• Corpus ID: 248722138

Dynamical quantum ergodicity from energy level statistics

  title={Dynamical quantum ergodicity from energy level statistics},
  author={Amit Vikram and Victor Galitski},
Ergodic theory provides a rigorous mathematical description of classical dynamical systems and in particular includes a formal definition of the ergodic hierarchy consisting of merely ergodic, weakly-, strongly-, and K-mixing systems. Closely related to this hierarchy is a less-known notion of cyclic approximate periodic transformations [see, e.g. , I. Cornfield, S. Fomin, and Y. Sinai, Ergodic theory (Springer-Verlag New York, 1982)], which maps any “ergodic” dynamical system to a cyclic… 

Exact universal bounds on quantum dynamics and fast scrambling

Quantum speed limits such as the Mandelstam-Tamm or Margolus-Levitin bounds offer a quan-titative formulation of the energy-time uncertainty principle that constrains dynamics over short times. We

Quantum tomography under perturbed Hamiltonian evolution and scrambling of errors -- a quantum signature of chaos

How much can we trust quantum simulations or other quantum information protocols under noisy many-body chaotic dynamics that will lead to a rapid scrambling of quantum information as well as errors



From dual-unitary to quantum Bernoulli circuits: Role of the entangling power in constructing a quantum ergodic hierarchy

Deterministic classical dynamical systems have an ergodic hierarchy, from ergodic through mixing, to Bernoulli systems that are “as random as a coin-toss”. Dual-unitary circuits have been recently

Theory of dynamical systems and general transformation groups with invariant measure

The theory of dynamical systems with invariant measure, or ergodic theory, is one of those domains of mathematics whose form changed radically in the last 15-20 years. This has to do both with the

Chaos and quantum thermalization.

  • Srednicki
  • Physics
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1994
It is shown that a bounded, isolated quantum system of many particles in a specific initial state will approach thermal equilibrium if the energy eigenfunctions which are superposed to form that state obey Berry's conjecture, and argued that these results constitute a sound foundation for quantum statistical mechanics.

The approach to thermal equilibrium in quantized chaotic systems

We consider many-body quantum systems that exhibit quantum chaos, in the sense that the observables of interest act on energy eigenstates like banded random matrices. We study the time-dependent

Semiclassical Foundation of Universality in Quantum Chaos

Fully chaotic dynamics enjoy ergodicity and thus visit everywhere in the accessible space with uniform likeli- hood, over long periods of time. Even long periodic orbits bring about such uniform

Quantum ergodicity and a quantum measure algebra

A quantum ergodic theory for finite systems (such as isolated molecules) is developed by introducing the concept of a quantum measure algebra. The basic concept in classical ergodic theory is that of

Universal dephasing mechanism of many-body quantum chaos

Ergodicity is a fundamental principle of statistical mechanics underlying the behavior of generic quantum many-body systems. However, how this universal many-body quantum chaotic regime emerges due

Statistical and dynamical properties of the quantum triangle map

We study the statistical and dynamical properties of the quantum triangle map, whose classical counterpart can exhibit ergodic and mixing dynamics, but is never chaotic. Numerical results show that

Spectral form factor of a quantum spin glass

It is widely expected that systems which fully thermalize are chaotic in the sense of exhibiting random-matrix statistics of their energy level spacings, whereas integrable systems exhibit Poissonian

Periodic-orbit theory of universality in quantum chaos.

We argue semiclassically, on the basis of Gutzwiller's periodic-orbit theory, that full classical chaos is paralleled by quantum energy spectra with universal spectral statistics, in agreement with