Transmission thresholds in time-periodically driven nonlinear disordered systems

Abstract

We study energy propagation in locally time-periodically driven disordered nonlinear chains. For frequencies inside the band of linear Anderson modes, three different regimes are observed with increasing driver amplitude: 1) Below threshold, localized quasiperiodic oscillations and no spreading; 2) Three different regimes in time close to threshold, with almost regular oscillations initially, weak chaos and slow spreading for intermediate times, and finally strong diffusion; 3) Immediate spreading for strong driving. The thresholds are due to simple bifurcations, obtained analytically for a single oscillator, and numerically as turning-points of the nonlinear response manifold for a full chain. Generically, the threshold is nonzero also for infinite chains.

6 pages, 6 figures, to be published in EPL. Revised version: minor clarifications and updates of references

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• Weak chaos detection in the Fermi-Pasta-Ulam-$\alpha$ system using $q$-Gaussian statistics
• Complex Statistics and Diffusion in Nonlinear Disordered Particle Chains
• Dynamics and transport in the boundary-driven dissipative Klein-Gordon chain
• Nonlinear bandgap transmission by discrete rogue waves induced in a pendulum chain
• Coupled symplectic maps as models for subdiffusive processes in disordered Hamiltonian lattices
• Heat flow in a periodically forced, thermostatted chain II
• Thermally driven classical Heisenberg model in one dimension with a local time-varying field
• Inversion of coherent backscattering with interacting Bose-Einstein condensates in two-dimensional disorder : a Truncated Wigner approach
• Supratransmission in Lattices with Purely Nonlinear Coupling