# Dynamical quantum ergodicity from energy level statistics

@inproceedings{Vikram2022DynamicalQE, title={Dynamical quantum ergodicity from energy level statistics}, author={Amit Vikram and Victor Galitski}, year={2022} }

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…

## 2 Citations

### Exact universal bounds on quantum dynamics and fast scrambling

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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

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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…

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