-random forcing. Employing the path integral relation between stochastic classical field theories and quantum field theories, we give a prescription, in terms of Feynman diagrams, for computing correlation functions in this system. We explicitly compute the two-point and four-point functions of the field to next-to-leading order in the coupling. Through an appropriate choice of forcing and dissipation, these correspond to correlation functions in the wave turbulent state. In particular, we derive the kinetic equation to next-to-leading order.

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Broad excitations in a 2+1D overoccupied gluon plasma

Boguslavski

Kurkela

Lappi

et al. 2021

J. High Energ. Phys.

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Motivated by the initial stages of high-energy heavy-ion collisions, we study excitations of far-from-equilibrium 2+1 dimensional gauge theories using classical-statistical lattice simulations. We evolve field perturbations over a strongly overoccupied background undergoing self-similar evolution. While in 3+1D the excitations are described by hard-thermal loop theory, their structure in 2+1D is nontrivial and nonperturbative. These nonperturbative interactions lead to broad excitation peaks in spectral and statistical correlation functions. Their width is comparable to the frequency of soft excitations, demonstrating the absence of soft quasiparticles in these theories. Our results also suggest that excitations at higher momenta are sufficiently long-lived, such that an effective kinetic theory description for 2+1 dimensional Glasma-like systems may exist, but its collision kernel must be nonperturbatively determined.

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Universal self-similar dynamics of relativistic and nonrelativistic field theories near nonthermal fixed points

Cited by 102 publications

References 47 publications

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

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

Feynman rules for forced wave turbulence

Broad excitations in a 2+1D overoccupied gluon plasma

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