Ergodic theory ≈ Ergodic theory
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Large Intelligent Surface-Assisted Wireless Communication Exploiting Statistical CSI Open
Large intelligent surface (LIS)-assisted wireless communications have drawn attention worldwide. With the use of low-cost LIS on building walls, signals can be reflected by the LIS and sent out along desired directions by controlling its p…
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Using machine learning to replicate chaotic attractors and calculate Lyapunov exponents from data Open
We use recent advances in the machine learning area known as “reservoir computing” to formulate a method for model-free estimation from data of the Lyapunov exponents of a chaotic process. The technique uses a limited time series of measur…
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Quantum many-body scars and Hilbert space fragmentation: a review of exact results Open
The discovery of quantum many-body scars (QMBS) both in Rydberg atom simulators and in the Affleck–Kennedy–Lieb–Tasaki spin-1 chain model, have shown that a weak violation of ergodicity can still lead to rich experimental and theoretical p…
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Performance Evaluation of Non-Orthogonal Multiple Access in Visible Light Communication Open
In this paper, the performance of non-orthogonal multiple access (NOMA) is characterized in a downlink visible light communication system for two separate cases. In the case of guaranteed quality of service (QoS) provisioning, we derive an…
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Stability and instability towards delocalization in many-body localization systems Open
We propose a theory that describes quantitatively the (in)stability of fully\nMBL systems due to ergodic, i.e. delocalized, grains, that can be for example\ndue to disorder fluctuations. The theory is based on the ETH hypothesis and\neleme…
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Quantum chaos challenges many-body localization Open
Characterizing states of matter through the lens of their ergodic properties is a fascinating new direction of research. In the quantum realm, the many-body localization (MBL) was proposed to be the paradigmatic ergodicity breaking phenome…
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Combinatorial optimization by simulating adiabatic bifurcations in nonlinear Hamiltonian systems Open
Nonlinear Hamiltonian systems search optimal solutions exploiting their adiabatic and chaotic evolutions.
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Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems Open
International audience
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Absence of Diffusion in an Interacting System of Spinless Fermions on a One-Dimensional Disordered Lattice Open
We study the infinite temperature dynamics of a prototypical one-dimensional system expected to exhibit many-body localization. Using numerically exact methods, we establish the dynamical phase diagram of this system based on the statistic…
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Extended slow dynamical regime close to the many-body localization transition Open
5 pages, 3 figures
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Constructing local integrals of motion in the many-body localized phase Open
Many-body localization provides a generic mechanism of ergodicity breaking in\nquantum systems. In contrast to conventional ergodic systems, many-body\nlocalized (MBL) systems are characterized by extensively many local integrals\nof motio…
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Weak Ergodicity Breaking and Quantum Many-Body Scars in Spin-1 Magnets Open
We study the spin-1 XY model on a hypercubic lattice in d dimensions and show that this well-known nonintegrable model hosts an extensive set of anomalous finite-energy-density eigenstates with remarkable properties. Namely, they exhibit s…
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Diffusive and Subdiffusive Spin Transport in the Ergodic Phase of a Many-Body Localizable System Open
We study high temperature spin transport in a disordered Heisenberg chain in the ergodic regime. By employing a density matrix renormalization group technique for the study of the stationary states of the boundary-driven Lindblad equation …
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Entanglement transition from variable-strength weak measurements Open
We show that weak measurements can induce a quantum phase transition of interacting many-body systems from an ergodic thermal phase with a large entropy to a nonergodic localized phase with a small entropy, but only if the measurement stre…
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Multifractal Scalings Across the Many-Body Localization Transition Open
In contrast with Anderson localization where a genuine localization is observed in real space, the many-body localization (MBL) problem is much less understood in Hilbert space, the support of the eigenstates. In this Letter, using exact d…
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Asynchronous Parallel Stochastic Gradient for Nonconvex Optimization Open
