1,347 research outputs found
ac-driven Brownian motors: a Fokker-Planck treatment
We consider a primary model of ac-driven Brownian motors, i.e., a classical
particle placed in a spatial-time periodic potential and coupled to a heat
bath. The effects of fluctuations and dissipations are studied by a
time-dependent Fokker-Planck equation. The approach allows us to map the
original stochastic problem onto a system of ordinary linear algebraic
equations. The solution of the system provides complete information about
ratchet transport, avoiding such disadvantages of direct stochastic
calculations as long transients and large statistical fluctuations. The
Fokker-Planck approach to dynamical ratchets is instructive and opens the space
for further generalizations
Domain statistics in a finite Ising chain
We present a comprehensive study for the statistical properties of random
variables that describe the domain structure of a finite Ising chain with
nearest-neighbor exchange interactions and free boundary conditions. By use of
extensive combinatorics we succeed in obtaining the one-variable probability
functions for (i) the number of domain walls, (ii) the number of up domains,
and (iii) the number of spins in an up domain. The corresponding averages and
variances of these probability distributions are calculated and the limiting
case of an infinite chain is considered. Analyzing the averages and the
transition time between differing chain states at low temperatures, we also
introduce a criterion of the ferromagnetic-like behavior of a finite Ising
chain. The results can be used to characterize magnetism in monatomic metal
wires and atomic-scale memory devices.Comment: 19 page
Strong coupling theory for tunneling and vibrational relaxation in driven bistable systems
A study of the dynamics of a tunneling particle in a driven bistable
potential which is moderately-to-strongly coupled to a bath is presented. Upon
restricting the system dynamics to the Hilbert space spanned by the M lowest
energy eigenstates of the bare static potential, a set of coupled non-Markovian
master equations for the diagonal elements of the reduced density matrix,
within the discrete variale representation, is derived. The resulting dynamics
is in good agreement with predictions of ab-initio real-time path integral
simulations. Numerous results, analytical as well as numerical, for the quantum
relaxation rate and for the asymptotic populations are presented. Our method is
particularly convenient to investigate the case of shallow, time-dependent
potential barriers and moderate-to-strong damping, where both a semi-classical
and a Redfield-type approach are inappropriate.Comment: 37 pages, 23 figure
Thermodynamics and Fluctuation Theorems for a Strongly Coupled Open Quantum System: An Exactly Solvable Case
We illustrate recent results concerning the validity of the work fluctuation
theorem in open quantum systems [M. Campisi, P. Talkner, and P. H\"{a}nggi,
Phys. Rev. Lett. {\bf 102}, 210401 (2009)], by applying them to a solvable
model of an open quantum system. The central role played by the thermodynamic
partition function of the open quantum system, -- a two level fluctuator with a
strong quantum nondemolition coupling to a harmonic oscillator --, is
elucidated. The corresponding quantum Hamiltonian of mean force is evaluated
explicitly. We study the thermodynamic entropy and the corresponding specific
heat of this open system as a function of temperature and coupling strength and
show that both may assume negative values at nonzero low temperatures.Comment: 8 pages, 6 figure
Coexistence of absolute negative mobility and anomalous diffusion
Using extensive numerical studies we demonstrate that absolute negative
mobility of a Brownian particle (i.e. the net motion into the direction
opposite to a constant biasing force acting around zero bias) does coexist with
anomalous diffusion. The latter is characterized in terms of a nonlinear
scaling with time of the mean-square deviation of the particle position. Such
anomalous diffusion covers "coherent" motion (i.e. the position dynamics x(t)
approaches in evolving time a constant dispersion), ballistic diffusion,
subdiffusion, superdiffusion and hyperdiffusion. In providing evidence for this
coexistence we consider a paradigmatic model of an inertial Brownian particle
moving in a one-dimensional symmetric periodic potential being driven by both
an unbiased time-periodic force and a constant bias. This very setup allows for
various sorts of different physical realizations
Levy--Brownian motion on finite intervals: Mean first passage time analysis
We present the analysis of the first passage time problem on a finite
interval for the generalized Wiener process that is driven by L\'evy stable
noises. The complexity of the first passage time statistics (mean first passage
time, cumulative first passage time distribution) is elucidated together with a
discussion of the proper setup of corresponding boundary conditions that
correctly yield the statistics of first passages for these non-Gaussian noises.
The validity of the method is tested numerically and compared against
analytical formulae when the stability index approaches 2, recovering
in this limit the standard results for the Fokker-Planck dynamics driven by
Gaussian white noise.Comment: 9 pages, 13 figure
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.
Interplay of frequency-synchronization with noise: current resonances, giant diffusion and diffusion-crests
We elucidate how the presence of noise may significantly interact with the
synchronization mechanism of systems exhibiting frequency-locking. The response
of these systems exhibits a rich variety of behaviors, such as resonances and
anti-resonances which can be controlled by the intensity of noise. The
transition between different locked regimes provokes the development of a
multiple enhancement of the effective diffusion. This diffusion behavior is
accompanied by a crest-like peak-splitting cascade when the distribution of the
lockings is self-similar, as it occurs in periodic systems that are able to
exhibit a Devil's staircase sequence of frequency-lockings.Comment: 7 pages, 6 figures, epl.cls. Accepted for publication in Europhysics
Letter
Nonclassical Kinetics in Constrained Geometries: Initial Distribution Effects
We present a detailed study of the effects of the initial distribution on the
kinetic evolution of the irreversible reaction A+B -> 0 in one dimension. Our
analytic as well as numerical work is based on a reaction-diffusion model of
this reaction. We focus on the role of initial density fluctuations in the
creation of the macroscopic patterns that lead to the well-known kinetic
anomalies in this system. In particular, we discuss the role of the long
wavelength components of the initial fluctuations in determining the long-time
behavior of the system. We note that the frequently studied random initial
distribution is but one of a variety of possible distributions leading to
interesting anomalous behavior. Our discussion includes an initial distribution
with correlated A-B pairs and one in which the initial distribution forms a
fractal pattern. The former is an example of a distribution whose long
wavelength components are suppressed, while the latter exemplifies one whose
long wavelength components are enhanced, relative to those of the random
distribution.Comment: To appear in International Journal of Bifurcation and Chaos Vol. 8
No.
Use and Abuse of a Fractional Fokker-Planck Dynamics for Time-Dependent Driving
We investigate a subdiffusive, fractional Fokker-Planck dynamics occurring in
time-varying potential landscapes and thereby disclose the failure of the
fractional Fokker-Planck equation (FFPE) in its commonly used form when
generalized in an {\it ad hoc} manner to time-dependent forces. A modified FFPE
(MFFPE) is rigorously derived, being valid for a family of dichotomously
alternating force-fields. This MFFPE is numerically validated for a rectangular
time-dependent force with zero average bias. For this case subdiffusion is
shown to become enhanced as compared to the force free case. We question,
however, the existence of any physically valid FFPE for arbitrary varying
time-dependent fields that differ from this dichotomous varying family.Comment: 4 pages, 2 figure
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