Thermalization process in a one-dimensional lattice with two-dimensional motions: The role of angular momentum conservation.

We study the thermalization process in a one-dimensional lattice with two-dimensional motions. The phonon modes in such a lattice consist of two branches. Unlike in general nonlinear Hamiltonian systems, for which the only conserved quantity is the total energy, the total angular momentum J is also conserved in this system. Consequently, the intra- and interbranch energy transports behave significantly differently. For the intrabranch transport, all the existing rules for the one-dimensional systems including the Chirikov overlap criterion apply. As for the interbranch transport, some trivial processes in one-dimensional lattices become nontrivial. During these processes, all the conservation laws can be satisfied exactly; thus the Chirikov criterion does not apply. These processes provide some fast channels for the interbranch transport, although the thermalization cannot be reached through them alone. A system with nonzero-J initial state, however, can never be thermalized to an equipartition state having zero J. Quite counterintuitively, the corresponding asymptotic mode energy distribution greatly concentrates to a few lowest-frequency modes in one branch.