scholarly journals Quantum many-body attractors

2020 ◽  
Author(s):  
Berislav Buca ◽  
Archak Purkayastha ◽  
Giacomo Guarnieri ◽  
Mark Mitchison ◽  
Dieter Jaksch ◽  
...  
Keyword(s):  
Classical Limit ◽  
Initial Conditions ◽  
Quantum Level ◽  
Many Body ◽  
Dynamical Symmetries ◽  
Oscillatory Dynamics ◽  
Quantum Magnet ◽  
Interacting Systems ◽  
Symmetry Operators ◽  
Many Body Systems

Abstract Real-world complex systems often show robust, persistent oscillatory dynamics, e.g.~non-trivial attractors. On the quantum level this behaviour has only been found in semi-classical or weakly correlated systems under restrictive assumptions. However, strongly interacting systems without classical limits, e.g.~electrons on a lattice or spins, typically relax quickly to a stationary state (trivial attractors). This raises the puzzling question of how non-trivial attractors can arise from the quantum laws. Here, we introduce strictly local dynamical symmetries that lead to extremely robust and persistent oscillations in quantum many-body systems without a classical limit. Observables that do not have overlap with the symmetry operators can relax, losing memory of their initial conditions. The remaining observables enter complex dynamical cycles, signalling the emergence of a quantum many-body attractor. We provide a recipe for constructing Hamiltonians featuring local dynamical symmetries. As an example, we introduce the spin lace – a model of a quasi-1D quantum magnet.

scholarly journals Machine learning active-nematic hydrodynamics

2021 ◽  
Vol 118 (10) ◽  
pp. e2016708118
Author(s):  
Jonathan Colen ◽  
Ming Han ◽  
Rui Zhang ◽  
Steven A. Redford ◽  
Linnea M. Lemma ◽  
...  
Keyword(s):  
Machine Learning ◽  
Neural Networks ◽  
Initial Conditions ◽  
Molecular Motor ◽  
Machine Learning Algorithms ◽  
Many Body ◽  
Hydrodynamic Parameters ◽  
Many Body Systems ◽  
And Control ◽  
Macroscopic Parameters

Hydrodynamic theories effectively describe many-body systems out of equilibrium in terms of a few macroscopic parameters. However, such parameters are difficult to determine from microscopic information. Seldom is this challenge more apparent than in active matter, where the hydrodynamic parameters are in fact fields that encode the distribution of energy-injecting microscopic components. Here, we use active nematics to demonstrate that neural networks can map out the spatiotemporal variation of multiple hydrodynamic parameters and forecast the chaotic dynamics of these systems. We analyze biofilament/molecular-motor experiments with microtubule/kinesin and actin/myosin complexes as computer vision problems. Our algorithms can determine how activity and elastic moduli change as a function of space and time, as well as adenosine triphosphate (ATP) or motor concentration. The only input needed is the orientation of the biofilaments and not the coupled velocity field which is harder to access in experiments. We can also forecast the evolution of these chaotic many-body systems solely from image sequences of their past using a combination of autoencoders and recurrent neural networks with residual architecture. In realistic experimental setups for which the initial conditions are not perfectly known, our physics-inspired machine-learning algorithms can surpass deterministic simulations. Our study paves the way for artificial-intelligence characterization and control of coupled chaotic fields in diverse physical and biological systems, even in the absence of knowledge of the underlying dynamics.

Electron systems out of equilibrium: Nonequilibrium Green's function approach

2014 ◽  
Vol 28 (23) ◽  
pp. 1430013 ◽  
Author(s):  
Václav Špička ◽  
Bedřich Velický ◽  
Anděla Kalvová
Keyword(s):  
Green’S Function ◽  
Master Equation ◽  
Green's Function ◽  
Initial Conditions ◽  
Kinetic Equations ◽  
Many Body ◽  
Initial State ◽  
Nonequilibrium Green's Function ◽  
Nonequilibrium Green’S Function ◽  
Many Body Systems

