Exponential growth of out-of-time-order correlator without chaos: inverted harmonic oscillator
arXiv:2007.04746 · doi:10.1007/JHEP11(2020)068
Abstract
We provide a detailed examination of a thermal out-of-time-order correlator (OTOC) growing exponentially in time in systems without chaos. The system is a one-dimensional quantum mechanics with a potential whose part is an inverted harmonic oscillator. We numerically observe the exponential growth of the OTOC when the temperature is higher than a certain threshold. The Lyapunov exponent is found to be of the order of the classical Lyapunov exponent generated at the hilltop, and it remains non-vanishing even at high temperature. We adopt various shape of the potential and find these features universal. The study confirms that the exponential growth of the thermal OTOC does not necessarily mean chaos when the potential includes a local maximum. We also provide a bound for the Lyapunov exponent of the thermal OTOC in generic quantum mechanics in one dimension, which is of the same form as the chaos bound obtained by Maldacena, Shenker and Stanford.
arXiv comment24 pages, 14 figures; v2: Appendix B (studying other operator orderings of OTOC) added, a reference added
References in corpus (40)
- The Large N Limit of Superconformal Field Theories and Supergravity
- M Theory As A Matrix Model: A Conjecture
- A bound on chaos
- Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
- Comments on the Sachdev-Ye-Kitaev model
- Black holes and the butterfly effect
- Multiple Shocks
- Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System
- Out-of-time-order correlators in quantum mechanics
- Scrambling and thermalization in a diffusive quantum many-body system
- Does scrambling equal chaos?
- Scrambling and entanglement spreading in long-range spin chains
- Many-body chaos at weak coupling
- Quantum and Classical Lyapunov Exponents in Atom-Field Interaction Systems
- Universality in Chaos of Particle Motion near Black Hole Horizon
- Positive quantum Lyapunov exponents in experimental systems with a regular classical limit
- Chaos signatures in the short and long time behavior of the out-of-time ordered correlator
- Presence of horizon makes particle motion chaotic
- Many-Body Quantum Interference and the Saturation of Out-of-Time-Order Correlators
- Disrupting Entanglement of Black Holes
- Gauging classical and quantum integrability through out-of-time ordered correlators
- Reversible quantum information spreading in many-body systems near criticality
- Linear growth of the entanglement entropy and the Kolmogorov-Sinai rate
- Semiclassical theory of out-of-time-order correlators for low-dimensional classically chaotic systems
- Early-Time Exponential Instabilities in Non-Chaotic Quantum Systems
- Scrambling and Complexity in Phase Space
- Chaos in Classical D0-Brane Mechanics
- The Black Hole S-Matrix from Quantum Mechanics
- Universal level statistics of the out-of-time-ordered operator
- Out-of-time-order correlator in coupled harmonic oscillators
- Chaos in the BMN matrix model
- Out-of-time-ordered correlator in the quantum bakers map and truncated unitary matrices
- Scrambling in strongly chaotic weakly coupled bipartite systems: Universality beyond the Ehrenfest time-scale
- Thermal Emission from Semi-classical Dynamical Systems
- Chaos in chiral condensates in gauge theories
- Quantum chaos, thermalization and entanglement generation in real-time simulations of the BFSS matrix model
- OTOC, complexity and entropy in bi-partite systems
- The smallest matrix black hole model in the classical limit
- Similar early growth of out-of-time-ordered correlators in quantum chaotic and integrable Ising chains
- Out-of-time-order correlators in bipartite nonintegrable systems
Cited by in corpus (73)
- Krylov complexity in saddle-dominated scrambling
- Information Scrambling over Bipartitions: Equilibration, Entropy Production, and Typicality
- Information Scrambling and Chaos in Open Quantum Systems
- Krylov complexity and chaos in quantum mechanics
- The Multi-faceted Inverted Harmonic Oscillator: Chaos and Complexity
- Scrambling is Necessary but Not Sufficient for Chaos
- Ubiquitous quantum scarring does not prevent ergodicity
- Spectral and Krylov Complexity in Billiard Systems
- Bounds in Nonequilibrium Quantum Dynamics
- Classifying pole-skipping points
- Quantum chaos, scrambling and operator growth in deformed SYK models
- Bound of diffusion constants from pole-skipping points: spontaneous symmetry breaking and magnetic field
- Saddle-point scrambling without thermalisation
- Spread complexity in saddle-dominated scrambling
