1,161 research outputs found
Mapping the Arnold web with a GPU-supercomputer
The Arnold diffusion constitutes a dynamical phenomenon which may occur in
the phase space of a non-integrable Hamiltonian system whenever the number of
the system degrees of freedom is . The diffusion is mediated by a
web-like structure of resonance channels, which penetrates the phase space and
allows the system to explore the whole energy shell. The Arnold diffusion is a
slow process; consequently the mapping of the web presents a very
time-consuming task. We demonstrate that the exploration of the Arnold web by
use of a graphic processing unit (GPU)-supercomputer can result in distinct
speedups of two orders of magnitude as compared to standard CPU-based
simulations.Comment: 7 pages, 4 figures, a video supplementary provided at
http://www.physik.uni-augsburg.de/~seiberar/arnold/Energy15_HD_frontNback.av
Relativistic Brownian motion: From a microscopic binary collision model to the Langevin equation
The Langevin equation (LE) for the one-dimensional relativistic Brownian
motion is derived from a microscopic collision model. The model assumes that a
heavy point-like Brownian particle interacts with the lighter heat bath
particles via elastic hard-core collisions. First, the commonly known,
non-relativistic LE is deduced from this model, by taking into account the
non-relativistic conservation laws for momentum and kinetic energy.
Subsequently, this procedure is generalized to the relativistic case. There, it
is found that the relativistic stochastic force is still \gd-correlated
(white noise) but does \emph{no} longer correspond to a Gaussian white noise
process. Explicit results for the friction and momentum-space diffusion
coefficients are presented and discussed.Comment: v2: Eqs. (17c) and (28) corrected; v3: discussion extended, Eqs. (33)
added, thereby connection to earlier work clarified; v4: final version,
accepted for publication in Phys. Rev.
What do phase space methods tell us about disordered quantum systems?
Introduction
Phase space methods in quantum mechanics
- The Wigner function
- The Husimi function
- Inverse participation ratio
Anderson model in phase space
- Husimi functions
- Inverse participation ratiosComment: 14 pages, 4 figures. To be published in "The Anderson Transition and
its Ramifications - Localisation, Quantum Interference, and Interactions",
ed. by T. Brandes and S. Kettemann, Lecture Notes in Physics
(http://link.springer.de/series/lnpp/) (Springer Verlag,
Berlin-Heidelberg-New York
Stochastic equation for a jumping process with long-time correlations
A jumping process, defined in terms of jump size distribution and waiting
time distribution, is presented. The jumping rate depends on the process value.
The process, which is Markovian and stationary, relaxes to an equilibrium and
is characterized by the power-law autocorrelation function. Therefore, it can
serve as a model of the 1/f noise as well as a model of the stochastic force in
the generalized Langevin equation. This equation is solved for the noise
correlations 1/t; the resulting velocity distribution has sharply falling
tails. The system preserves the memory about the initial condition for a very
long time.Comment: 7 pages, 5 Postscript figure
Frequency and Phase Synchronization in Stochastic Systems
The phenomenon of frequency and phase synchronization in stochastic systems
requires a revision of concepts originally phrased in the context of purely
deterministic systems. Various definitions of an instantaneous phase are
presented and compared with each other with special attention payed to their
robustness with respect to noise. We review the results of an analytic approach
describing noise-induced phase synchronization in a thermal two-state system.
In this context exact expressions for the mean frequency and the phase
diffusivity are obtained that together determine the average length of locking
episodes. A recently proposed method to quantify frequency synchronization in
noisy potential systems is presented and exemplified by applying it to the
periodically driven noisy harmonic oscillator. Since this method is based on a
threshold crossing rate pioneered by S.O. Rice the related phase velocity is
termed Rice frequency. Finally, we discuss the relation between the phenomenon
of stochastic resonance and noise-enhanced phase coherence by applying the
developed concepts to the periodically driven bistable Kramers oscillator.Comment: to appear in the Chaos focus issue on "Control, communication, and
synchronization in chaotic dynamical systems
Time-scale invariance of relaxation processes of density fluctuation in slow neutron scattering in liquid cesium
The realization of idea of time-scale invariance for relaxation processes in
liquids has been performed by the memory functions formalism. The best
agreement with experimental data for the dynamic structure factor
of liquid cesium near melting point in the range of wave vectors (0.4
\ang^{-1} \leq k \leq 2.55 \ang^{-1}) is found with the assumption of
concurrence of relaxation scales for memory functions of third and fourth
orders. Spatial dispersion of the four first points in spectrum of statistical
parameter of non-Markovity at has allowed
to reveal the non-Markov nature of collective excitations in liquid cesium,
connected with long-range memory effect.Comment: REVTEX +3 ps figure
Theory of the Relativistic Brownian Motion. The (1+1)-Dimensional Case
We construct a theory for the 1+1-dimensional Brownian motion in a viscous
medium, which is (i) consistent with Einstein's theory of special relativity,
and (ii) reduces to the standard Brownian motion in the Newtonian limit case.
In the first part of this work the classical Langevin equations of motion,
governing the nonrelativistic dynamics of a free Brownian particle in the
presence of a heat bath (white noise), are generalized in the framework of
special relativity. Subsequently, the corresponding relativistic Langevin
equations are discussed in the context of the generalized Ito (pre-point
discretization rule) vs. the Stratonovich (mid-point discretization rule)
dilemma: It is found that the relativistic Langevin equation in the
Haenggi-Klimontovich interpretation (with the post-point discretization rule)
is the only one that yields agreement with the relativistic Maxwell
distribution. Numerical results for the relativistic Langevin equation of a
free Brownian particle are presented.Comment: see cond-mat/0607082 for an improved theor
Ratchet-like dynamics of fluxons in annular Josephson junctions driven by bi-harmonic microwave fields
Experimental observation of the unidirectional motion of a topological
soliton driven by a bi-harmonic ac force of zero mean is reported. The
observation is made by measuring the current-voltage characteristics for a
fluxon trapped in an annular Josephson junction that was placed into a
microwave field. The measured dependence of the fluxon mean velocity (rectified
voltage) at zero dc bias versus the phase shift between the first and second
harmonic of the driving force is in qualitative agreement with theoretical
expectations.Comment: 6 figure
Capacitance fluctuations causing channel noise reduction in stochastic Hodgkin-Huxley systems
Voltage-dependent ion channels determine the electric properties of axonal
cell membranes. They not only allow the passage of ions through the cell
membrane but also contribute to an additional charging of the cell membrane
resulting in the so-called capacitance loading. The switching of the channel
gates between an open and a closed configuration is intrinsically related to
the movement of gating charge within the cell membrane. At the beginning of an
action potential the transient gating current is opposite to the direction of
the current of sodium ions through the membrane. Therefore, the excitability is
expected to become reduced due to the influence of a gating current. Our
stochastic Hodgkin-Huxley like modeling takes into account both the channel
noise -- i.e. the fluctuations of the number of open ion channels -- and the
capacitance fluctuations that result from the dynamics of the gating charge. We
investigate the spiking dynamics of membrane patches of variable size and
analyze the statistics of the spontaneous spiking. As a main result, we find
that the gating currents yield a drastic reduction of the spontaneous spiking
rate for sufficiently large ion channel clusters. Consequently, this
demonstrates a prominent mechanism for channel noise reduction.Comment: 18 page
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