1,294 research outputs found
Obtaining Breathers in Nonlinear Hamiltonian Lattices
We present a numerical method for obtaining high-accuracy numerical solutions
of spatially localized time-periodic excitations on a nonlinear Hamiltonian
lattice. We compare these results with analytical considerations of the spatial
decay. We show that nonlinear contributions have to be considered, and obtain
very good agreement between the latter and the numerical results. We discuss
further applications of the method and results.Comment: 21 pages (LaTeX), 8 figures in ps-files, tar-compressed uuencoded
file, Physical Review E, in pres
Breathers on lattices with long range interaction
We analyze the properties of breathers (time periodic spatially localized
solutions) on chains in the presence of algebraically decaying interactions
. We find that the spatial decay of a breather shows a crossover from
exponential (short distances) to algebraic (large distances) decay. We
calculate the crossover distance as a function of and the energy of the
breather. Next we show that the results on energy thresholds obtained for short
range interactions remain valid for and that for (anomalous
dispersion at the band edge) nonzero thresholds occur for cases where the short
range interaction system would yield zero threshold values.Comment: 4 pages, 2 figures, PRB Rapid Comm. October 199
On the Existence of Localized Excitations in Nonlinear Hamiltonian Lattices
We consider time-periodic nonlinear localized excitations (NLEs) on
one-dimensional translationally invariant Hamiltonian lattices with arbitrary
finite interaction range and arbitrary finite number of degrees of freedom per
unit cell. We analyse a mapping of the Fourier coefficients of the NLE
solution. NLEs correspond to homoclinic points in the phase space of this map.
Using dimensionality properties of separatrix manifolds of the mapping we show
the persistence of NLE solutions under perturbations of the system, provided
NLEs exist for the given system. For a class of nonintegrable Fermi-Pasta-Ulam
chains we rigorously prove the existence of NLE solutions.Comment: 13 pages, LaTeX, 2 figures will be mailed upon request (Phys. Rev. E,
in press
Acoustic breathers in two-dimensional lattices
The existence of breathers (time-periodic and spatially localized lattice
vibrations) is well established for i) systems without acoustic phonon branches
and ii) systems with acoustic phonons, but also with additional symmetries
preventing the occurence of strains (dc terms) in the breather solution. The
case of coexistence of strains and acoustic phonon branches is solved (for
simple models) only for one-dimensional lattices.
We calculate breather solutions for a two-dimensional lattice with one
acoustic phonon branch. We start from the easy-to-handle case of a system with
homogeneous (anharmonic) interaction potentials. We then easily continue the
zero-strain breather solution into the model sector with additional quadratic
and cubic potential terms with the help of a generalized Newton method. The
lattice size is . The breather continues to exist, but is dressed
with a strain field. In contrast to the ac breather components, which decay
exponentially in space, the strain field (which has dipole symmetry) should
decay like . On our rather small lattice we find an exponent
Discrete breathers in systems with homogeneous potentials - analytic solutions
We construct lattice Hamiltonians with homogeneous interaction potentials
which allow for explicit breather solutions. Especially we obtain exponentially
localized solutions for -dimensional lattices with .Comment: 10 page
Quantum dynamics of localized excitations in a symmetric trimer molecule
We study the time evolution of localized (local bond) excitations in a
symmetric quantum trimer molecule. We relate the dynamical properties of
localized excitations such as their spectral intensity and their temporal
evolution (survival probability and tunneling of bosons) to their degree of
overlap with quantum tunneling pair states. We report on the existence of
degeneracy points in the trimer eigenvalue spectrum for specific values of
parameters due to avoided crossings between tunneling pair states and
additional states. The tunneling of localized excitations which overlap with
these degenerate states is suppressed on all times. As a result local bond
excitations may be strongly localized forever, similar to their classical
counterparts.Comment: 9 pages, 12 figures. Improved version with more discussions. Some
figures were replaced for better understanding. Accepted in Phys. Rev.
Energy thresholds for discrete breathers in one-, two- and three-dimensional lattices
Discrete breathers are time-periodic, spatially localized solutions of
equations of motion for classical degrees of freedom interacting on a lattice.
They come in one-parameter families. We report on studies of energy properties
of breather families in one-, two- and three-dimensional lattices. We show that
breather energies have a positive lower bound if the lattice dimension of a
given nonlinear lattice is greater than or equal to a certain critical value.
These findings could be important for the experimental detection of discrete
breathers.Comment: 10 pages, LaTeX, 4 figures (ps), Physical Review Letters, in prin
The phase plane of moving discrete breathers
We study anharmonic localization in a periodic five atom chain with
quadratic-quartic spring potential. We use discrete symmetries to eliminate the
degeneracies of the harmonic chain and easily find periodic orbits. We apply
linear stability analysis to measure the frequency of phonon-like disturbances
in the presence of breathers and to analyze the instabilities of breathers. We
visualize the phase plane of breather motion directly and develop a technique
for exciting pinned and moving breathers. We observe long-lived breathers that
move chaotically and a global transition to chaos that prevents forming moving
breathers at high energies.Comment: 8 pages text, 4 figures, submitted to Physical Review Letters. See
http://www.msc.cornell.edu/~houle/localization
Edge-localized states in quantum one-dimensional lattices
In one-dimensional quantum lattice models with open boundaries, we find and
study localization at the lattice edge. We show that edge-localized eigenstates
can be found in both bosonic and fermionic systems, specifically, in the
Bose-Hubbard model with on-site interactions and in the spinless fermion model
with nearest-neighbor interactions. We characterize the localization through
spectral studies via numerical diagonalization and perturbation theory, through
considerations of the eigenfunctions, and through the study of explicit time
evolution. We concentrate on few-particle systems, showing how more complicated
edge states appear as the number of particles is increased.Comment: 9 pages, 12 figure
Discrete breathers in classical spin lattices
Discrete breathers (nonlinear localised modes) have been shown to exist in
various nonlinear Hamiltonian lattice systems. In the present paper we study
the dynamics of classical spins interacting via Heisenberg exchange on spatial
-dimensional lattices (with and without the presence of single-ion
anisotropy). We show that discrete breathers exist for cases when the continuum
theory does not allow for their presence (easy-axis ferromagnets with
anisotropic exchange and easy-plane ferromagnets). We prove the existence of
localised excitations using the implicit function theorem and obtain necessary
conditions for their existence. The most interesting case is the easy-plane one
which yields excitations with locally tilted magnetisation. There is no
continuum analogue for such a solution and there exists an energy threshold for
it, which we have estimated analytically. We support our analytical results
with numerical high-precision computations, including also a stability analysis
for the excitations.Comment: 15 pages, 12 figure
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