Aspects of non-equilibrium in classical and quantum systems: slow relaxation and glasses, dynamical large deviations, quantum non-ergodicity, and open quantum dynamics

Abstract

In these four lectures I describe basic ideas and methods applicable to both classical and quantum systems displaying slow relaxation and non-equilibrium dynamics. The first half of these notes considers classical systems, and the second half, quantum systems. In Lecture 1, I briefly review the glass transition problem as a paradigm of slow relaxation and dynamical arrest in classical many-body systems. I discuss theoretical perspectives on how to think about glasses, and in particular how to model them in terms of kinetically constrained dynamics. In Lecture 2, I describe how via large deviation methods it is possible to define a statistical mechanics of trajectories which reveals the dynamical phase structure of systems with complex relaxation such as glasses. Lecture 3 is about closed (i.e. isolated) many-body quantum systems. I review thermalisation and many-body localisation, and consider the possibility of slow thermalisation and quantum non-ergodicity in the absence of disorder, thus connecting with some of the ideas of the first lecture. Lecture 4 is about open quantum systems, that is, quantum systems interacting with an environment. I review the description of open quantum dynamics within the Markovian approximation in terms of quantum master equations and stochastic quantum trajectories, and explain how to extend the dynamical large deviation method to study the statistical properties of ensembles of quantum jump trajectories. My overall aim is to draw analogies between classical and quantum non-equilibrium and find connections in the way we think about problems in these areas.

Lecture notes for the Summer School on Fundamental Problems in Statistical Physics XIV, July 2017, Bruneck

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• The large deviation approach to statistical mechanics
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• Many body localization in Heisenberg XXZ magnet in a random field
• Phenomenology of fully many-body-localized systems
• Quantum trajectories and open many-body quantum systems
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• Glassy dynamics of kinetically constrained models
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• Anomalous diffusion and Griffiths effects near the many-body localization transition
• Dephasing and the steady state in quantum many-particle systems
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• Fluctuations and response of nonequilibrium states
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• Absence of diffusion in an interacting system of spinless fermions on a one-dimensional disordered lattice
• Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
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• Dynamics in many-body localized quantum systems without disorder
• Quantum revivals and many-body localization
• Lengthscale dependence of dynamic four-point susceptibilities in glass formers
• Purification and many-body localization in cold atomic gases
• Characterization of dynamical phase transitions in quantum jump trajectories beyond the properties of the stationary state
• Finite-temperature critical point of a glass transition
• Scenario for delocalization in translation invariant systems
• Thermalization in a coherently driven ensemble of two-level systems
• Mappings between reaction-diffusion and kinetically constrained systems: A+A <-> A and the FA model have upper critical dimension d_c=2
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Cited by in corpus (109)

