Out-of-time-order correlator in coupled harmonic oscillators
arXiv:2004.04381 · doi:10.1007/JHEP08(2020)013
Abstract
Exponential growth of thermal out-of-time-order correlator (OTOC) is an indicator of a possible gravity dual, and a simple toy quantum model showing the growth is being looked for. We consider a system of two harmonic oscillators coupled nonlinearly with each other, and numerically observe that the thermal OTOC grows exponentially in time. The system is well-known to be classically chaotic, and is a reduction of Yang-Mills-Higgs theory. The exponential growth is certified because the growth exponent (quantum Lyapunov exponent) of the thermal OTOC is well matched with the classical Lyapunov exponent, including their energy/temperature dependence. Even in the presence of the exponential growth in the OTOC, the energy level spacings are not sufficient to judge a Wigner distribution, hence the OTOC is a better indicator of quantum chaos.
arXiv comment27 pages, 14 figures. v2: analysis of level statistics improved, references and comments added
References in corpus (45)
- M Theory As A Matrix Model: A Conjecture
- A bound on chaos
- Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
- Localization of interacting fermions at high temperature
- Comments on the Sachdev-Ye-Kitaev model
- Black holes and the butterfly effect
- The distribution of the ratio of consecutive level spacings in random matrix ensembles
- 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
- Many-body chaos at weak coupling
- Out-of-time-ordered correlators in quantum Ising chain
- 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
- Out-of-Time-Order Correlation at a Quantum Phase Transition
- Presence of horizon makes particle motion chaotic
- Chaos and Complexity in Quantum Mechanics
- Many-Body Quantum Interference and the Saturation of Out-of-Time-Order Correlators
- Disrupting Entanglement of Black Holes
- Generalized Conformal Symmetry in D-Brane Matrix Models
- Space-Time Uncertainty Principle and Conformal Symmetry in D-Particle Dynamics
- 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
- Hamiltonian Dynamics of Yang-Mills Fields on a Lattice
- Chaotic behavior in classical Yang-Mills dynamics
- Static Equilibria of Charged Particles Around Charged Black Holes: Chaos Bound and Its Violations
- Chaos in Classical D0-Brane Mechanics
- Probing excited-state quantum phase transition in a quantum many body system via out-of-time-ordered correlator
- Detection of quantum phases via out-of-time-order correlators
- Universal level statistics of the out-of-time-ordered operator
- Timescales in the quench dynamics of many-body quantum systems: Participation ratio vs out-of-time ordered correlator
- Thermal Emission from Semi-classical Dynamical Systems
- Chaos in chiral condensates in gauge theories
- Chaos in Matrix Models and Black Hole Evaporation
- Chaos of Wilson Loop from String Motion near Black Hole Horizon
- Out-of-time-ordered correlators in short-range and long-range hard-core boson models and in the Luttinger-liquid model
- Induction of chaotic fluctuations in particle dynamics in a uniformly accelerated frame
- Quantum chaos, thermalization and entanglement generation in real-time simulations of the BFSS matrix model
- 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
- Phase diagram of QCD chaos in linear sigma models and holography
- Interactions resolve state-dependence in a toy-model of AdS black holes
- Chaos and Scrambling in Quantum Small Worlds
Cited by in corpus (34)
- Krylov complexity in saddle-dominated scrambling
- Exponential growth of out-of-time-order correlator without chaos: inverted harmonic oscillator
- Krylov complexity and chaos in quantum mechanics
- Spread complexity in saddle-dominated scrambling
- Chaos in coupled Kerr-nonlinear parametric oscillators
- Quantum chaos without false positives
- Refined quantum Lyapunov exponents from replica out-of-time-order correlators
- Out-of-Time-Order Correlation as a Witness for Topological Phase Transitions
- Extracting classical Lyapunov exponent from one-dimensional quantum mechanics
- Quantum chaos in supersymmetric quantum mechanics: an exact diagonalization study
- Quantum Mechanical Out-Of-Time-Ordered-Correlators for the Anharmonic (Quartic) Oscillator
- Fingerprint of chaos and quantum scars in kicked Dicke model: An out-of-time-order correlator study
- Information scrambling -- a quantum thermodynamic perspective
- The Cosmological OTOC: A New Proposal for Quantifying Auto-Correlated Random Non-Chaotic Primordial Fluctuations
- Thermalization in different phases of charged SYK model
- Classical approach to equilibrium of out-of-time ordered correlators in mixed systems
- Classical and quantum butterfly effect in nonlinear vector mechanics
- Quantum Lyapunov exponent in dissipative systems
- Excited-State Quantum Phase Transitions in the Anharmonic Lipkin-Meshkov-Glick Model: Dynamical Aspects
- Analyticity constraints bound the decay of the spectral form factor
- Chaos in Yang-Mills Chern-Simons Matrix Model
- Relevant OTOC operators: footprints of the classical dynamics
- Out-of-Time-Order-Correlator for van der Waals potential
- Scrambling under quench
- Quantum instability and Ehrenfest time for an inverted harmonic oscillator
- Disorder-free Sachdev-Ye-Kitaev models: Integrability and a precursor of chaos
- Quantum signatures of chaos in a cavity-QED-based stimulated Raman adiabatic passage
- Quantum Signatures of Chaos in Anisotropic Quantum Rabi Model
- Cosmological Geometric Phase From Pure Quantum States: A study without/with having Bell's inequality violation
- Detecting few-body quantum chaos: out-of-time ordered correlators at saturation
- Chaos in the holographic matrix models for meson and baryon
- Deconfinement of classical Yang-Mills color fields in a disorder potential
- Out-of-Time-Order-Correlation in perturbed quantum wells
- Existence of a supersymmetric extension of the gauged non-linear -model and the transition from integrability to chaos