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Register a new userQuantifying hidden order out of equilibrium
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While the equilibrium properties, states, and phase transitions of interacting systems are well described by statistical mechanics, the lack of suitable state parameters has hindered the understanding of non-equilibrium phenomena in diverse settings, from glasses to driven systems to biology. The length of a losslessly compressed data file is a direct measure of its information content: The more ordered the data is, the lower its information content and the shorter the length of its encoding can be made. Here, we describe how data compression enables the quantification of order in non-equilibrium and equilibrium many-body systems, both discrete and continuous, even when the underlying form of order is unknown. We consider absorbing state models on and off-lattice, as well as a system of active Brownian particles undergoing motility-induced phase separation. The technique reliably identifies non-equilibrium phase transitions, determines their character, quantitatively predicts certain critical exponents without prior knowledge of the order parameters, and reveals previously unknown ordering phenomena. This technique should provide a quantitative measure of organization in condensed matter and other systems exhibiting collective phase transitions in and out of equilibrium.
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In this paper we first compute the out-of-time-order correlators (OTOC) for both a phenomenological model and a random-field XXZ model in the many-body localized phase. We show that the OTOC decreases in power law in a many-body localized system at the scrambling time. We also find that the OTOC can also be used to distinguish a many-body localized phase from an Anderson localized phase, while a normal correlator cannot. Furthermore, we prove an exact theorem that relates the growth of the second Renyi entropy in the quench dynamics to the decay of the OTOC in equilibrium. This theorem works for a generic quantum system. We discuss various implications of this theorem.
Exponential growth of thermal out-of-time-order correlator (OTOC) is an indicator of a possible gravity dual, and a simple toy quantum model showing the growth is being looked for. We consider a system of two harmonic oscillators coupled nonlinearly with each other, and numerically observe that the thermal OTOC grows exponentially in time. The system is well-known to be classically chaotic, and is a reduction of Yang-Mills-Higgs theory. The exponential growth is certified because the growth exponent (quantum Lyapunov exponent) of the thermal OTOC is well matched with the classical Lyapunov exponent, including their energy/temperature dependence. Even in the presence of the exponential growth in the OTOC, the energy level spacings are not sufficient to judge a Wigner distribution, hence the OTOC is a better indicator of quantum chaos.
We introduce and study random bipartite networks with hidden variables. Nodes in these networks are characterized by hidden variables which control the appearance of links between node pairs. We derive analytic expressions for the degree distribution, degree correlations, the distribution of the number of common neighbors, and the bipartite clustering coefficient in these networks. We also establish the relationship between degrees of nodes in original bipartite networks and in their unipartite projections. We further demonstrate how hidden variable formalism can be applied to analyze topological properties of networks in certain bipartite network models, and verify our analytical results in numerical simulations.
In this work, our prime focus is to study the one to one correspondence between the conduction phenomena in electrical wires with impurity and the scattering events responsible for particle production during stochastic inflation and reheating implemented under a closed quantum mechanical system in early universe cosmology. In this connection, we also present a derivation of fourth order corrected version of the Fokker Planck equation and its analytical solution for studying the dynamical features of the particle creation events in the stochastic inflation and reheating stage of the universe. It is explicitly shown from our computation that quantum corrected Fokker Planck equation describe the particle creation phenomena better for Dirac delta type of scatterer. In this connection, we additionally discuss It$hat{o}$, Stratonovich prescription and the explicit role of finite temperature effective potential for solving the probability distribution profile. Furthermore, we extend our discussion to describe the quantum description of randomness involved in the dynamics. We also present a computation to derive the expression for the measure of the stochastic non-linearity arising in the stochastic inflation and reheating epoch of the universe, often described by Lyapunov Exponent. Apart from that, we quantify the quantum chaos arising in a closed system by a more strong measure, commonly known as Spectral Form Factor using the principles of Random Matrix Theory (RMT). Additionally, we discuss the role of out of time order correlation (OTOC) function to describe quantum chaos in the present non-equilibrium field theoretic setup. Finally, for completeness, we also provide a bound on the measure of quantum chaos arising due to the presence of stochastic non-linear dynamical interactions into the closed quantum system of the early universe in a completely model-independent way.
Closed quantum many-body systems out of equilibrium pose several long-standing problems in physics. Recent years have seen a tremendous progress in approaching these questions, not least due to experiments with cold atoms and trapped ions in instances of quantum simulations. This article provides an overview on the progress in understanding dynamical equilibration and thermalisation of closed quantum many-body systems out of equilibrium due to quenches, ramps and periodic driving. It also addresses topics such as the eigenstate thermalisation hypothesis, typicality, transport, many-body localisation, universality near phase transitions, and prospects for quantum simulations.
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