Random-matrix approach to time-dependent forcing in many-body quantum systems
arXiv:2409.10052 · doi:10.1103/PhysRevB.110.144308
Abstract
Changing some of its parameters over time is a paradigmatic way of driving an otherwise isolated many-body quantum system out of equilibrium, and a vital ingredient for building quantum computers and simulators. Here, we further develop a recently proposed nonlinear response theory which is based on typicality and random-matrix methods, and which is applicable to a wide variety of such parametrically perturbed systems in and out of equilibrium: We derive analytical approximations of the characteristic response function for the two limiting cases of fast driving and of strong and short-ranged-in-energy driving. Furthermore, we work out implications and predictions for common applications, including finite-time quenches and time-dependent forcing that breaks conservation laws of the underlying undriven system. Finally, we verify all predictions by numerical examples and discuss the theory's scope and limitations.
arXiv comment16 pages, 7 figures
References in corpus (62)
- Many-Body Physics with Ultracold Gases
- Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
- Chaos and Quantum Thermalization
- Thermalization and its mechanism for generic isolated quantum systems
- Quantum Simulation
- Floquet Topological Insulator in Semiconductor Quantum Wells
- Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
- Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
- The Magnus expansion and some of its applications
- Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices
- Observation of discrete time-crystalline order in a disordered dipolar many-body system
- Floquet Engineering of Quantum Materials
- Controlled Collisions for Multiparticle Entanglement of Optically Trapped Atoms
- Measuring out-of-time-order correlations and multiple quantum spectra in a trapped ion quantum magnet
- Equilibrium states of generic quantum systems subject to periodic driving
- Long-time behavior of periodically driven isolated interacting lattice systems
- Many-body localization in periodically driven systems
- Floquet-Magnus Theory and Generic Transient Dynamics in Periodically Driven Many-Body Quantum Systems
- Exponentially slow heating in periodically driven many-body systems
- Quantum Chaos and Thermalization in Isolated Systems of Interacting Particles
- Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems
- Effective Hamiltonians, prethermalization and slow energy absorption in periodically driven many-body systems
- Ultracold atoms out of equilibrium
- Realization of an anomalous Floquet topological system with ultracold atoms
- Periodically Driving a Many-Body Localized Quantum System
- A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems
- Pre-thermal phases of matter protected by time-translation symmetry
- Exploring Localization in Nuclear Spin Chains
- Equilibration and Order in Quantum Floquet Matter
- Floquet Fractional Chern Insulator in Doped Graphene
- Many-body energy localization transition in periodically driven systems
- Floquet engineering with quasienergy bands of periodically driven optical lattices
- Tailoring quantum gases by Floquet engineering
- Off-diagonal matrix elements of local operators in many-body quantum systems
- Long-Time Behavior of Macroscopic Quantum Systems: Commentary Accompanying the English Translation of John von Neumann's 1929 Article on the Quantum Ergodic Theorem
- Typical fast thermalization processes in closed many-body systems
- Wigner Random Banded Matrices with Sparse Structure: Local Spectral Density of States
- Observation of Floquet prethermalization in dipolar spin chains
- Eigenstate thermalization and quantum chaos in the Holstein polaron model
- Floquet prethermalization in a Bose-Hubbard system
- Long-Range Prethermal Phases of Nonequilibrium Matter
- Emergent prethermalization signatures in out-of-time ordered correlations
- Sensitivity of quantum information to environment perturbations measured with a non-local out-of-time-order correlation function
- Connecting global and local energy distributions in quantum spin models on a lattice
- Heating Rates in Periodically Driven Strongly Interacting Quantum Many-Body Systems
- Equilibration time scales in closed many-body quantum systems
- Thermalisation of Local Observables in Small Hubbard Lattices
- Off-Diagonal Observable Elements from Random Matrix Theory: Distributions, Fluctuations, and Eigenstate Thermalization
- Relaxation theory for perturbed many-body quantum systems versus numerics and experiment
- Suppressing dissipation in a Floquet-Hubbard system
- Atypicality of Most Few-Body Observables
- Quantum Chaotic Fluctuation-Dissipation Theorem: Effective Brownian Motion in Closed Quantum Systems
- Heating in integrable time-periodic systems
- Exponential damping induced by random and realistic perturbations
- Quantifying the sensitivity to errors in analog quantum simulation
- Transportless equilibration in isolated many-body quantum systems
- Typical relaxation of perturbed quantum many-body systems
- Thermalization away from Integrability and the Role of Operator Off-Diagonal Elements
- Refining Deutsch's approach to thermalization
- Modification of quantum many-body relaxation by perturbations exhibiting a banded matrix structure
- Modelling equilibration of local many-body quantum systems by random graph ensembles
- Stalled response near thermal equilibrium in periodically driven systems