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We investigate the energy relaxation process produced by thermal baths atzero temperature acting on the boundary atoms of chains of classical anharmonicoscillators. Time-dependent perturbation theory allows us to obtain an explicitsolution of the harmonic problem: even in such a simple system nontrivialfeatures emerge from the interplay of the different decay rates of Fouriermodes. In particular, a crossover from an exponential to an inverse-square-rootlaw occurs on a time scale proportional to the system size $N$. A furthercrossover back to an exponential law is observed only at much longer times (ofthe order $N^3$). In the nonlinear chain, the relaxation process is initiallyequivalent to the harmonic case over a wide time span, as illustrated bysimulations of the $\beta$ Fermi-Pasta-Ulam model. The distinctive feature isthat the second crossover is not observed due to the spontaneous appearance ofbreathers, i.e. space-localized time-periodic solutions, that keep a finiteresidual energy in the lattice. We discuss the mechanism yielding suchsolutions and also explain why it crucially depends on the boundary conditions.Comment: 16 pages, 6 figure

Slow energy relaxation and localization in 1D lattices