1,158 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
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
Bounds for Non-Locality Distillation Protocols
Non-locality can be quantified by the violation of a Bell inequality. Since
this violation may be amplified by local operations an alternative measure has
been proposed - distillable non-locality. The alternative measure is difficult
to calculate exactly due to the double exponential growth of the parameter
space. In this article we give a way to bound the distillable non-locality of a
resource by the solutions to a related optimization problem. Our upper bounds
are exponentially easier to compute than the exact value and are shown to be
meaningful in general and tight in some cases.Comment: 8 pages, 3 figures; small changes in introduction and application
section due to the exact verification of distillation bounds using a symbolic
computation package (Maple 14); added journal re
Non-Markovian Stochastic Resonance
The phenomenological linear response theory of non-Markovian Stochastic
Resonance (SR) is put forward for stationary two-state renewal processes. In
terms of a derivation of a non-Markov regression theorem we evaluate the
characteristic SR-quantifiers; i.e. the spectral power amplification (SPA) and
the signal-to-noise ratio (SNR), respectively. In clear contrast to Markovian
SR, a characteristic benchmark of genuine non-Markovian SR is its distinctive
dependence of the SPA and SNR on small (adiabatic) driving frequencies;
particularly, the adiabatic SNR becomes strongly suppressed over its Markovian
counterpart. This non-Markovian SR theory is elucidated for a fractal gating
dynamics of a potassium ion channel possessing an infinite variance of closed
sojourn times.Comment: 4 pages, 1 figur
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
Checking the validity of truncating the cumulant hierarchy description of a small system
We analyze the behavior of the first few cumulant in an array with a small
number of coupled identical particles. Desai and Zwanzig (J. Stat. Phys., {\bf
19}, 1 (1978), p. 1) studied noisy arrays of nonlinear units with global
coupling and derived an infinite hierarchy of differential equations for the
cumulant moments. They focused on the behavior of infinite size systems using a
strategy based on truncating the hierarchy. In this work we explore the
reliability of such an approach to describe systems with a small number of
elements. We carry out an extensive numerical analysis of the truncated
hierarchy as well as numerical simulations of the full set of Langevin
equations governing the dynamics. We find that the results provided by the
truncated hierarchy for finite systems are at variance with those of the
Langevin simulations for large regions of parameter space. The truncation of
the hierarchy leads to a dependence on initial conditions and to the
coexistence of states which are not consistent with the theoretical
expectations based on the multidimensional linear Fokker-Planck equation for
finite arrays
Nonlocality is transitive
We show a transitivity property of nonlocal correlations: There exist
tripartite nonsignaling correlations of which the bipartite marginals between A
and B as well as B and C are nonlocal and any tripartite nonsignaling system
between A, B, and C consistent with them must be such that the bipartite
marginal between A and C is also nonlocal. This property represents a step
towards ruling out certain alternative models for the explanation of quantum
correlations such as hidden communication at finite speed. Whereas it is not
possible to rule out this model experimentally, it is the goal of our approach
to demonstrate this explanation to be logically inconsistent: either the
communication cannot remain hidden, or its speed has to be infinite. The
existence of a three-party system that is pairwise nonlocal is of independent
interest in the light of the monogamy property of nonlocality.Comment: 4 pages, 2 figures, v2: published versio
Fluctuation theorems: Work is not an observable
The characteristic function of the work performed by an external
time-dependent force on a Hamiltonian quantum system is identified with the
time-ordered correlation function of the exponentiated system's Hamiltonian. A
similar expression is obtained for the averaged exponential work which is
related to the free energy difference of equilibrium systems by the Jarzynski
work theorem
Entropic stochastic resonance: the constructive role of the unevenness
We demonstrate the existence of stochastic resonance (SR) in confined systems
arising from entropy variations associated to the presence of irregular
boundaries. When the motion of a Brownian particle is constrained to a region
with uneven boundaries, the presence of a periodic input may give rise to a
peak in the spectral amplification factor and therefore to the appearance of
the SR phenomenon. We have proved that the amplification factor depends on the
shape of the region through which the particle moves and that by adjusting its
characteristic geometric parameters one may optimize the response of the
system. The situation in which the appearance of such entropic stochastic
resonance (ESR) occurs is common for small-scale systems in which confinement
and noise play an prominent role. The novel mechanism found could thus
constitute an important tool for the characterization of these systems and can
put to use for controlling their basic properties.Comment: 8 pages, 8 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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