Asynchronous parallel implementations of stochastic gradient (SG) have been broadly used in solving deep neural network and received many successes in practice recently. However, existing theories cannot explain their convergence and speed…
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Spectral statistics across the many-body localization transition Open
The many-body localization transition (MBLT) between ergodic and many-body\nlocalized phase in disordered interacting systems is a subject of much recent\ninterest. Statistics of eigenenergies is known to be a powerful probe of\ncrossovers…
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Asynchronous Parallel Stochastic Gradient for Nonconvex Optimization Open
Asynchronous parallel implementations of stochastic gradient (SG) have been broadly used in solving deep neural network and received many successes in practice recently. However, existing theories cannot explain their convergence and speed…
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Individual Differences and the Ergodicity Problem Open
Traditional research into individual differences (ID) in second language (L2) learning is based on group studies with the implicit assumption that findings can be generalized to the individual. In this article, we challenge this view. We a…
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Artificial-Noise-Aided Secure Transmission With Directional Modulation Based on Random Frequency Diverse Arrays Open
In this paper, a random frequency diverse array-based directional modulation with artificial noise (RFDA-DM-AN) scheme is proposed to enhance physical layer security of wireless communications. Specifically, we first design the RFDA-DM-AN …
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Anomalous Thermalization in Ergodic Systems Open
It is commonly believed that quantum isolated systems satisfying the eigenstate thermalization hypothesis (ETH) are diffusive. We show that this assumption is too restrictive since there are systems that are asymptotically in a thermal sta…
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Golden ratio algorithms for variational inequalities Open
The paper presents a fully adaptive algorithm for monotone variational inequalities. In each iteration the method uses two previous iterates for an approximation of the local Lipschitz constant without running a linesearch. Thus, every ite…
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Many-Body Delocalization as a Quantum Avalanche Open
We propose a multiscale diagonalization scheme to study disordered one-dimensional chains, in particular, the transition between many-body localization (MBL) and the ergodic phase, expected to be governed by resonant spots. Our scheme focu…
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On the Capacity Comparison Between MIMO-NOMA and MIMO-OMA Open
Non-orthogonal multiple access (NOMA) has been shown in the literature to have a better performance than OMA in terms of sum channel capacity; however, the capacity superiority of NOMA over OMA has been only proved for single antenna syste…
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Many-body localization and delocalization in large quantum chains Open
We theoretically study the quench dynamics for an isolated Heisenberg spin\nchain with a random on-site magnetic field, which is one of the paradigmatic\nmodels of a many-body localization transition. We use the time-dependent\nvariational…
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How a Small Quantum Bath Can Thermalize Long Localized Chains Open
We investigate the stability of the many-body localized phase for a system in contact with a single ergodic grain modeling a Griffiths region with low disorder. Our numerical analysis provides evidence that even a small ergodic grain consi…
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Quantum Information Scrambling in a Trapped-Ion Quantum Simulator with Tunable Range Interactions Open
In ergodic many-body quantum systems, locally encoded quantum information becomes, in the course of time evolution, inaccessible to local measurements. This concept of "scrambling" is currently of intense research interest, entailing a dee…
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Statistical localization: From strong fragmentation to strong edge modes Open
Certain disorder-free Hamiltonians can be non-ergodic due to a \\emph{strong\nfragmentation} of the Hilbert space into disconnected sectors. Here, we\ncharacterize such systems by introducing the notion of `statistically localized\nintegra…
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A Brief Review of Generalized Entropies Open
Entropy appears in many contexts (thermodynamics, statistical mechanics, information theory, measure-preserving dynamical systems, topological dynamics, etc.) as a measure of different properties (energy that cannot produce work, disorder,…
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Anderson localization and ergodicity on random regular graphs Open
A numerical study of Anderson transition on random regular graphs (RRG) with diagonal disorder is performed. The problem can be described as a tight-binding model on a lattice with N sites that is locally a tree with constant connectivity.…