Bounds in Nonequilibrium Quantum Dynamics

Abstract

We review various bounds concerning out-of-equilibrium dynamics in few-level and many-body quantum systems. We primarily focus on closed quantum systems but will also mention some related results for open quantum systems and classical stochastic systems. We start from the speed limits, the universal bounds on the speeds of (either quantum or classical) dynamical evolutions. We then turn to review the bounds that address how good and how long would a quantum system equilibrate or thermalize. Afterward, we focus on the stringent constraint set by locality in many-body systems, rigorously formalized as the Lieb-Robinson bound. We also review the bounds related to the dynamics of entanglement, a genuine quantum property. Apart from some other miscellaneous topics, several notable error bounds for approximated quantum dynamics are discussed. While far from comprehensive, this topical review covers a considerable amount of recent progress and thus could hopefully serve as a convenient starting point and up-to-date guidance for interested readers.

arXiv comment87 pages, 11 figures. Commissioned review paper submitted to International Journal of Modern Physics B, (close to) final version

References in corpus (276)

• Many-Body Physics with Ultracold Gases
• Theory of Bose-Einstein condensation in trapped gases
• A nonequilibrium equality for free energy differences
• Quantum sensing
• Advances in Quantum Metrology
• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Chaos and Quantum Thermalization
• Thermalization and its mechanism for generic isolated quantum systems
• Quantum Simulation
• Area laws for the entanglement entropy - a review
• Nonequilibrium dynamics of closed interacting quantum systems
• Probing many-body dynamics on a 51-atom quantum simulator
• Many body localization and thermalization in quantum statistical mechanics
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• A bound on chaos
• Edge states and topological invariants of non-Hermitian systems
• The large deviation approach to statistical mechanics
• 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
• Many-body localization, thermalization, and entanglement
• Non-Hermitian Physics
• Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons
• Average Entropy of a Subsystem
• Black holes and the butterfly effect
• The many-body localization phase transition
• Entropy production along a stochastic trajectory and an integral fluctuation theorem
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Topological Origin of Non-Hermitian Skin Effects
• Quantum Resource Theories
• Colloquium. Quantum Fluctuation Relations: Foundations and Applications
• Quantum many-body systems out of equilibrium
• Atomic quantum gases in periodically driven optical lattices
• Observation of a Discrete Time Crystal
• Many-Body Physics with Individually-Controlled Rydberg Atoms
• An Area Law for One Dimensional Quantum Systems
• Observation of discrete time-crystalline order in a disordered dipolar many-body system
• Thermodynamic uncertainty relation for biomolecular processes
• Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
• Floquet Engineering of Quantum Materials
• Quantum many-body scars
• Many body localization in Heisenberg XXZ magnet in a random field
• Floquet Time Crystals
• Quantum Thermodynamics
• The role of quantum information in thermodynamics --- a topical review
• Realizing a lattice spin model with polar molecules
• Quantum Time Crystals
• The maximum speed of dynamical evolution
• Observation of entanglement propagation in a quantum many-body system
• Light-cone-like spreading of correlations in a quantum many-body system
• Hamiltonian Simulation by Qubitization
• Steady State Thermodynamics of Langevin Systems
• Non-local propagation of correlations in long-range interacting quantum systems
• Fundamental limitations for quantum and nano thermodynamics
• Reduced density matrices and entanglement entropy in free lattice models
• Quantum Fisher information matrix and multiparameter estimation
• The second laws of quantum thermodynamics
• Chaos in quantum channels
• Dissipation bounds all steady-state current fluctuations
• The Spectrum in the Sachdev-Ye-Kitaev Model
• Quantum Quench in the Transverse Field Ising Chain
• Lieb-Schultz-Mattis in Higher Dimensions
• Efficient quantum algorithms for simulating sparse Hamiltonians
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Quench dynamics and relaxation in isolated integrable quantum spin chains
