Classical and quantum systems: transport due to rare events

Abstract

We review possible mechanisms for energy transfer based on 'rare' or 'non-perturbative' effects, in physical systems that present a many-body localized phenomenology. The main focus is on classical systems, with or without quenched disorder. For non-quantum systems, the breakdown of localization is usually not regarded as an issue, and we thus aim at identifying the fastest channels for transport. Next, we contemplate the possibility of applying the same mechanisms in quantum systems, including disorder free systems (e.g. Bose-Hubbard chain), disordered many-body localized systems with mobility edges at energies below the edge, and strongly disordered lattice systems in $d>1$. For quantum mechanical systems, the relevance of these considerations for transport is currently a matter of debate.

Review paper. To appear on the special issue on Many-body Localization in Annalen der Physik

References in corpus (19)

• Localization of interacting fermions at high temperature
• Many-body localization edge in the random-field Heisenberg chain
• Phenomenology of fully many-body-localized systems
• Integrals of motion in the Many-Body localized phase
• Anomalous diffusion and Griffiths effects near the many-body localization transition
• Stability and instability towards delocalization in MBL systems
• Diagonalization and Many-Body Localization for a Disordered Quantum Spin Chain
• Rare region effects and dynamics near the many-body localization transition
• A momentum conserving model with anomalous thermal conductivity in low dimension
• Dynamics in many-body localized quantum systems without disorder
• Density propagator for many-body localization: finite size effects, transient subdiffusion, and exponential decay
• Effect of phonon-phonon interactions on localization
• Scenario for delocalization in translation invariant systems
• Many-body localization beyond eigenstates in all dimensions
• Localized systems coupled to small baths: from A${}_{nderson}$ to Z${}_{eno}$
• General theory of many body localized systems coupled to baths
• Nonlinear lattice waves in heterogeneous media
• Spreading in Disordered Lattices with Different Nonlinearities
• Spin-catalyzed hopping conductivity in disordered strongly interacting quantum wires

Cited by in corpus (12)

• Recent progress in many-body localization
• The Ergodic Side of the Many-Body Localization Transition
• How a small quantum bath can thermalize long localized chains
• Energy transport in a disordered spin chain with broken U(1) symmetry: Diffusion, subdiffusion, and many-body localization
• Many-body localization in spin chains with the long-range transverse interactions: scaling of critical disorder with the system size
• Fragile Many Body Ergodicity
• Absence of localization in interacting spin chains with a discrete symmetry
• Identifying Correlation Clusters in Many-Body Localized Systems
• Glassy dynamics in strongly anharmonic chains of oscillators
• Thermalization of isolated harmonic networks under conservative noise
• Exact solution of the minimalist Stark many body localization problem in terms of spin pair hopping
• Large-deviations approach to thermalization: the case of harmonic chains with conservative noise