Nonexponential fidelity decay in isolated interacting quantum systems

Abstract

We study isolated finite interacting quantum systems after an instantaneous perturbation and show three scenarios in which the probability for finding the initial state later in time (fidelity) decays nonexponentially, often all the way to saturation. The decays analyzed involve Gaussian, Bessel of the first kind, and cosine squared functions. The Gaussian behavior emerges in systems with two-body interactions in the limit of strong perturbation. The Bessel function, associated with the evolution under full random matrices, is obtained with surprisingly sparse random matrices. The cosine squared behavior, established by the energy-time uncertainty relation, is approached after a local perturbation in space.

9 pages, 5 figures, version as published

References in corpus (57)

• Random Matrix Theories in Quantum Physics: Common Concepts
• Probing the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas
• Time-resolved Observation and Control of Superexchange Interactions with Ultracold Atoms in Optical Lattices
• Dynamics of Loschmidt echoes and fidelity decay
• Environment-independent decoherence rate in classically chaotic systems
• Quantum dynamics of a single, mobile spin impurity
• Optimal Control at the Quantum Speed Limit
• Quantum limits to dynamical evolution
• The Statistics of the Work Done on a Quantum Critical System by Quenching a Control Parameter
• Golden rule decay versus Lyapunov decay of the quantum Loschmidt echo
• Dynamical quantum phase transitions and the Loschmidt echo: A transfer matrix approach
• On general relation between quantum ergodicity and fidelity of quantum dynamics
• Loschmidt Echo
• Decoherence, Entanglement and Irreversibility in Quantum Dynamical Systems with Few Degrees of Freedom
• Statistical Theory of Finite Fermi-Systems Based on the Structure of Chaotic Eigenstates
• What determines the spreading of a wave packet?
• Controlling Correlated Tunneling and Superexchange Interactions with AC-Driven Optical Lattices
• Integrability of a disordered Heisenberg spin-1/2 chain
• Fidelity Decay as an Efficient Indicator of Quantum Chaos
• Onset of chaos and relaxation in isolated systems of interacting spins-1/2: energy shell approach
• Wigner Random Banded Matrices with Sparse Structure: Local Spectral Density of States
• Chaos and statistical relaxation in quantum systems of interacting particles
• Quantum chaos: an introduction via chains of interacting spins-1/2
• Sensitivity of Quantum Motion for Classically Chaotic Systems
• Simulations of Information Transport in Spin Chains
• Measuring the Lyapunov exponent using quantum mechanics
• Quenches in a quasi-disordered integrable lattice system: Dynamics and statistical description of observables after relaxation
• Local quenches with global effects in interacting quantum systems
• Exact infinite-time statistics of the Loschmidt echo for a quantum quench
• A random matrix formulation of fidelity decay
• Long-time behavior of many-particle quantum decay
• Level repulsion in integrable and almost-integrable quantum spin models
• Quench Dynamics of Isolated Many-Body Quantum Systems
• Time Fluctuations in Isolated Quantum Systems of Interacting Particles
• General Features of the Relaxation Dynamics of Interacting Quantum Systems
• Excited Eigenstates and Strength Functions for Isolated Systems of Interacting Particles
• Absence of exponential sensitivity to small perturbations in nonintegrable systems of spins 1/2
• Transient Orthogonality Catastrophe in a Time Dependent Nonequilibrium Environment
• Entropy production and wave packet dynamics in the Fock space of closed chaotic many-body systems
• Unconventional decay law for excited states in closed many-body systems
• Single-particle and many-body analyses of a quasiperiodic integrable system after a quench
• Experimental characterization of coherent magnetization transport in a one-dimensional spin system
• Level Statistics of XXZ Spin Chains with Discrete Symmetries: Analysis through Finite-size Effects
• Effects of the interplay between initial state and Hamiltonian on the thermalization of isolated quantum many-body systems
• Short time decay of the Loschmidt echo
• Structure of wavefunctions in (1+2)-body random matrix ensembles
• Quantum quenches in the Dicke model: statistics of the work done and of other observables
• Return probability: Exponential versus Gaussian decay
• The X-ray edge singularity in Quantum Dots
• Quantum quenches and work distributions in ultra-low-density systems
• Dynamics of thermalisation in small Hubbard-model systems
• The Loschmidt Echo as a robust decoherence quantifier for many-body systems
• Strength functions, entropies and duality in weakly to strongly interacting fermionic systems
• Critical Fidelity
• Bivariate $t$-distribution for transition matrix elements in Breit-Wigner to Gaussian domains of interacting particle systems
• Sensitivity to perturbations and quantum phase transitions
• Fidelity decay in interacting two-level boson systems: Freezing and revivals

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• Thouless and relaxation time scales in many-body quantum systems
• Scrambling the spectral form factor: unitarity constraints and exact results
• Generic dynamical features of quenched interacting quantum systems: Survival probability, density imbalance and out-of-time-ordered correlator
• Extended nonergodic states in disordered many-body quantum systems
• Excited-state quantum phase transitions in many-body systems with infinite-range interaction: Localization, dynamics, and bifurcation
• Structure of eigenstates and quench dynamics at an excited state quantum phase transition
• Cooperative shielding in many-body systems with long-range interaction
• Nonexponential quantum decay under environmental decoherence
• Dynamical Manifestations of Quantum Chaos: Correlation Hole and Bulge
• Inevitable Power-law Behavior of Isolated Many-Body Quantum Systems and How It Anticipates Thermalization
• Power-law decay exponents: a dynamical criterion for predicting thermalization
• Realistic many-body quantum systems vs full random matrices: static and dynamical properties
• Relaxation and Thermalization of Isolated Many-Body Quantum Systems
• Quantum Speed Limits for Observables
• Exact Quantum Decay of an Interacting Many-Particle System: the Calogero-Sutherland model
• Overlap distributions for quantum quenches in the anisotropic Heisenberg chain
• Effects of excited state quantum phase transitions on system dynamics
• Chaos and quantum scars in a coupled top model
• Self-averaging in many-body quantum systems out of equilibrium. II. Approach to the localized phase
• Level Repulsion and Dynamics in the Finite One-Dimensional Anderson Model
• Decay of a Thermofield-Double State in Chaotic Quantum Systems
• Analytical description of the survival probability of coherent states in regular regimes
• Signatures of chaos and thermalization in the dynamics of many-body quantum systems
• Bose-Hubbard ladder subject to effective magnetic field: quench dynamics in a harmonic trap
• Return amplitude after a quantum quench in the XY chain
• Proliferation of effective interactions: decoherence-induced equilibration in a closed many-body system
• Loschmidt echo in many-spin systems: a quest for intrinsic decoherence and emergent irreversibility
• Non-exponential tunneling ionization of atoms by an intense laser field
• Effects of auto-correlated disorder on the dynamics in the vicinity of the many-body localization transition
• Relaxation dynamics of ultracold bosons in a double-well potential: Thermalization and prethermalization in a nearly integrable model
• Generalized Survival Probability
• Spectral form factor and energy correlations in banded random matrices
• Nonequilibrium many-body quantum dynamics: from full random matrices to real systems
• Non-exponential Auger decay
• Many Body Density of States of a system of non interacting spinless fermions
• Anomalous energy correlations and spectral form factor in the nonergodic phase of the $\beta$-ensemble
• Nonequilibrium localization and the interplay between disorder and interactions
• Unconventional early-time relaxation in the Rydberg chain
• Quantum transitions, ergodicity, and quantum scars in the coupled top model