Quantum dynamics with stochastic reset

Abstract

We study non-equilibrium dynamics of integrable and non-integrable closed quantum systems whose unitary evolution is interrupted with stochastic resets, characterized by a reset rate $r$, that project the system to its initial state. We show that the steady state density matrix of a non-integrable system, averaged over the reset distribution, retains its off-diagonal elements for any finite $r$. Consequently a generic observable $\hat{O}$, whose expectation value receives contribution from these off-diagonal elements, never thermalizes under such dynamics for any finite $r$. We demonstrate this phenomenon by exact numerical studies of experimentally realizable models of ultracold bosonic atoms in a tilted optical lattice. For integrable Dirac-like fermionic models driven periodically between such resets, the reset-averaged steady state is found to be described by a family of generalized Gibbs ensembles (GGE s) characterized by $r$. We also study the spread of particle density of a non-interacting one-dimensional fermionic chain, starting from an initial state where all fermions occupy the left half of the sample, while the right half is empty. When driven by resetting dynamics, the density profile approaches at long times to a nonequilibrium stationary profile that we compute exactly. We suggest concrete experiments that can possibly test our theory.

Final version: 15 pages, 10 figs

References in corpus (39)

• The electronic properties of graphene
• Many-Body Physics with Ultracold Gases
• Thermalization and its mechanism for generic isolated quantum systems
• Quantum Simulation of Antiferromagnetic Spin Chains in an Optical Lattice
• Equilibrium states of generic quantum systems subject to periodic driving
• Universal adiabatic dynamics across a quantum critical point
• First Passage Under Restart
• First order transition for the optimal search time of Lévy flights with resetting
• Periodically driven ergodic and many-body localized quantum systems
• Quench dynamics across quantum critical points
• Diffusion in a potential landscape with stochastic resetting
• Defect production in non-linear quench across a quantum critical point
• Mott insulators in strong electric fields
• Dynamical transition in the temporal relaxation of stochastic processes under resetting
• Full counting statistics in a propagating quantum front and random matrix spectra
• Exact results for quench dynamics and defect production in a two-dimensional model
• Optimal non-linear passage through a quantum critical point
• Stochastic Search with Poisson and Deterministic Resetting
• Monotonous continuous-time random walks with drift and stochastic reset events
• Logarithmic current fluctuations in non-equilibrium quantum spin chains
• Quench dynamics and defect production in the Kitaev and extended Kitaev models
• Integral Fluctuation Theorems for Stochastic Resetting Systems
• Localization transition induced by learning in random searches
• Detection of a quantum particle on a lattice under repeated projective measurements
• Path-integral formalism for stochastic resetting: Exactly solved examples and shortcuts to confinement
• Holevo's bound from a general quantum fluctuation theorem
• First detected arrival of a quantum walker on an infinite line
• Spectral properties of simple classical and quantum reset processes
• Continuous-time random walks with reset events: Historical background and new perspectives
• Aperiodically driven integrable systems and their emergent steady states
• Phase transitions in large deviations of reset processes
• Feedback controlled heat transport in quantum devices: Theory and solid state experimental proposal
• Dynamic freezing and defect suppression in the tilted one-dimensional Bose-Hubbard model
• Nondestructive imaging of an ultracold lattice gas
• Condensation transition in joint large deviations of linear statistics
• Non-equilibrium quantum-heat statistics under stochastic projective measurements
• An exactly solvable quench protocol for integrable spin models
• Ramp and periodic dynamics across non-Ising critical points
• The induced motion of a probe coupled to a bath with random resettings

Cited by in corpus (75)

