Glassy dynamics in strongly anharmonic chains of oscillators
arXiv:1904.07742 · doi:10.1016/j.crhy.2019.08.007
Abstract
We review the mechanism for transport in strongly anharmonic chains of oscillators near the atomic limit where all oscillators are decoupled. In this regime, the motion of most oscillators remains close to integrable, i.e. quasi-periodic, on very long time scales, while a few chaotic spots move very slowly and redistribute the energy across the system. The material acquires several characteristic properties of dynamical glasses: intermittency, jamming and a drastic reduction of the mobility as a function of the thermodynamical parameters. We consider both classical and quantum systems, though with more emphasis on the former, and we discuss also the connections with quenched disordered systems, which display a similar physics to a large extent.
arXiv commentReview paper. Invited submission to the CRAS (special issue on Fourier's legacy). 16 pages, 3 figures
References in corpus (61)
- Many body localization and thermalization in quantum statistical mechanics
- Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
- Localization of interacting fermions at high temperature
- Thermal conduction in classical low-dimensional lattices
- Interacting electrons in disordered wires: Anderson localization and low-temperature transport
- Many-body localization: an introduction and selected topics
- On Many-Body Localization for Quantum Spin Chains
- Destruction of Anderson localization by a weak nonlinearity
- Anomalous diffusion and Griffiths effects near the many-body localization transition
- Stability and instability towards delocalization in MBL systems
- Recent progress in many-body localization
- Universal spreading of wavepackets in disordered nonlinear systems
- Diagonalization and Many-Body Localization for a Disordered Quantum Spin Chain
- Rare region effects and dynamics near the many-body localization transition
- Localization and Glassy Dynamics Of Many-Body Quantum Systems
- A momentum conserving model with anomalous thermal conductivity in low dimension
- How a small quantum bath can thermalize long localized chains
- Many-body delocalization as a quantum avalanche
- Absence of many-body mobility edges
- Quasi Many-body Localization in Translation Invariant Systems
- Griffiths effects and slow dynamics in nearly many-body localized systems
- A lecture on the classical KAM theorem
- Dynamics in many-body localized quantum systems without disorder
- Quantum Disentangled Liquids
- Energy transport in disordered classical spin chains
- Weak chaos in the disordered nonlinear Schroedinger chain: destruction of Anderson localization by Arnold diffusion
- Non-ergodic metallic and insulating phases of Josephson junction chains
- Effect of phonon-phonon interactions on localization
- Many-body localization in disorder-free systems: the importance of finite-size constraints
- The Nonlinear Schroedinger Equation with a random potential: Results and Puzzles
- A simple statistical explanation for the localization of energy in nonlinear lattices with two conserved quantities
- Asymptotic quantum many-body localization from thermal disorder
- Scenario for delocalization in translation invariant systems
- Energy Transport in Weakly Anharmonic Chains
- Dynamical Thermalization of Disordered Nonlinear Lattices
- Weakly nonergodic dynamics in the Gross--Pitaevskii lattice
- Ideal quantum glass transitions: many-body localization without quenched disorder
- Signatures of many-body localisation in a system without disorder and the relation to a glass transition
- Negative Temperature States in the Discrete Nonlinear Schroedinger Equation
- Universal Nonlinear Disordered Wave Packet Subdiffusion: 12 Decades
- Long time Anderson localization for nonlinear random Schroedinger equation
- Anderson localization or nonlinear waves? A matter of probability
- Energy Spreading in Strongly Nonlinear Disordered Lattices
- Nonlinear lattice waves in heterogeneous media
- Perturbation theory for the Nonlinear Schroedinger Equation with a random potential
- Slow Dynamics in Translation-Invariant Quantum Lattice Models
- Dynamical Glass and Ergodization Times in Classical Josephson Junction Chains
- Spreading in Disordered Lattices with Different Nonlinearities
- Normal Heat Conductivity in a strongly pinned chain of anharmonic oscillators
- Dynamical glass in weakly non-integrable Klein-Gordon chains
- Heat conduction in the disordered Fermi-Pasta-Ulam chain
- Non-equilibrium steady states for chains of four rotors
- Non-equilibrium steady state and subgeometric ergodicity for a chain of three coupled rotors
- Non-Equilibrium Steady States for Networks of Oscillators
- Drastic fall-off of the thermal conductivity for disordered lattices in the limit of weak anharmonic interactions
- On the relaxation rate of short chains of rotors interacting with Langevin thermostats
- Classical and quantum systems: transport due to rare events
- Kinetic theory of phonons in weakly anharmonic particle chains
- Energy Dissipation in Hamiltonian Chains of Rotators
- Step Heat Profile in Localized Chains
- Energy transport through rare collisions