2023/10/21 by Umesh Kumar, Seemant Mishra, Kumar, Umesh +5 · 3 citations
Computer Science · Physics and Astronomy · #Advanced Fiber Laser Technologies #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2310.14072
openalex publication_date 2023/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a Klein-Gordon chain that is periodically driven at one end and has dissipation at one or both boundaries. An interesting numerical observation in a recent study~[arXiv:2209.03977] was that for driving frequency in the phonon band, there is a range of values of the driving amplitude Fd∈ (F1, F2) over which the energy current remains constant. In this range, the system exhibits a "resonant nonlinear wave" (RNW) mode of energy transmission which is a time and space periodic solution. It was noted that the range (F1,F2), for which the RNW mode occurs, shrinks with increasing system size N and disappears eventually. Remarkably, we find that the RNW mode is in fact a stable solution even for Fd much larger than F2 and quite large N (≈ 1000). For Fd>F2, there exists a second attractor which is chaotic. Both attractors have finite basins of attraction and can be reached by appropriate choice of initial conditions. Corresponding to the two attractors for large Fd, the system can now be in two nonequilibrium steady states. We improve the perturbative treatment of [arXiv:2209.03977] for the RNW mode by including the contributions of the third harmonics. We also consider the effect of thermal noise at the boundaries and find that the RNW mode is stable for small temperatures. Finally, we present results for a different driving protocol studied in [arXiv:2205.03839] where Fd is taken to scale with system size as N-1/2 and there is dissipation only at the non-driven end. We find that the steady state can be characterized by Fourier's law as in [arXiv:2205.03839] for a stochastic model. We point out interesting differences that occur since our dynamics is nonlinear and Hamiltonian. Our results suggest the intriguing possibility of observing the high current carrying RNW phase in experiments by careful preparation of initial conditions.