This review deals with the state of the art and perspectives of description of nonequilibrium many-body systems using the nonequilibrium Green's function (NGF) method. The basic aim is to describe time evolution of the many-body system from its initial state over its transient dynamics to its long time asymptotic evolution. First, we discuss basic aims of transport theories to motivate the introduction of the NGF techniques. Second, this article summarizes the present view on construction of the electron transport equations formulated within the NGF approach to nonequilibrium. We discuss incorporation of complex initial conditions to the NGF formalism, and the NGF reconstruction theorem, which serves as a tool to derive simplified kinetic equations. Three stages of evolution of the nonequilibrium, the first described by the full NGF description, the second by a non-Markovian generalized master equation and the third by a Markovian master equation will be related to each other.

scholarly journals On intermediate statistics across many-body localization transition

2021 ◽  
Author(s):  
Bitan De ◽  
Piotr Sierant ◽  
Jakub Zakrzewski
Keyword(s):  
Joint Probability ◽  
Single Parameter ◽  
Joint Probability Distribution ◽  
Many Body ◽  
Localization Transition ◽  
Physical Systems ◽  
Level Statistics ◽  
Interacting Systems ◽  
Many Body Systems ◽  
Two Parameter

Abstract The level statistics in the transition between delocalized and localized {phases of} many body interacting systems is {considered}. We recall the joint probability distribution for eigenvalues resulting from the statistical mechanics for energy level dynamics as introduced by Pechukas and Yukawa. The resulting single parameter analytic distribution is probed numerically {via Monte Carlo method}. The resulting higher order spacing ratios are compared with data coming from different {quantum many body systems}. It is found that this Pechukas-Yukawa distribution compares favorably with {$\beta$--Gaussian ensemble -- a single parameter model of level statistics proposed recently in the context of disordered many-body systems.} {Moreover, the Pechukas-Yukawa distribution is also} only slightly inferior to the two-parameter $\beta$-h ansatz shown {earlier} to reproduce {level statistics of} physical systems remarkably well.

scholarly journals Euler-scale dynamical correlations in integrable systems with fluid motion

2020 ◽  
Vol 3 (2) ◽  
Author(s):  
Frederik Skovbo Møller ◽  
Gabriele Perfetto ◽  
Benjamin Doyon ◽  
Jörg Schmiedmayer
Keyword(s):  
Iterative Scheme ◽  
Scaling Limit ◽  
Fluid Motion ◽  
Many Body ◽  
Fluctuation Dissipation ◽  
Long Time ◽  
Interacting Systems ◽  
Point Correlation ◽  
Many Body Systems ◽  
Scale Limit

We devise an iterative scheme for numerically calculating dynamical two-point correlation functions in integrable many-body systems, in the Eulerian scaling limit. Expressions for these were originally derived in Ref. [1] by combining the fluctuation-dissipation principle with generalized hydrodynamics. Crucially, the scheme is able to address non-stationary, inhomogeneous situations, when motion occurs at the Euler-scale of hydrodynamics. In such situations, in interacting systems, the simple correlations due to fluid modes propagating with the flow receive subtle corrections, which we test. Using our scheme, we study the spreading of correlations in several integrable models from inhomogeneous initial states. For the classical hard-rod model we compare our results with Monte-Carlo simulations and observe excellent agreement at long time-scales, thus providing the first demonstration of validity for the expressions derived in Ref. [1]. We also observe the onset of the Euler-scale limit for the dynamical correlations.

REGULAR STRUCTURE OF LOW-LYING STATES FOR ATOMIC NUCLEI UNDER RANDOM INTERACTIONS

2008 ◽  
Vol 17 (supp01) ◽  
pp. 304-317
Author(s):  
Y. M. ZHAO
Keyword(s):  
Ground State ◽  
Collective Motion ◽  
Regular Structure ◽  
Positive Parity ◽  
Many Body ◽  
Random Interactions ◽  
Atomic Nuclei ◽  
Many Body Systems

In this paper we review regularities of low-lying states for many-body systems, in particular, atomic nuclei, under random interactions. We shall discuss the famous problem of spin zero ground state dominance, positive parity dominance, collective motion, odd-even staggering, average energies, etc., in the presence of random interactions.

scholarly journals Emergence of a Renormalized 1/N Expansion in Quenched Critical Many-Body Systems

2021 ◽  
Vol 126 (11) ◽  
Author(s):  
Benjamin Geiger ◽  
Juan Diego Urbina ◽  
Klaus Richter
Keyword(s):  
Many Body ◽  
Many Body Systems
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