Related papers: Weak Quantum Ergodicity
We describe an interpretation of quantum mechanics based on reduced density matrices of sub-systems from which the standard Copenhagen interpretation emerges as an effective description for macro-systems. The interpretation is a modal one,…
We present evidence that anomalous transport in the classical standard map results in strong enhancement of fluctuations in the localization length of quasienergy states in the corresponding quantum dynamics. This generic effect occurs even…
The concept of non-ergodicity in quantum many body systems can be discussed in the context of the wave functions of the many body system or as a property of the dynamical observables, such as time-dependent spin correlators. In the former…
Quasiperiodic systems in one dimension can host non-ergodic states, e.g. localized in position or momentum. Periodic quenches within localized phases yield Floquet eigenstates of the same nature, i.e. spatially localized or ballistic.…
This paper contains a very simple and general proof that eigenfunctions of quantizations of classically ergodic systems become uniformly distributed in phase space. This ergodicity property of eigenfunctions f is shown to follow from a…
Ergodicity of quantum dynamics is often defined through statistical properties of energy eigenstates, as exemplified by Berry's conjecture in single-particle quantum chaos and the eigenstate thermalization hypothesis in many-body settings.…
We show that some $C^*$--dynamical systems obtained by "quantizing" classical ones on the free Fock space, enjoy very strong ergodic properties. Namely, if the classical dynamical system $(X, T, \m)$ is ergodic but not weakly mixing, then…
By analytical mapping of the eigenvalue problem in rough billiards on to a band random matrix model a new regime of Wigner ergodicity is found. There the eigenstates are extended over the whole energy surface but have a strongly peaked…
We perform a qualitative analysis of the critical equation associated with a stationary ergodic Hamiltonian through a stochastic version of the metric method, where the notion of closed random stationary set, issued from stochastic…
This paper is withdrawn. While almost all findings reported here remain valid, some of our comments on the fate of weak localization corrections to the conductance in the deep semiclassical limit are now obsolete. Contrarily to what was…
For a large class of quantized ergodic flows the quantum ergodicity theorem due to Shnirelman, Zelditch, Colin de Verdi\`ere and others states that almost all eigenfunctions become equidistributed in the semiclassical limit. In this work we…
The notion of `weak classical limit' for coupled N-level quantum systems as N -> infinity is introduced to understand the precise sense in which one attains classicality. There exist proofs that a system becomes classical at large N. On the…
The theoretical cornerstone of statistical mechanics is the ergodic assumption that all accessible configurations of a physical system are equally likely. Here we show how such property arises when an open quantum system is continuously…
A successful method to describe the asymptotic behavior of various deterministic and stochastic processes such as asymptotically autonomous differential equations or stochastic approximation processes is to relate it to an appropriately…
We generalize Page's result on the entanglement entropy of random pure states to the many-body eigenstates of realistic disordered many-body systems subject to long range interactions. This extension leads to two principal conclusions:…
We study the breaking of ergodicity measured in terms of return probability in the evolution of a quantum state of a spin chain. In the non ergodic phase a quantum state evolves in a much smaller fraction of the Hilbert space than would be…
We investigate the behavior of weak localization, conductance fluctuations, and shot noise of a chaotic scatterer in the semiclassical limit. Time resolved numerical results, obtained by truncating the time-evolution of a kicked quantum map…
We study the eigenstates of open maps whose classical dynamics is pseudointegrable and for which the corresponding closed quantum system has multifractal properties. Adapting the existing general framework developed for open chaotic quantum…
This work will incorporate a few related tools for addressing the conceptual difficulties arising from sewing together classical and quantum mechanics: deterministic operators, weak measurements and post-selection. Weak Measurement, based…
We study the ergodic properties of quantized ergodic maps of the torus. It is known that these satisfy quantum ergodicity: For almost all eigenstates, the expectation values of quantum observables converge to the classical phase-space…