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

Abstract

Nonlinear interaction between normal modes dramatically affects energy equipartition, heat conduction and other fundamental processes in extended systems. In their celebrated experiment Fermi, Pasta and Ulam (FPU, 1955) observed that in simple one-dimensional nonlinear atomic chains the energy must not always be equally shared among the modes. Recently, it was shown that exact and stable time-periodic orbits, coined $q$-breathers (QBs), localize the mode energy in normal mode space in an exponential way, and account for many aspects of the FPU problem. Here we take the problem into more physically important cases of two- and three-dimensional acoustic lattices to find existence and principally different features of QBs. By use of perturbation theory and numerical calculations we obtain that the localization and stability of QBs is enhanced with increasing system size in higher lattice dimensions opposite to their one-dimensional analogues.

arXiv comment4 pages, 5 figures

References in corpus (4)

• q-Breathers and the Fermi-Pasta-Ulam Problem
• The Fermi-Pasta-Ulam problem revisited: stochasticity thresholds in nonlinear Hamiltonian systems
• q-Breathers in Fermi-Pasta-Ulam chains: existence, localization and stability
• Low energy chaos in the Fermi-Pasta-Ulam problem

Cited by in corpus (14)

• The Fermi-Pasta-Ulam problem: periodic orbits, normal forms and resonance overlap criteria
• Tail resonances of FPU q-breathers and their impact on the pathway to equipartition
• Driven localized excitations in the acoustic spectrum of small nonlinear macroscopic and microscopic lattices
• Scaling properties of $q$-breathers in nonlinear acoustic lattices
• Weak chaos detection in the Fermi-Pasta-Ulam-$\alpha$ system using $q$-Gaussian statistics
• Quantum q-breathers in a finite Bose-Hubbard chain: The case of two interacting bosons
• Self-organized escape of oscillator chains in nonlinear potentials
• Low-dimensional q-Tori in FPU Lattices: Dynamics and Localization Properties
• Boundary effects on quantum q-breathers in a Bose-Hubbard chain
• Periodic orbits, localization in normal mode space, and the Fermi-Pasta-Ulam problem
• $q$-Breathers in finite lattices: nonlinearity and weak disorder
• q-breathers in Discrete Nonlinear Schroedinger lattices
• Extensive packet excitations in FPU and Toda lattices
• q-Breathers in Discrete Nonlinear Schroedinger arrays with weak disorder