TY - JOUR

T1 - Slow energy relaxation and localization in 1D lattices

AU - Piazza, F

AU - Lepri, S.

AU - Livi, R.

PY - 2001/11/23

Y1 - 2001/11/23

N2 - We investigate the energy loss process produced by damping the boundary atoms of a chain of classical anharmonic oscillators. Time-dependent perturbation theory allows us to obtain an explicit solution of the harmonic problem: even in such a simple system nontrivial features emerge from the interplay of the different decay rates of Fourier modes. In particular, a crossover from an exponential to an inverse-square-root law occurs on a timescale proportional to the system size N. A further crossover back to an exponential law is observed only at much longer times (of the order N3). In the nonlinear chain, the relaxation process is initially equivalent to the harmonic case over a wide time span, as illustrated by simulations of the ß Fermi-Pasta-Ulam model. The distinctive feature is that the second crossover is not observed due to the spontaneous appearance of breathers, i.e. space-localized time-periodic solutions, that keep a finite residual energy in the lattice. We discuss the mechanism yielding such solutions and also explain why it crucially depends on the boundary conditions.

AB - We investigate the energy loss process produced by damping the boundary atoms of a chain of classical anharmonic oscillators. Time-dependent perturbation theory allows us to obtain an explicit solution of the harmonic problem: even in such a simple system nontrivial features emerge from the interplay of the different decay rates of Fourier modes. In particular, a crossover from an exponential to an inverse-square-root law occurs on a timescale proportional to the system size N. A further crossover back to an exponential law is observed only at much longer times (of the order N3). In the nonlinear chain, the relaxation process is initially equivalent to the harmonic case over a wide time span, as illustrated by simulations of the ß Fermi-Pasta-Ulam model. The distinctive feature is that the second crossover is not observed due to the spontaneous appearance of breathers, i.e. space-localized time-periodic solutions, that keep a finite residual energy in the lattice. We discuss the mechanism yielding such solutions and also explain why it crucially depends on the boundary conditions.

UR - http://www.scopus.com/inward/record.url?scp=0035941174&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/34/46/304

DO - 10.1088/0305-4470/34/46/304

M3 - Article

VL - 34

SP - 9803

EP - 9814

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

SN - 0305-4470

IS - 46

ER -