• Stochastic Resetting and Applications
• Run and tumble particle under resetting: a renewal approach
• First passage under stochastic resetting in an interval
• Entanglement Transitions from Stochastic Resetting of Non-Hermitian Quasiparticles
• Stochastic resetting: A (very) brief review
• First passage under restart with branching
• Symmetric Exclusion Process under Stochastic Resetting
• Ising model with stochastic resetting
• First passage under restart for discrete space and time: application to one dimensional confined lattice random walks
• Stochastic resetting in underdamped Brownian motion
• Restart expedites quantum walk hitting times
• Stochastic resetting in interacting particle systems: A review
• Mobility edge and multifractality in a periodically driven Aubry-André model
• Extremal statistics for stochastic resetting systems
• Local time of diffusion with stochastic resetting
• Random acceleration process under stochastic resetting
• Resetting with stochastic return through linear confining potential
• Number of distinct sites visited by a resetting random walker
• Diffusion processes with Gamma-distributed resetting and non-instantaneous returns
• Synchronization in the Kuramoto model in presence of stochastic resetting
• Controlling particle currents with evaporation and resetting from an interval
• Discrete space-time resetting model: Application to first-passage and transmission statistics
• Dark states of quantum search cause imperfect detection
• Emergent quantum correlations and collective behavior in non-interacting quantum systems subject to stochastic resetting
• Condensation transition in large deviations of self-similar Gaussian processes with stochastic resetting
• Ornstein-Uhlenbeck process and generalizations: particle's dynamics under comb constraints and stochastic resetting
• Quantum walks: the first detected transition time
• From classical to quantum walks with stochastic resetting on networks
• Quantum unitary evolution interspersed with repeated non-unitary interactions at random times: The method of stochastic Liouville equation, and two examples of interactions in the context of a tight-binding chain
• A Floquet perturbation theory for periodically driven weakly-interacting fermions
• First detection probability in quantum resetting via random projective measurements
• Restart uncertainty relation for monitored quantum dynamics
• Generating Entanglement by Quantum Resetting
• Quantum resetting in continuous measurement induced dynamics of a qubit
• Quantum state preparation via engineered ancilla resetting
• Multilayered density profile for noninteracting fermions in a rotating two-dimensional trap
• Uncertainty and symmetry bounds for the quantum total detection probability
• Instability in the quantum restart problem
• Dynamics of closed quantum systems under stochastic resetting
• Stochastic resets in the context of a tight-binding chain driven by an oscillating field
• Accelerating Quantum Relaxation via Temporary Reset: A Mpemba-Inspired Approach
• A large deviation perspective on ratio observables in reset processes: robustness of rate functions
• Kuramoto model subject to subsystem resetting: How resetting a part of the system may synchronize the whole of it
• Dynamically emergent correlations in bosons via quantum resetting
• Tight-binding model subject to conditional resets at random times
• Unravelling Metastable Markovian Open Quantum Systems
• Non-Hermitian and Zeno limit of quantum systems under rapid measurements
• Perturbation Analysis of Quantum Reset Models
• Stochastic resetting in discrete-time quantum dynamics: steady states and correlations in few-qubit systems
• Biased random walk on random networks in presence of stochastic resetting: Exact results
• Search with stochastic home-returns can expedite classical first passage under resetting
• Measurement-induced resetting in open quantum systems
• Stochastic resetting with refractory periods: pathway formulation and exact results
• Resonances of recurrence time of monitored quantum walks
• Causality, localization, and universality of monitored quantum walks with long-range hopping
• Thermodynamic phases in first detected return times of quantum many-body systems
• Manipulating phases in many-body interacting systems with subsystem resetting
• Quest for optimal quantum resetting: protocols for a particle on a chain
• Exact nonequilibrium quantum observable statistics: A large-deviation approach
• Dynamically emergent correlations in Brownian particles subject to simultaneous non-Poissonian resetting protocols
• Control of spatiotemporal chaos by stochastic resetting
• Drift-diffusive resetting search process with stochastic returns: speed-up beyond optimal instantaneous return
• Stochastic resetting in a networked multiparticle system with correlated transitions
• Stationary-state dynamics of interacting phase oscillators in presence of noise and stochastic resetting
• Unified approach to reset processes and application to coupling between process and reset
• Topological Defects from Quantum Reset Dynamics
• Semi-Markov Processes in Open Quantum Systems. II. Counting Statistics with Resetting
• Gauge freedoms in unravelled quantum dynamics: When do different continuous measurements yield identical quantum trajectories?
• Exact fluctuation and long-range correlations in a single-file model under resetting
• Ising Model with Power Law Resetting
• An exactly solvable predator prey model with resetting
• Designing non-equilibrium states of quantum matter through stochastic resetting
• Thermodynamics of quantum-jump trajectories of open quantum systems subject to stochastic resetting
• Optimal detection of quantum states via projective measurements
• Experimental evidence for strong emergent correlations between particles in a switching trap