- Quantum coherence as a signature of chaos
- Spectral kissing and its dynamical consequences in the squeeze-driven Kerr oscillator
- Complexity from the Reduced Density Matrix: a new Diagnostic for Chaos
- Random Matrix Theory of the Isospectral twirling
- Circuit Complexity as a novel probe of Quantum Entanglement: A study with Black Hole Gas in arbitrary dimensions
- Chaos in coupled Kerr-nonlinear parametric oscillators
- Fokker-Planck equation for black holes in thermal potential
- Chaos and Complexity for Inverted Harmonic Oscillators
- Homoclinic orbit and the violation of the chaos bound around a black hole with anisotropic matter fields
- Two-step phantom relaxation of out-of-time-ordered correlations in random circuits
- The Squeezed OTOC and Cosmology
- Krylov Complexity and Dynamical Phase Transition in the quenched LMG model
- Inverted harmonic oscillator dynamics of the nonequilibrium phase transition in the Dicke model
- Refined quantum Lyapunov exponents from replica out-of-time-order correlators
- Quantum chaos without false positives
- Surprises in the Deep Hilbert Space of all-to-all systems: From super-exponential scrambling to slow entanglement growth
- Extracting classical Lyapunov exponent from one-dimensional quantum mechanics
- Krylov Complexity in Mixed Phase Space
- Quantum-classical correspondence of a system of interacting bosons in a triple-well potential
- Quantum chaos in supersymmetric quantum mechanics: an exact diagonalization study
- Quasinormal Modes and Universality of the Penrose Limit of Black Hole Photon Rings
- Dynamical transition from localized to uniform scrambling in locally hyperbolic systems
- Witnessing quantum chaos using observational entropy
- Slow relaxation of out-of-time-ordered correlators in interacting integrable and nonintegrable spin-1/2 XYZ chains
- Chaos and multifold complexity for an inverted harmonic oscillator
- Krylov Complexity as a Probe for Chaos
- Classical and quantum butterfly effect in nonlinear vector mechanics
- Quantum-classical correspondence of strongly chaotic many-body spin models
- Classical approach to equilibrium of out-of-time ordered correlators in mixed systems
- Microscope for Quantum Dynamics with Planck Cell Resolution
- Classical route to ergodicity and scarring in collective quantum systems
- Probing Dynamical Sensitivity of a Non-KAM System Through Out-of-Time-Order Correlators
- Excited-State Quantum Phase Transitions in the Anharmonic Lipkin-Meshkov-Glick Model: Dynamical Aspects
- Scaling at the OTOC Wavefront: free versus chaotic models
- Excited state quantum phase transition and Loschmidt echo spectra in a spinor Bose-Einstein condensate
- Free Independence and the Noncrossing Partition Lattice in Dual-Unitary Quantum Circuits
- Duality between the quantum inverted harmonic oscillator and inverse square potentials
- Evolution of circuit complexity in a harmonic chain under multiple quenches
- Signatures of the interplay between chaos and local criticality on the dynamics of scrambling in many-body systems
- D-commuting SYK model: building quantum chaos from integrable blocks
- Temporal fluctuations of correlators in integrable and chaotic quantum systems
- Correlation functions for open strings and chaos
- Degeneracy in excited-state quantum phase transitions of two-level bosonic models and its influence on system dynamics
- Out-of-Time Ordered Correlators in Kicked Coupled Tops: Information Scrambling in Mixed Phase Space and the Role of Conserved Quantities
- Non-Markovian environment induced chaos in optomechanical system
- Out-of-Time-Order-Correlator for van der Waals potential
- Causality Constraint on Circuit Complexity from
- Manifestation of strange nonchaotic attractors in extended systems: A study through out-of-time-ordered correlators
- Disorder-free Sachdev-Ye-Kitaev models: Integrability and a precursor of chaos
- Quantum instability and Ehrenfest time for an inverted harmonic oscillator
- Dependence of Krylov complexity on the initial operator and state
- Spectral chaos bounds from scaling theory of maximally efficient quantum-dynamical scrambling
- Quantum Signatures of Chaos in Anisotropic Quantum Rabi Model
- Anatomy of information scrambling and decoherence in the integrable Sachdev-Ye-Kitaev model
- Study of double kicked top: a classical and quantum perspective
- Detecting few-body quantum chaos: out-of-time ordered correlators at saturation
- Information acquisition, scrambling, and sensitivity to errors in quantum chaos
- False signals of chaos from quantum probes
- Out-of-Time-Order-Correlation in perturbed quantum wells