• Unravelling the large deviation statistics of Markovian open quantum systems
• Large work extraction and the Landauer limit in a continuous Maxwell demon
• Operator growth and eigenstate entanglement in an interacting integrable Floquet system
• Quantum East model: localization, non-thermal eigenstates and slow dynamics
• Dynamical Localization in ${\mathbb{Z}}_2$ Lattice Gauge Theories
• Using matrix product states to study the dynamical large deviations of kinetically constrained models
• Subdiffusion and many-body quantum chaos with kinetic constraints
• Universality in driven open quantum matter
• Rule 54: Exactly solvable model of nonequilibrium statistical mechanics
• The inverse scattering of the Zakharov-Shabat system solves the weak noise theory of the Kardar-Parisi-Zhang equation
• Exact large deviation statistics and trajectory phase transition of a deterministic boundary driven cellular automaton
• Absence of Normal Fluctuations in an Integrable Magnet
• Emergent Glassy Dynamics in a Quantum Dimer Model
• A reinforcement learning approach to rare trajectory sampling
• Hilbert space fragmentation and slow dynamics in particle-conserving quantum East models
• Theory of classical metastability in open quantum systems
• Generalized hydrodynamics: a perspective
• Anomalous transport from hot quasiparticles in interacting spin chains
• Localization in spin chains with facilitation constraints and disordered interactions
• Building continuous time crystals from rare events
• Strong ergodicity breaking due to local constraints in a quantum system
• Enhancing correlation times for edge spins through dissipation
• Measurement-induced phases of matter require feedback
• Vibrational dressing in Kinetically Constrained Rydberg Spin Systems
• Dynamics and large deviation transitions of the XOR-Fredrickson-Andersen kinetically constrained model
• Kinetically Constrained Quantum Dynamics in Superconducting Circuits
• Exact solution of the Floquet-PXP cellular automaton
• Matrix product state of multi-time correlations
• Multi-magnon quantum many-body scars from tensor operators
• Trajectory phase transitions in non-interacting spin systems
• Finite time large deviations via matrix product states
• Rydberg platform for non-ergodic chiral quantum dynamics
• Optimal sampling of dynamical large deviations via matrix product states
• Nonequilibrium diffusion processes via non-Hermitian electromagnetic quantum mechanics with application to the statistics of entropy production in the Brownian gyrator
• Exact quench dynamics of the Floquet quantum East model at the deterministic point
• Optimal sampling of dynamical large deviations in two dimensions via tensor networks
• Dynamical large deviations of two-dimensional kinetically constrained models using a neural-network state ansatz
• Effective Hamiltonians and Lagrangians for conditioned Markov processes at large volume
• Glassy dynamics due to a trajectory phase transition in dissipative Rydberg gases
• Slow dynamics and large deviations in classical stochastic Fredkin chains
• Designing open quantum systems with known steady states: Davies generators and beyond
• Generating discrete-time constrained random walks and Lévy flights
• Mean-field dynamics of open quantum systems with collective operator-valued rates: validity and application
• Phase diagram of quantum generalized Potts-Hopfield neural networks
• Catching and reversing quantum jumps and thermodynamics of quantum trajectories
• Anomalous dynamical large deviations of local empirical densities and activities in the pure and in the random kinetically-constrained East Model
• Conditioned diffusion processes with an absorbing boundary condition for finite or infinite horizon
• Large deviations for metastable states of Markov processes with absorbing states with applications to population models in stable or randomly switching environment
• A Deep Learning Functional Estimator of Optimal Dynamics for Sampling Large Deviations
• Quantum slush state in Rydberg atom arrays
• Generating stochastic trajectories with global dynamical constraints
• Dynamical criticality in open systems: non-perturbative physics, microscopic origin and direct observation
• Glassy word problems: ultraslow relaxation, Hilbert space jamming, and computational complexity
• Exact pre-transition effects in kinetically constrained circuits: dynamical fluctuations in the Floquet-East model
• Generating constrained run-and-tumble trajectories
• The Fredkin staircase: An integrable system with a finite-frequency Drude peak
• Large deviations for the Pearson family of ergodic diffusion processes involving a quadratic diffusion coefficient and a linear force
• Symmetry-induced fluctuation relations for dynamical observables irrespective of their behaviour under time-reversal
• Microcanonical conditioning of Markov processes on time-additive observables
• Microscopic biasing of discrete-time quantum trajectories
• Coherent spin-phonon scattering in facilitated Rydberg lattices
• Spectral signatures of symmetry-breaking dynamical phase transitions
• Exact solution of the Rule 150 reversible cellular automaton
• Theory for Glassy Behavior of Supercooled Liquid Mixtures
• Dynamical heterogeneity and large deviations in the open quantum East glass model from tensor networks
• Efficient large deviation estimation based on importance sampling
• Revisiting boundary-driven non-equilibrium Markov dynamics in arbitrary potentials via supersymmetric quantum mechanics and explicit large deviations at various levels
• Modeling non-linear dielectric susceptibilities of supercooled molecular liquids
• Enhanced many-body localization in a kinetically constrained model
• Large deviations and conditioning for chaotic non-invertible deterministic maps: analysis via the forward deterministic dynamics and the backward stochastic dynamics
• Quantum jump statistics with a shifted jump operator in a chiral waveguide
• An introduction to large deviations with applications in physics
• Field theories and quantum methods for stochastic reaction-diffusion systems
• Nanoscopic time crystal obtained by nonergodic spin dynamics
• Exact results on the dynamics of the stochastic Floquet-East model
• Conditioning diffusion processes with respect to the local time at the origin
• Disorder-Free Localization as a Purely Classical Effect
• Dissipative Quantum Hopfield Network: A numerical analysis
• Efficient post-selection in light-cone correlations of monitored quantum circuits
• Space-time correlations in monitored kinetically constrained discrete-time quantum dynamics
• Large deviations at level 2.5 and for trajectories observables of diffusion processes : the missing parts with respect to their random-walks counterparts
• Explicit dynamical properties of the Pelikan random map in the chaotic region and at the intermittent critical point towards the non-chaotic region
• Trajectory phase transitions in non-interacting systems: all-to-all dynamics and the random energy model
• Transport properties of diffusive particles conditioned to survive in trapping environments
• On the Kemeny time for continuous-time reversible and irreversible Markov processes with applications to stochastic resetting and to conditioning towards forever-survival
• State-dependent mobility edge in kinetically constrained models
• Joint distribution of two Local Times for diffusion processes with the application to the construction of various conditioned processes
• Emergence of the Gibbs ensemble as a steady state in Lindbladian dynamics
• Probing Hilbert space fragmentation using controlled dephasing
• A Tensor Network Approach to Finite Markov Decision Processes
• Anomalous relaxation of density waves in a ring-exchange system
• The singularities of the rate function of quantum coherent work in one-dimensional transverse field Ising model
• Rejection-free quantum Monte Carlo in continuous time from transition path sampling
• Large deviations for trajectory observables of diffusion processes in dimension $d>1$ in the double limit of large time and small diffusion coefficient
• A supersymmetric quantum perspective on the explicit large deviations for reversible Markov jump processes, with applications to pure and random spin chains
• Graph theory and tunable slow dynamics in quantum East Hamiltonians
• Subexponential decay of local correlations from diffusion-limited dephasing
• Tunable superdiffusion in integrable spin chains using correlated initial states
• Inverse problem in the conditioning of Markov processes on trajectory observables : what canonical conditionings can connect two given Markov generators ?
• Witnessing non-classicality through large deviations in quantum optics
• Markov spin models for image generation : explicit large deviations with respect to the number of pixels
• Conditioning two diffusion processes with respect to their first-encounter properties
• Complete ergodicity in one-dimensional reversible cellular automata
• Exact large deviations and emergent long-range correlations in sequential quantum East circuits
• Identifying mobility edge from finite temperature spectral form factor
• Revealing emergent many-body phenomena by analyzing large-scale space-time records of monitored quantum systems
• Loss of ergodicity in a quantum hopping model of a dense many body system with repulsive interactions
• Theory of the correlated quantum Zeno effect in a monitored qubit dimer
• Thermodynamics of quantum-jump trajectories of open quantum systems subject to stochastic resetting