• Extractable work from ensembles of quantum batteries. Entanglement helps
• Maximal work extraction from quantum systems
• Dynamics of Loschmidt echoes and fidelity decay
• Quantum mechanical evolution towards thermal equilibrium
• Non-Hermitian skin effect and chiral damping in open quantum systems
• The Physics of Maxwell's demon and information
• Phase space representation of quantum dynamics
• Discrete time crystals: rigidity, criticality, and realizations
• Spectral Gap and Exponential Decay of Correlations
• Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
• Schrieffer-Wolff transformation for quantum many-body systems
• Black Holes and Random Matrices
• Equilibrium states of generic quantum systems subject to periodic driving
• The approach to thermal equilibrium in quantized chaotic systems
• Quantum Many-Body Scars and Weak Breaking of Ergodicity
• Breakdown of thermalization in finite one-dimensional systems
• Foundation of Statistical Mechanics under experimentally realistic conditions
• Generalized Jarzynski Equality under Nonequilibrium Feedback Control
• Thermalization and prethermalization in isolated quantum systems: a theoretical overview
• Localization from Hilbert space shattering: from theory to physical realizations
• Quantum speed limit for physical processes
• Quantum speed limit for non-Markovian dynamics
• Optimal Control at the Quantum Speed Limit
• Quantum speed limits in open system dynamics
• Time crystals: a review
• Local constraints can globally shatter Hilbert space: a new route to quantum information protection
• Absence of Quantum Time Crystals
• Second Law of Thermodynamics with Discrete Quantum Feedback Control
• Floquet-Magnus Theory and Generic Transient Dynamics in Periodically Driven Many-Body Quantum Systems
• Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
• Exponentially slow heating in periodically driven many-body systems
• From Quantum Dynamics to the Canonical Distribution: General Picture and a Rigorous Example
• Minimal Energy Cost for Thermodynamic Information Processing: Measurement and Information Erasure
• Exponential localization of Wannier functions in insulators
• Lieb-Robinson Bounds and the Exponential Clustering Theorem
• Commensurability, excitation gap and topology in quantum many-particle systems on a periodic lattice
• Quasi-adiabatic Continuation of Quantum States: The Stability of Topological Ground State Degeneracy and Emergent Gauge Invariance
• Universal trade-off between power, efficiency, and constancy in steady-state heat engines
• Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models
• Entropy, entanglement, and area: analytical results for harmonic lattice systems
• Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems
• Topological quantum order: stability under local perturbations
• Effective Hamiltonians, prethermalization and slow energy absorption in periodically driven many-body systems
• Effect of Rare Fluctuations on the Thermalization of Isolated Quantum Systems
• Exact Spectral Form Factor in a Minimal Model of Many-Body Quantum Chaos
• Entanglement Generation is Not Necessary for Optimal Work Extraction
• Non-stationary coherent quantum many-body dynamics through dissipation
• Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System
• Discrete Time Crystals
• Systematic Construction of Counterexamples to the Eigenstate Thermalization Hypothesis
• Boundary time crystals
• The fundamental limit on the rate of quantum dynamics: the unified bound is tight
• Gate count estimates for performing quantum chemistry on small quantum computers
• Semiclassical Foundation of Universality in Quantum Chaos
• A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems
• Observation of Discrete-Time-Crystal Signatures in an Ordered Dipolar Many-Body System
• Emergent statistical mechanics of entanglement in random unitary circuits
• Proof of the Finite-Time Thermodynamic Uncertainty Relation for Steady-State Currents
• Observation of a dissipative time crystal
• Discrete Time-Crystalline Order in Cavity and Circuit QED Systems
• Speed Limit for Classical Stochastic Processes
• Trade-off between speed and cost in shortcuts to adiabaticity
• Quantum equilibration in finite time
• Fluctuation theorem uncertainty relation
• Observation of a prethermal discrete time crystal
• An entanglement-area law for general bosonic harmonic lattice systems
• Towards a theory of metastability in open quantum dynamics
• Thermodynamic uncertainty relations from exchange fluctuation theorems
• Does scrambling equal chaos?
