We explore the far-from-equilibrium dynamics of Bose gases in a universal regime associated to nonthermal fixed points. While previous investigations concentrated on scaling functions and exponents describing equal-time correlations, we compute the additional scaling functions and dynamic exponent $z$ characterizing the frequency dependence or dispersion from unequal-time correlations. This allows us to compare the characteristic condensation and correlation times from a finite-size scaling analysis depending on the system's volume.
We explore the far-from-equilibrium dynamics of Bose gases in a universal regime associated to nonthermal fixed points. While previous investigations concentrated on scaling functions and exponents describing equal-time correlations, we compute the additional scaling functions and dynamic exponent z characterizing the frequency dependence or dispersion from unequal-time correlations. This allows us to compare the characteristic condensation and correlation times from a finite-size scaling analysis depending on the system's volume.
We study the emergence of universal scaling in the time-evolving momentum distribution of a harmonically trapped three-dimensional Bose-Einstein condensate, parametrically driven to a turbulent state. We demonstrate that the out-of-equilibrium dynamics post excitation is described by a single function due to nearby nonthermal fixed points. The observed behavior connects the dynamics of a quantum turbulent state to several far-from-equilibrium phenomena. We present a controllable protocol to explore universality in such systems, obtaining the associated scaling exponents. Our experimental results thus offer a promising route to investigate the complex dynamics of the quantum turbulent regime.
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.
Universal phenomena far from equilibrium exhibit additional independent scaling exponents and functions as compared to thermal universal behavior. For the example of an ultracold Bose gas we simulate nonequilibrium transport processes in a universal scaling regime and show how they lead to the breaking of the fluctuation-dissipation relation. As a consequence, the scaling of spectral functions (commutators) and statistical correlations (anticommutators) between different points in time and space become linearly independent with distinct dynamic scaling exponents. As a macroscopic signature of this phenomenon, we identify a transport peak in the statistical two-point correlator, which is absent in the spectral function showing the quasiparticle peaks of the Bose gas.
Recent progress in out-of-equilibrium closed quantum systems has significantly advanced the understanding of mechanisms behind their evolution toward thermalization. Notably, the concept of nonthermal fixed points (NTFPs)-responsible for the emergence of spatiotemporal universal scaling in far-from-equilibrium systems-has played a crucial role in both theoretical and experimental investigations. In this work, we introduce a differential equation that has the universal scaling associated with NTFPs as a solution. The advantage of working with a differential equation, rather than only with its solution, is that we can extract several insightful properties not necessarily present in the solution alone. How the differential equation is derived allows physical interpretation of the universal exponents in terms of the time dependence of the amplitude of the distributions and their momentum scaling. Employing two limiting cases of the equation, we determined the universal exponents related to the scaling using the distributions near just two momentum values. We established a solid agreement with previous investigations by validating this approach with three distinct physical systems. This consistency highlights the universal nature of scaling due to NTFPs and emphasizes the predictive capabilities of the proposed differential equation. Moreover, under specific conditions, the equation predicts a power-law related to the ratio of the two universal exponents, leading to implications concerning particle and energy transport. This suggests that the observed power-laws in far-from-equilibrium turbulent fluids could be related to the universal scaling due to NTFPs, potentially offering insights into the study of turbulence.
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.