2025/07/02 by Garrido, Pedro L., Komorowski, Tomasz, Lebowitz, Joel L. +1
#FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.2507.02065
We investigate the long time behavior of a pinned chain of 2N+1 oscillators, indexed by x ∈\-N,…, N\. The system is subjected to an external driving force on the particle at x=0, of period θ=2π/ω, and to frictional damping γ>0 at both endpoints x=-N and N. The oscillators interact with a pinned and nearest neighbor harmonic plus anharmonic potentials of the form (ω02 qx2)/(2)+\frac12 (qx-qx-1)2 +ν[V(qx)+U(qx-qx-1) ], with V'' and U'' bounded and ν∈ ℝ. We recall the recently proven convergence and the global stability of a perturbation series in powers of ν for |ν| < ν0, yielding the long time periodic state of the system. Here ν0 depends only on the supremum norms of V'' and U'' and the distance of the set of non-negative integer multiplicities of ω from the interval [ω0,√(ω02+4)] - the spectrum of the infinite harmonic chain for ν=0. We describe also some numerical studies of this system going beyond our rigorous results.