Universal level statistics of the out-of-time-ordered operator
arXiv:1801.10591 · doi:10.1103/PhysRevB.100.035112
Abstract
The out-of-time-ordered correlator has been proposed as an indicator of chaos in quantum systems due to its simple interpretation in the semiclassical limit. In particular, its rate of possible exponential growth at is closely related to the classical Lyapunov exponent. Here we explore how this approach to quantum chaos relates to the random-matrix theoretical description. To do so, we introduce and study the level statistics of the logarithm of the out-of-time-ordered operator, , that we dub the "Lyapunovian" or "Lyapunov operator" for brevity. The Lyapunovian's level statistics is calculated explicitly for the quantum stadium billiard. It is shown that in the bulk of the filtered spectrum, this statistics perfectly aligns with the Wigner-Dyson distribution. One of the advantages of looking at the spectral statistics of this operator is that it has a well-defined semiclassical limit where it reduces to the matrix of uncorrelated classical finite-time Lyapunov exponents in a partitioned phase space. We provide a heuristic picture interpolating these two limits using Moyal quantum mechanics. Our results show that the Lyapunov operator may serve as a useful tool to characterize quantum chaos and in particular quantum-to-classical correspondence in chaotic systems, by connecting the semiclassical Lyapunov growth at early times, when the quantum effects are weak, to universal level repulsion that hinges on strong quantum interference effects.
arXiv comment8 pages, 5 figures
References in corpus (27)
- A bound on chaos
- Comments on the Sachdev-Ye-Kitaev model
- Decoherence, Chaos, and the Second Law
- Bekenstein-Hawking Entropy and Strange Metals
- Measuring the scrambling of quantum information
- Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System
- Sachdev-Ye-Kitaev Model as Liouville Quantum Mechanics
- Out-of-Time-Order Correlation for Many-Body Localization
- Chaos, Complexity, and Random Matrices
- Out-of-time-order correlators in quantum mechanics
- Slow scrambling in disordered quantum systems
- Out-of-time-ordered correlators in many-body localized systems
- Microscopic model of quantum butterfly effect: out-of-time-order correlators and traveling combustion waves
- Divergence of the Classical trajectories and Weak Localization
- Quantum Chaos, Irreversible Classical Dynamics and Random Matrix Theory
- Diffusion and localization in chaotic billiards
- Measuring the Lyapunov exponent using quantum mechanics
- Semiclassical Field Theory Approach to Quantum Chaos
- Universal Logarithmic Scrambling in Many Body Localization
- Out-of-time-order Operators and the Butterfly Effect
- Chaos in Classical D0-Brane Mechanics
- Unstable Periodic Orbits in the Stadium Billiard
- Role of divergence of classical trajectories in quantum chaos
- Sensitivity to perturbations in a quantum chaotic billiard
- Experimental vs. Numerical Eigenvalues of a Bunimovich Stadium Billiard -- A Comparison
- Universality in Chaos: Lyapunov Spectrum and Random Matrix Theory
- Sigma models for quantum chaotic dynamics
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- Many-body level statistics of single-particle quantum chaos
- Early-Time Exponential Instabilities in Non-Chaotic Quantum Systems
- Probing excited-state quantum phase transition in a quantum many body system via out-of-time-ordered correlator
- Sensitivity of quantum information to environment perturbations measured with a non-local out-of-time-order correlation function
- Out-of-time-order correlator in coupled harmonic oscillators
- Nonlinear sigma model approach to many-body quantum chaos: Regularized and unregularized out-of-time-ordered correlators
- Timescales in the quench dynamics of many-body quantum systems: Participation ratio vs out-of-time ordered correlator
- The Lyapunov Spectrum of Quantum Thermalisation
- Scrambling in strongly chaotic weakly coupled bipartite systems: Universality beyond the Ehrenfest time-scale
- Out-of-time-order correlations and Floquet dynamical quantum phase transition
- Chaos and quantum scars in a coupled top model
- Spectral decoupling in many-body quantum chaos
- Quantum vs classical dynamics in a spin-boson system: manifestations of spectral correlations and scarring
- OTOC, complexity and entropy in bi-partite systems
- Quantum echo dynamics in the Sherrington-Kirkpatrick model
- The Squeezed OTOC and Cosmology
- Out-of-Time-Order Correlation as a Witness for Topological Phase Transitions
- Multifractality in quasienergy space of coherent states as a signature of quantum chaos
- Super-exponential scrambling of Out-of-time-ordered correlators
- Quantum bounds on the generalized Lyapunov exponents
- Extracting classical Lyapunov exponent from one-dimensional quantum mechanics
- Phenomenological implications of asymmetric shockwave collision studies for heavy ion physics
- Out-of-time-ordered correlators of the Hubbard model: SYK strange metal in the spin freezing crossover region
- Quantum chaos in supersymmetric quantum mechanics: an exact diagonalization study
- Dynamics of spectral correlations in the entanglement Hamiltonian of the Aubry-André-Harper model
- Fingerprint of chaos and quantum scars in kicked Dicke model: An out-of-time-order correlator study
- Quantum Information Scrambling in Molecules
- Relative asymptotic oscillations of the out-of-time-ordered correlator as a quantum chaos indicator
- Classical route to ergodicity and scarring in collective quantum systems
- Exponential speedup in measuring out-of-time-ordered correlators with a single bit of quantum information
- Single-Particle Universality of the Many-Body Spectral Form Factor
- Primordial cosmic complexity and effects of reheating
- Dynamical Detection of Level Repulsion in the One-Particle Aubry-André Model
- Out-of-Time Ordered Correlators in Kicked Coupled Tops: Information Scrambling in Mixed Phase Space and the Role of Conserved Quantities
- Quantum Kolmogorov-Sinai entropy and Pesin relation
- Nonequilibrium many-body quantum dynamics: from full random matrices to real systems
- Disorder-free Sachdev-Ye-Kitaev models: Integrability and a precursor of chaos
- Chaos and the dynamics of information in dissipative electronic systems
- False signals of chaos from quantum probes
- Out-of-time-order correlators of nonlocal block-spin and random observables in integrable and nonintegrable spin chains
- Out-of-Time-Order-Correlation in perturbed quantum wells
- Path-Integral Approach to Quantum Acoustics