• Adiabatic Elimination in a Lambda System
• Nearly-linear light cones in long-range interacting quantum systems
• Equilibration of quantum systems and subsystems
• General entanglement scaling laws from time evolution
• Relaxation times of dissipative many-body quantum systems
• Energy-time uncertainty relation for driven quantum systems
• Periodic-Orbit Theory of Universality in Quantum Chaos
• Liouvillian Skin Effect: Slowing Down of Relaxation Processes without Gap Closing
• Long-Time Behavior of Macroscopic Quantum Systems: Commentary Accompanying the English Translation of John von Neumann's 1929 Article on the Quantum Ergodic Theorem
• Nearly optimal lattice simulation by product formulas
• Geometric derivation of the quantum speed limit
• Entanglement capabilities of non-local Hamiltonians
• Locality in Quantum and Markov Dynamics on Lattices and Networks
• The Dynamics of 1D Quantum Spin Systems Can Be Approximated Efficiently
• Quantum Speed Limits Across the Quantum-to-Classical Transition
• Thermodynamic uncertainty relation for time-dependent driving
• Exponential Decay of Correlations Implies Area Law
• Weak Quantum Chaos
• Quantum Speed Limit is Not Quantum
• Universal Work Fluctuations during Shortcuts To Adiabaticity by Counterdiabatic Driving
• Long-range Ising and Kitaev Models: Phases, Correlations and Edge Modes
• Thouless energy and multifractality across the many-body localization transition
• Microcanonical and resource-theoretic derivations of the thermal state of a quantum system with noncommuting charges
• Index theory of one dimensional quantum walks and cellular automata
• Discrete time crystals in the absence of manifest symmetries or disorder in open quantum systems
• On the Approach to Thermal Equilibrium of Macroscopic Quantum Systems
• The Fisher information and the quantum Cramer-Rao sensitivity limit of continuous measurements
• Multidimensional thermodynamic uncertainty relations
• Quantum thermodynamic uncertainty relation for continuous measurement
• Uncertainty relations in stochastic processes: An information inequality approach
• Dicke time crystals in driven-dissipative quantum many-body systems
• Lieb-Robinson Bound and Locality for General Markovian Quantum Dynamics
• Typical fast thermalization processes in closed many-body systems
• On the capacities of bipartite Hamiltonians and unitary gates
• An area law for entanglement from exponential decay of correlations
• A review of Quantum Cellular Automata
• Fluctuation-Dissipation Theorem in an Isolated System of Quantum Dipolar Bosons after a Quench
• A non-equilibrium quantum Landauer principle
• Speed limit for open quantum systems
• Matrix Product Unitaries: Structure, Symmetries, and Topological Invariants
• Quantum Time Crystals from Hamiltonians with Long-Range Interactions
• Time-information uncertainty relations in thermodynamics
• Universality classes of non-Hermitian random matrices
• Geometrical Bounds of the Irreversibility in Markovian Systems
• Dynamics of entanglement and transport in 1D systems with quenched randomness
• Scrambling in Random Unitary Circuits: Exact Results
• Finite speed of quantum scrambling with long range interactions
• Persistence of locality in systems with power-law interactions
• Operator entanglement entropy of the time evolution operator in chaotic systems
• Unified Approach to Classical Speed Limit and Thermodynamic Uncertainty Relation
• A general framework for quantum macroscopicity in terms of coherence
• Finite-Size Scaling Analysis of the Eigenstate Thermalization Hypothesis in a One-Dimensional Interacting Bose gas
• Thermodynamic uncertainty relation for general open quantum systems
• Geometric lower bound for a quantum coherence measure
• Thermodynamic Uncertainty Relation for Arbitrary Initial States
• Exponential growth of out-of-time-order correlator without chaos: inverted harmonic oscillator
• Entanglement rates and area laws
• Fluctuation Theorem for Many-Body Pure Quantum States
• Resolving Discrepancy between Liouvillian Gap and Relaxation Time in Boundary-Dissipated Quantum Many-Body Systems
• On the time scales in the approach to equilibrium of macroscopic quantum systems
• Onset of Floquet Thermalisation
• Simulating adiabatic evolution of gapped spin systems
• Entropic bounds on currents in Langevin systems
• The Lieb-Robinson light cone for power-law interactions
• Reliability of lattice gauge theories
• Entanglement area laws for long-range interacting systems
• Generalization of von Neumann's Approach to Thermalization
• Eigenstate Thermalization, Random Matrix Theory and Behemoths
• Clustering of conditional mutual information for quantum Gibbs states above a threshold temperature
• Classical Prethermal Phases of Matter
• Geometric quantum speed limits: a case for Wigner phase space
• Exact convergence times for generation of random bipartite entanglement
• Extremely quick thermalization in a macroscopic quantum system for a typical nonequilibrium subspace
