Fragile Many Body Ergodicity

Abstract

Weakly nonintegrable many-body systems can restore ergodicity in distinctive ways depending on the range of the interaction network in action space. Action resonances seed chaotic dynamics into the networks. Long range networks provide well connected resonances with ergodization controlled by the individual resonance chaos time scales. Short range networks instead yield a dramatic slowing down of ergodization in action space, and lead to rare resonance diffusion. We use Josephson junction chains as a paradigmatic study case. We exploit finite time average distributions to characterize the thermalizing dynamics of actions. We identify a novel action resonance diffusion regime responsible for the slowing down. We extract the diffusion coefficient of that slow process and measure its dependence on the proximity to the integrable limit. Independent measures of correlation functions confirm our findings. The observed fragile diffusion is relying on weakly chaotic dynamics in spatially isolated action resonances. It can be suppressed, and ergodization delayed, by adding weak action noise, as a proof of concept.

References in corpus (25)

• Many body localization and thermalization in quantum statistical mechanics
• Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
• Discrete Breathers
• Finite thermal conductivity in 1d lattices
• Statistical mechanics of a nonlinear discrete system
• Absence of many-body mobility edges
• q-Breathers and the Fermi-Pasta-Ulam Problem
• 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
• Intermittent many-body dynamics at equilibrium
• New families of symplectic splitting methods for numerical integration in dynamical astronomy
• Weakly nonergodic dynamics in the Gross--Pitaevskii lattice
• Negative Temperature States in the Discrete Nonlinear Schroedinger Equation
• Dynamical freezing of relaxation to equilibrium
• Dynamical Glass and Ergodization Times in Classical Josephson Junction Chains
• Dynamical glass in weakly non-integrable Klein-Gordon chains
• Coupled transport in rotor models
• On the local nature and scaling of chaos in weakly nonlinear disordered chains
• Temperature dependence of thermal conductivities of coupled rotator lattice and the momentum diffusion in standard map
• Non-Gibbs states on a Bose-Hubbard lattice
• Classical and quantum systems: transport due to rare events
• Transport, correlations, and chaos in a classical disordered anharmonic chain
• Thermal conductivity of nonlinear waves in disordered chains
• Glassy dynamics in strongly anharmonic chains of oscillators

Cited by in corpus (6)

• Lyapunov spectrum scaling for classical many-body dynamics close to integrability
• Thermalization slowing down in multidimensional Josephson junction networks
• How close Are Integrable and Non-integrable Models: A Parametric Case Study Based on the Salerno Model
• Local integrability breaking and exponential localization of leading Lyapunov vectors
• Trotter transition in BCS pairing dynamics
• Thermalization dynamics of macroscopic weakly nonintegrable maps