2004/01/31 by Michael Kästner, Michael Kastner
Computer Science · Physics and Astronomy · #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Quantum chaos and dynamical systems #cond-mat.other #nlin.PS
paper · pdf · doi:10.1088/0951-7715/17/5/018
published as Nonlinearity 17 (2004) 1923-1939 · 20 pages, 5 figures
arxiv created 2004/05/28 · openalex publication_date 2004/07/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
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. We study the existence of energy thresholds for discrete breathers, i.e. the question of whether, in a certain system, discrete breathers of arbitrarily low energy exist, or whether a threshold has to be overcome in order to excite a discrete breather. Breather energies are found to have a positive lower bound if the lattice dimension d is greater than or equal to a certain critical value d c , whereas no energy threshold is observed for d < d c . The critical dimension d c is system dependent and can be computed explicitly, taking on values between zero and infinity. Three classes of Hamiltonian systems are distinguished, being characterized by different mechanisms affecting the existence (or non-existence) of an energy threshold.