Energy thresholds for discrete breathers

Discrete breathers are time-periodic, spatially localized solutions of the equations of motion for a system of classical degrees of freedom interacting on a lattice. An important issue, not only from a theoretical point of view but also for their experimental detection, is their energy properties. We considerably enlarge the scenario of possible energy properties presented by Flach, Kladko, and MacKay Phys. Rev. Lett. 78, 1207 (1997)]]. Breather energies have a positive lower bound if the lattice dimension is greater than or equal to a certain critical value dc. We show that dc can generically be greater than 2 for a large class of Hamiltonian systems. Furthermore, examples are provided for systems where discrete breathers exist but do not emerge from the bifurcation of a band edge plane wave. Some of these systems support breathers of arbitrarily low energy in any spatial dimension.