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Energy thresholds for discrete breathers.

Michael Kastner1

  • 1I.N.F.M., UdR Firenze, Via Giovanni Sansone 1, 50019 Sesto Fiorentino (FI), Italy. Michael.Kastner@uni-bayreuth.de

Physical Review Letters
|April 20, 2004
PubMed
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Discrete breathers, localized energy packets in lattices, can possess a minimum energy threshold dependent on lattice dimension. This study expands understanding of their energy properties and existence conditions.

Area of Science:

  • Nonlinear dynamics
  • Condensed matter physics
  • Lattice dynamics

Background:

  • Discrete breathers are localized, time-periodic solutions in classical lattice systems.
  • Understanding breather energy properties is crucial for theoretical analysis and experimental detection.
  • Previous work established conditions for a positive lower bound on breather energies.

Purpose of the Study:

  • To significantly expand the known range of energy properties for discrete breathers.
  • To investigate the critical lattice dimension (dc) for a positive energy lower bound.
  • To explore discrete breathers that do not arise from band edge plane wave bifurcations.

Main Methods:

  • Analysis of Hamiltonian systems with classical degrees of freedom on a lattice.

Related Experiment Videos

  • Theoretical investigation of energy properties and existence conditions for discrete breathers.
  • Numerical and analytical exploration of specific lattice models.

    • Main Results:

    • Demonstrated that the critical lattice dimension (dc) for a positive breather energy lower bound can exceed 2 in many Hamiltonian systems.
    • Identified systems supporting discrete breathers that do not emerge from band edge plane wave bifurcations.
    • Found systems with discrete breathers of arbitrarily low energy across various spatial dimensions.

    Conclusions:

    • The energy landscape of discrete breathers is richer than previously understood, with critical dimensions varying significantly.
    • New classes of discrete breathers exist, broadening their potential relevance in physical systems.
    • The existence of low-energy breathers in any dimension opens new avenues for research and applications.