Analyticity constraints bound the decay of the spectral form factor
arXiv:2202.11715 · doi:10.22331/q-2022-11-03-852
Abstract
Quantum chaos cannot develop faster than for systems in thermal equilibrium [Maldacena, Shenker & Stanford, JHEP (2016)]. This `MSS bound' on the Lyapunov exponent is set by the width of the strip on which the regularized out-of-time-order correlator is analytic. We show that similar constraints also bound the decay of the spectral form factor (SFF), that measures spectral correlation and is defined from the Fourier transform of the two-level correlation function. Specifically, the inflection exponent , that we introduce to characterize the early-time decay of the SFF, is bounded as . This bound is universal and exists outside of the chaotic regime. The results are illustrated in systems with regular, chaotic, and tunable dynamics, namely the single-particle harmonic oscillator, the many-particle Calogero-Sutherland model, an ensemble from random matrix theory, and the quantum kicked top. The relation of the derived bound with other known bounds, including quantum speed limits, is discussed.
arXiv comment9+3 pages, 6+3 figures. Accepted for publication in Quantum
References in corpus (65)
- Advances in Quantum Metrology
- A bound on chaos
- Ultimate physical limits to computation
- The maximum speed of dynamical evolution
- Dynamical Quantum Phase Transitions in the Transverse Field Ising Model
- Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
- Black Holes and Random Matrices
- Quantum speed limit for physical processes
- Optimal Control at the Quantum Speed Limit
- Quantum speed limits in open system dynamics
- Exact Spectral Form Factor in a Minimal Model of Many-Body Quantum Chaos
- Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System
- The fundamental limit on the rate of quantum dynamics: the unified bound is tight
- Black Holes and Superconformal Mechanics
- Chaos, Complexity, and Random Matrices
- Out-of-time-order correlators in quantum mechanics
- Black Holes and Calogero Models
- Unifying fast scrambling, thermalization and entanglement through the measurement of FOTOCs in the Dicke model
- Thermodynamics of an one-dimensional ideal gas with fractional exclusion statistics
- Quantum and Classical Lyapunov Exponents in Atom-Field Interaction Systems
- Quantum Supremacy of Many-Particle Thermal Machines
- Quantum Speed Limits Across the Quantum-to-Classical Transition
- Universal Work Fluctuations during Shortcuts To Adiabaticity by Counterdiabatic Driving
- Quantum Speed Limit is Not Quantum
- Positive quantum Lyapunov exponents in experimental systems with a regular classical limit
- Bounds on chaos from the eigenstate thermalization hypothesis
- Scrambling the spectral form factor: unitarity constraints and exact results
- Local Operators in the Eternal Black Hole
- The spectral form factor is not self-averaging
- Out-of-Time-Order Correlation at a Quantum Phase Transition
- Many-Body Chaos in the Sachdev-Ye-Kitaev Model
- Very Long Time Scales and Black Hole Thermal Equilibrium
- Nonlinear quantum metrology of many-body open systems
- Orthogonality Catastrophe as a Consequence of the Quantum Speed Limit
- Digital Quantum Simulation, Trotter Errors, and Quantum Chaos of the Kicked Top
- Unifying Quantum and Classical Speed Limits on Observables
- Gauging classical and quantum integrability through out-of-time ordered correlators
- Geometric Speed Limit of Accessible Many-Body State Preparation
- Thermofield dynamics: Quantum Chaos versus Decoherence
- Extreme Decoherence and Quantum Chaos
- Spectral Filtering Induced by Non-Hermitian Evolution with Balanced Gain and Loss: Enhancing Quantum Chaos
- Bounds on transport from univalence and pole-skipping
- Probing Quantum Speed Limits with Ultracold Gases
- Work Statistics, Loschmidt Echo and Information Scrambling in Chaotic Quantum Systems
- Out-of-time-order correlator in coupled harmonic oscillators
- Quantum work statistics, Loschmidt echo and information scrambling
- Exact Quantum Decay of an Interacting Many-Particle System: the Calogero-Sutherland model
- Bound on the exponential growth rate of out-of-time-ordered correlators
- Quantum Lyapunov Spectrum
- Long time scales and eternal black holes
- Quantum operator growth bounds for kicked tops and semiclassical spin chains
- Decoherence in Conformal Field Theory
- Out-of-time-order fluctuation-dissipation theorem
- Diverging quantum speed limits: a herald of classicality
- Universality in Chaos: Lyapunov Spectrum and Random Matrix Theory
- Quantum bounds and fluctuation-dissipation relations
- Butterfly Floquet Spectrum in Driven SU(2) Systems
- Out-of-time-ordered correlators and the Loschmidt echo in the quantum kicked top: How low can we go?
- Subleading Bounds on Chaos
- Scrambling dynamics and many-body chaos in a random dipolar spin model
- A Calogero formulation for four-dimensional black-hole micro states
- Generating a Fractal Butterfly Floquet Spectrum in a Class of Driven SU(2) Systems
- Low temperature quantum bounds on simple models
- An Inelastic Bound on Chaos
- Microscope for Quantum Dynamics with Planck Cell Resolution
Cited by in corpus (6)
- Quantum Dynamics in Krylov Space: Methods and Applications
- Exact universal bounds on quantum dynamics and fast scrambling
- Quantum Chaos and Coherence: Random Parametric Quantum Channels
- Universal Properties of the Spectral Form Factor in Open Quantum Systems
- Decomposing the Spectral Form Factor
- Family of Exact and Inexact Quantum Speed Limits for Completely Positive and Trace-Preserving Dynamics