Stretched--exponential relaxation in arrays of coupled rotators

Abstract

We consider the non--equilibrium dynamics of a chain of classical rotators coupled at its edges to an external reservoir at zero temperature. We find that the energy is released in a strongly discontinuous fashion, with sudden jumps alternated with long stretches during which dissipation is extremely weak. The jumps mark the disappearance of strongly localized structures, akin to the rotobreather solutions of the Hamiltonian model, which act as insulating boundaries of a hot central core. As a result of this complex kinetics, the ensemble--averaged energy follows a stretched exponential law until a residual pseudo--stationary state is attained, where the hot core has reduced to a single localized object. We give a statistical description of the relaxation pathway and connect it to the properties of return periods of rare events in correlated time series. This approach sheds some light into the microscopic mechanism underlying the slow dynamics of the system. Finally, we show that the stretched exponential law remains unaltered in the presence of isotopic disorder.

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References in corpus (11)

• Thermal conduction in classical low-dimensional lattices
• Discrete Breathers
• Glassy dynamics of kinetically constrained models
• Experimental Generation and Observation of Intrinsic Localized Spin Wave Modes in an Antiferromagnet
• Finite thermal conductivity in 1d lattices
• Localization and Equipartition of Energy in the beta-FPU Chain : Chaotic Breathers
• Cooling nonlinear lattices toward localisation
• Optical creation of vibrational intrinsic localized modes in anharmonic lattices with realistic interatomic potentials
• Slow energy relaxation and localization in 1D lattices
• Asymptotic Dynamics of Breathers in Fermi-Pasta-Ulam Chains
• Spontaneous creation of discrete breathers in Josephson arrays

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• Non-equilibrium steady states for chains of four rotors
• Coupled transport in rotor models
• Boundary-induced instabilities in coupled oscillators
• Energy thresholds of discrete breathers in thermal equilibrium and relaxation processes
• Nonequilibrium phenomena in nonlinear lattices: from slow relaxation to anomalous transport
• Rotobreathers in a chain of coupled elastic rotators