3,684 research outputs found
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.
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
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
Experimentally observed evolution between dynamic patterns and intrinsic localized modes in a driven nonlinear electrical cyclic lattice
Locked intrinsic localized modes (ILMs) and large amplitude lattice spatial
modes (LSMs) have been experimentally measured for a driven 1-D nonlinear
cyclic electric transmission line, where the nonlinear element is a saturable
capacitor. Depending on the number of cells and electrical lattice damping a
LSM of fixed shape can be tuned across the modal spectrum. Interestingly, by
tuning the driver frequency away from this spectrum an LSM can be continuously
converted into ILMs and visa versa. The differences in pattern formation
between simulations and experimental findings are due to a low concentration of
impurities. Through this novel nonlinear excitation and switching channel in
cyclic lattices either energy balanced or unbalanced LSMs and ILMs may occur.
Because of the general nature of these dynamical results for nonintegrable
lattices applications are to be expected. The ultimate stability of driven aero
machinery containing nonlinear periodic structures may be one example.Comment: 7 pages 7 figure
Generation of Intrinsic Vibrational Gap Modes in Three-Dimensional Ionic Crystals
The existence of anharmonic localization of lattice vibrations in a perfect
3-D diatomic ionic crystal is established for the rigid-ion model by molecular
dynamics simulations. For a realistic set of NaI potential parameters, an
intrinsic localized gap mode vibrating in the [111] direction is observed for
fcc and zinc blende lattices. An axial elastic distortion is an integral
feature of this mode which forms more readily for the zinc blende than for the
fcc structure. Molecular dynamics simulations verify that in each structure
this localized mode may be stable for at least 200 cycles.Comment: 5 pages, 4 figures, RevTeX, using epsf.sty. To be published in Phys.
Rev. B. Also available at http://www.msc.cornell.edu/~kiselev
Controlled switching of intrinsic localized modes in a 1-D antiferromagnet
Nearly steady-state locked intrinsic localized modes (ILMs) in the quasi-1d
antiferromagnet (C2H5NH3)2CuCl4 are detected via four-wave mixing emission or
the uniform mode absorption. Exploiting the long-time stability of these locked
ILMs, repeatable nonlinear switching is observed by varying the sample
temperature, and localized modes with various amplitudes are created by
modulation of the microwave driver power. This steady-state ILM locking
technique could be used to produce energy localization in other atomic
lattices.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Lett. v.2 :
clarifications of text and figures in response to comment
Optical manipulation of intrinsic localized vibrational energy in cantilever arrays
Optically-induced real-time impurity modes are used to shepherd intrinsic
localized vibrational modes (discrete breathers) along micromechanical arrays
via either attractive or replulsive interactions. Adding an electrode to the
cantilever array provides control of the sign of lattice anharmonicity, hence
allowing both hard and soft nonlinearities to be studied. A number of dynamical
effects are demonstrated and explained, including the optical tweezing of
localized vibrational energy in a nonlinear lattice.Comment: 11 pages, 4 figures to be published in Europhysics Letter
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
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
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