Quantum Chaos and the Correspondence Principle

Abstract

The correspondence principle is a cornerstone in the entire construction of quantum mechanics. This principle has been recently challenged by the observation of an early-time exponential increase of the out-of-time-ordered correlator (OTOC) in classically non-chaotic systems [E.B. Rozenbaum et al., Phys. Rev. Lett. 125, 014101 (2020)], Here we show that the correspondence principle is restored after a proper treatment of the singular points. Furthermore our results show that the OTOC maintains its role as a diagnostic of chaotic dynamics.

7 pages, 7 figures

References in corpus (2)

• Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System
• Timescales in the quench dynamics of many-body quantum systems: Participation ratio vs out-of-time ordered correlator

Cited by in corpus (25)

• Random Matrix Theory of the Isospectral twirling
• From ETH to algebraic relaxation of OTOCs in systems with conserved quantities
• Statistical and dynamical properties of the quantum triangle map
• Scaling laws of the out-of-time-order correlators at the transition to the spontaneous $\mathcal{P}\mathcal{T}$-symmetry breaking in a Floquet system
• Effective protection of quantum coherence by non-Hermitian driving
• Stochastic Operator Variance: an observable to diagnose noise and scrambling
• Slow relaxation of out-of-time-ordered correlators in interacting integrable and nonintegrable spin-1/2 XYZ chains
• Relative asymptotic oscillations of the out-of-time-ordered correlator as a quantum chaos indicator
• Quantum information scrambling in two-dimensional Bose-Hubbard lattices
• Quantum-classical correspondence of strongly chaotic many-body spin models
• Effect of chaos on information gain in quantum tomography
• Quantum Lyapunov exponent in dissipative systems
• Probing Dynamical Sensitivity of a Non-KAM System Through Out-of-Time-Order Correlators
• Quantum Chaos and Circuit Parameter Optimization
• Scaling at the OTOC Wavefront: free versus chaotic models
• Temporal fluctuations of correlators in integrable and chaotic quantum systems
• Out-of-Time-Order-Correlator for van der Waals potential
• Canonical density matrices from eigenstates of mixed systems
• Relaxation exponents of OTOCs and overlap with local Hamiltonians
• Asymmetric Transmission Through a Classical Analogue of the Aharonov-Bohm Ring
• Unravelling quantum chaos using persistent homology
• Quantum instability and Ehrenfest time for an inverted harmonic oscillator
• Loschmidt echo and scrambling of systematic errors in tomography -- a quantum signature of chaos
• Quantum Signatures of Chaos in Anisotropic Quantum Rabi Model
• Behavior of correlation functions in the dynamics of the Multiparticle Quantum Arnol'd Cat