11,260 research outputs found
Linear response functions for a vibrational configuration interaction state
Linear response functions are implemented for a vibrational configuration interaction state allowing accurate analytical calculations of pure vibrational contributions to dynamical polarizabilities. Sample calculations are presented for the pure vibrational contributions to the polarizabilities of water and formaldehyde. We discuss the convergence of the results with respect to various details of the vibrational wave function description as well as the potential and property surfaces. We also analyze the frequency dependence of the linear response function and the effect of accounting phenomenologically for the finite lifetime of the excited vibrational states. Finally, we compare the analytical response approach to a sum-over-states approac
Fast algorithms for computing defects and their derivatives in the Regge calculus
Any practical attempt to solve the Regge equations, these being a large
system of non-linear algebraic equations, will almost certainly employ a
Newton-Raphson like scheme. In such cases it is essential that efficient
algorithms be used when computing the defect angles and their derivatives with
respect to the leg-lengths. The purpose of this paper is to present details of
such an algorithm.Comment: 38 pages, 10 figure
A numerical study of infinitely renormalizable area-preserving maps
It has been shown in (Gaidashev et al, 2010) and (Gaidashev et al, 2011) that
infinitely renormalizable area-preserving maps admit invariant Cantor sets with
a maximal Lyapunov exponent equal to zero. Furthermore, the dynamics on these
Cantor sets for any two infinitely renormalizable maps is conjugated by a
transformation that extends to a differentiable function whose derivative is
Holder continuous of exponent alpha>0.
In this paper we investigate numerically the specific value of alpha. We also
present numerical evidence that the normalized derivative cocycle with the base
dynamics in the Cantor set is ergodic. Finally, we compute renormalization
eigenvalues to a high accuracy to support a conjecture that the renormalization
spectrum is real
Nonlinearity-induced conformational instability and dynamics of biopolymers
We propose a simple phenomenological model for describing the conformational
dynamics of biopolymers via the nonlinearity-induced buckling and collapse
(i.e. coiling up) instabilities. Taking into account the coupling between the
internal and mechanical degrees of freedom of a semiflexible biopolymer chain,
we show that self-trapped internal excitations (such as amide-I vibrations in
proteins, base-pair vibrations in DNA, or polarons in proteins) may produce the
buckling and collapse instabilities of an initially straight chain. These
instabilities remain latent in a straight infinitely long chain, because the
bending of such a chain would require an infinite energy. However, they
manifest themselves as soon as we consider more realistic cases and take into
account a finite length of the chain. In this case the nonlinear localized
modes may act as drivers giving impetus to the conformational dynamics of
biopolymers. The buckling instability is responsible, in particular, for the
large-amplitude localized bending waves which accompany the nonlinear modes
propagating along the chain. In the case of the collapse instability, the chain
folds into a compact three-dimensional coil. The viscous damping of the aqueous
environment only slows down the folding of the chain, but does not stop it even
for a large damping. We find that these effects are only weakly affected by the
peculiarities of the interaction potentials, and thus they should be generic
for different models of semiflexible chains carrying nonlinear localized
excitations.Comment: 4 pages (RevTeX) with 5 figures (EPS
Linear response subordination to intermittent energy release in off-equilibrium aging dynamics
The interpretation of experimental and numerical data describing
off-equilibrium aging dynamics crucially depends on the connection between
spontaneous and induced fluctuations. The hypothesis that linear response
fluctuations are statistically subordinated to irreversible outbursts of
energy, so-called quakes, leads to predictions for averages and fluctuations
spectra of physical observables in reasonable agreement with experimental
results [see e.g. Sibani et al., Phys. Rev. B74:224407, 2006]. Using
simulational data from a simple but representative Ising model with plaquette
interactions, direct statistical evidence supporting the hypothesis is
presented and discussed in this work.
A strict temporal correlation between quakes and intermittent magnetization
fluctuations is demonstrated. The external magnetic field is shown to bias the
pre-existent intermittent tails of the magnetic fluctuation distribution, with
little or no effect on the Gaussian part of the latter. Its impact on energy
fluctuations is shown to be negligible.
Linear response is thus controlled by the quakes and inherits their temporal
statistics. These findings provide a theoretical basis for analyzing
intermittent linear response data from aging system in the same way as thermal
energy fluctuations, which are far more difficult to measure.Comment: 9 pages, 10 figures. Text improve
Kink propagation in a two-dimensional curved Josephson junction
We consider the propagation of sine-Gordon kinks in a planar curved strip as
a model of nonlinear wave propagation in curved wave guides. The homogeneous
Neumann transverse boundary conditions, in the curvilinear coordinates, allow
to assume a homogeneous kink solution. Using a simple collective variable
approach based on the kink coordinate, we show that curved regions act as
potential barriers for the wave and determine the threshold velocity for the
kink to cross. The analysis is confirmed by numerical solution of the 2D
sine-Gordon equation.Comment: 8 pages, 4 figures (2 in color
Localization of nonlinear excitations in curved waveguides
Motivated by the example of a curved waveguide embedded in a photonic
crystal, we examine the effects of geometry in a ``quantum channel'' of
parabolic form. We study the linear case and derive exact as well as
approximate expressions for the eigenvalues and eigenfunctions of the linear
problem. We then proceed to the nonlinear setting and its stationary states in
a number of limiting cases that allow for analytical treatment. The results of
our analysis are used as initial conditions in direct numerical simulations of
the nonlinear problem and localized excitations are found to persist, as well
as to have interesting relaxational dynamics. Analogies of the present problem
in contexts related to atomic physics and particularly to Bose-Einstein
condensation are discussed.Comment: 14 pages, 4 figure
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