• Fast State Transfer and Entanglement Renormalization Using Long-Range Interactions
• An improved Lieb-Robinson bound for many-body Hamiltonians with power-law interactions
• Adiabatic Theorem for Quantum Spin Systems
• Semiclassical theory of out-of-time-order correlators for low-dimensional classically chaotic systems
• Upper bounds on entangling rates of bipartite Hamiltonians
• Thermalization and Return to Equilibrium on Finite Quantum Lattice Systems
• Gauge protection in non-Abelian lattice gauge theories
• Out-of-time-order Operators and the Butterfly Effect
• Numerical Large Deviation Analysis of Eigenstate Thermalization Hypothesis
• Detection of Macroscopic Entanglement by Correlation of Local Observables
• Floquet prethermalization in periodically driven classical spin systems
• Stability of local quantum dissipative systems
• Absence of fast scrambling in thermodynamically stable long-range interacting systems
• Quantum Skew Divergence
• Connecting global and local energy distributions in quantum spin models on a lattice
• Floquet Phases of Matter via Classical Prethermalization
• Rapid mixing implies exponential decay of correlations
• Many-body Chern number without integration
• Strong Local Passivity in Finite Quantum Systems
• Entanglement-ergodic quantum systems equilibrate exponentially well
• Quantum Cellular Automata, Tensor Networks, and Area Laws
• Necessity of Eigenstate Thermalization
• Area law of non-critical ground states in 1D long-range interacting systems
• Insensitivity of bulk properties to the twisted boundary condition
• Speed Limits for Macroscopic Transitions
• Equilibration time scales in closed many-body quantum systems
• Unifying approach for fluctuation theorems from joint probability distributions
• Family-Vicsek Scaling of Roughness Growth in a Strongly Interacting Bose Gas
• Stabilizing lattice gauge theories through simplified local pseudo generators
• Bound on the exponential growth rate of out-of-time-ordered correlators
• Improving the Lieb-Robinson bound for long-range interactions
• Classical approaches to prethermal discrete time crystals in one, two, and three dimensions
• An area law for 2D frustration-free spin systems
• The entangling and disentangling power of unitary transformations are unequal
• Time scale for adiabaticity breakdown in driven many-body systems and orthogonality catastrophe
• Decay of Correlations in Fermi Systems at Non-zero Temperature
• Quantum Trajectory Thermodynamics with Discrete Feedback Control
• Lieb-Robinson bound and almost-linear light-cone in interacting boson systems
• From stochastic spin chains to quantum Kardar-Parisi-Zhang dynamics
• Fundamental limitations to local energy extraction in quantum systems
• Markovian Entanglement Dynamics under Locally Scrambled Quantum Evolution
• Chaos in a classical limit of the Sachdev-Ye-Kitaev model
• Test of Eigenstate Thermalization Hypothesis Based on Local Random Matrix Theory
• Atypicality of Most Few-Body Observables
• Lieb-Robinson bounds for commutator-bounded operators
• Mixing times and cutoffs in open quadratic fermionic systems
• Maximal speed for macroscopic particle transport in the Bose-Hubbard model
• Eigenstate Thermalization in Long-Range Interacting Systems
• A Cutoff Phenomenon for Quantum Markov Chains
• Bounds on Energy Absorption and Prethermalization in Quantum Systems with Long-Range Interactions
• Statistical Mechanics of Floquet Quantum Matter: Exact and Emergent Conservation Laws
• Eigenstate thermalization from the clustering property of correlation
• Topological lower bound on quantum chaos by entanglement growth
• Exact Universal Chaos, Speed Limit, Acceleration, Planckian Transport Coefficient, "Collapse" to equilibrium, and Other Bounds in Thermal Quantum Systems
• Correlation decay in fermionic lattice systems with power-law interactions at non-zero temperature
• Metastability associated with many-body explosion of eigenmode expansion coefficients
• Lieb-Robinson bounds for open quantum systems with long-ranged interactions
• Proof of the absence of long-range temporal orders in Gibbs states
• Dynamical Scaling of Surface Roughness and Entanglement Entropy in Disordered Fermion Models
• Reversible simulation of bipartite product Hamiltonians
• Error bounds for constrained dynamics in gapped quantum systems: Rigorous results and generalizations
• Tracking the quantized information transfer at the edge of a chiral Floquet phase
• Universal Error Bound for Constrained Quantum Dynamics
• Equilibration times in closed quantum many-body systems
• Universal constraint on nonlinear population dynamics
• Coarse-grained Entanglement and Operator Growth in Anomalous Dynamics
• Thermodynamic Reverse Bounds for General Open Quantum Processes
• Bounding the finite-size error of quantum many-body dynamics simulations
• False signals of chaos from quantum probes

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