q-breathers in finite two- and three-dimensional nonlinear acoustic lattices

摘要

Nonlinear interaction between normal modes dramatically affects energyequipartition, heat conduction and other fundamental processes in extendedsystems. In their celebrated experiment Fermi, Pasta and Ulam (FPU, 1955)observed that in simple one-dimensional nonlinear atomic chains the energy mustnot always be equally shared among the modes. Recently, it was shown that exactand stable time-periodic orbits, coined $q$-breathers (QBs), localize the modeenergy in normal mode space in an exponential way, and account for many aspectsof the FPU problem. Here we take the problem into more physically importantcases of two- and three-dimensional acoustic lattices to find existence andprincipally different features of QBs. By use of perturbation theory andnumerical calculations we obtain that the localization and stability of QBs isenhanced with increasing system size in higher lattice dimensions opposite totheir one-dimensional analogues.