290 research outputs found
Non-normalizable densities in strong anomalous diffusion: beyond the central limit theorem
Strong anomalous diffusion, where with a nonlinear spectrum \nu(q) \neq \mbox{const}, is wide spread
and has been found in various nonlinear dynamical systems and experiments on
active transport in living cells. Using a stochastic approach we show how this
phenomena is related to infinite covariant densities, i.e., the asymptotic
states of these systems are described by non-normalizable distribution
functions. Our work shows that the concept of infinite covariant densities
plays an important role in the statistical description of open systems
exhibiting multi-fractal anomalous diffusion, as it is complementary to the
central limit theorem.Comment: PRL, in pres
Universal fluctuations in subdiffusive transport
Subdiffusive transport in tilted washboard potentials is studied within the
fractional Fokker-Planck equation approach, using the associated continuous
time random walk (CTRW) framework. The scaled subvelocity is shown to obey a
universal law, assuming the form of a stationary Levy-stable distribution. The
latter is defined by the index of subdiffusion alpha and the mean subvelocity
only, but interestingly depends neither on the bias strength nor on the
specific form of the potential. These scaled, universal subvelocity
fluctuations emerge due to the weak ergodicity breaking and are vanishing in
the limit of normal diffusion. The results of the analytical heuristic theory
are corroborated by Monte Carlo simulations of the underlying CTRW
Pressure in an exactly solvable model of active fluid
We consider the pressure in the steady-state regime of three stochastic
models characterized by self-propulsion and persistent motion and widely
employed to describe the behavior of active particles, namely the Active
Brownian particle (ABP) model, the Gaussian colored noise (GCN) model and the
unified colored noise model (UCNA). Whereas in the limit of short but finite
persistence time the pressure in the UCNA model can be obtained by different
methods which have an analog in equilibrium systems, in the remaining two
models only the virial route is, in general, possible.
According to this method, notwithstanding each model obeys its own specific
microscopic law of evolution, the pressure displays a certain universal
behavior. For generic interparticle and confining potentials, we derive a
formula which establishes a correspondence between the GCN and the UCNA
pressures. In order to provide explicit formulas and examples, we specialize
the discussion to the case of an assembly of elastic dumbbells confined to a
parabolic well. By employing the UCNA we find that, for this model, the
pressure determined by the thermodynamic method coincides with the pressures
obtained by the virial and mechanical methods. The three methods when applied
to the GCN give a pressure identical to that obtained via the UCNA. Finally, we
find that the ABP virial pressure exactly agrees with the UCNA and GCN result.Comment: 12 pages, 1 figure Submitted for publication 23rd of January 2017 The
introduction has been modifie
Josephson-like currents in graphene for arbitrary time-dependent potential barriers
From the exact solution of the Dirac-Weyl equation we find unusual currents
j_y running in y-direction parallel to a time-dependent scalar potential
barrier W(x,t) placed upon a monolayer of graphene, even for vanishing momentum
component p_y. In their sine-like dependence on the phase difference of wave
functions, describing left and right moving Dirac fermions, these currents
resemble Josephson currents in superconductors, including the occurance of
Shapiro steps at certain frequencies of potential oscillations. The
Josephson-like currents are calculated for several specific time-dependent
barriers. A novel type of resonance is discovered when, accounting for the
Fermi velocity, temporal and spatial frequencies match.Comment: 8 pages, 4 figur
Time evolution towards q-Gaussian stationary states through unified Ito-Stratonovich stochastic equation
We consider a class of single-particle one-dimensional stochastic equations
which include external field, additive and multiplicative noises. We use a
parameter which enables the unification of the traditional
It\^o and Stratonovich approaches, now recovered respectively as the
and particular cases to derive the associated Fokker-Planck
equation (FPE). These FPE is a {\it linear} one, and its stationary state is
given by a -Gaussian distribution with , where characterizes the
strength of the confining external field, and is the (normalized)
amplitude of the multiplicative noise. We also calculate the standard kurtosis
and the -generalized kurtosis (i.e., the standard
kurtosis but using the escort distribution instead of the direct one). Through
these two quantities we numerically follow the time evolution of the
distributions. Finally, we exhibit how these quantities can be used as
convenient calibrations for determining the index from numerical data
obtained through experiments, observations or numerical computations.Comment: 9 pages, 2 figure
Scaling Relations and Exponents in the Growth of Rough Interfaces Through Random Media
The growth of a rough interface through a random media is modelled by a
continuous stochastic equation with a quenched noise. By use of the Novikov
theorem we can transform the dependence of the noise on the interface height
into an effective temporal correlation for different regimes of the evolution
of the interface. The exponents characterizing the roughness of the interface
can thus be computed by simple scaling arguments showing a good agreement with
recent experiments and numerical simulations.Comment: 4 pages, RevTex, twocolumns, two figures (upon request). To appear in
Europhysics Letter
Viscosity Dependence of the Folding Rates of Proteins
The viscosity dependence of the folding rates for four sequences (the native
state of three sequences is a beta-sheet, while the fourth forms an
alpha-helix) is calculated for off-lattice models of proteins. Assuming that
the dynamics is given by the Langevin equation we show that the folding rates
increase linearly at low viscosities \eta, decrease as 1/\eta at large \eta and
have a maximum at intermediate values. The Kramers theory of barrier crossing
provides a quantitative fit of the numerical results. By mapping the simulation
results to real proteins we estimate that for optimized sequences the time
scale for forming a four turn \alpha-helix topology is about 500 nanoseconds,
whereas the time scale for forming a beta-sheet topology is about 10
microseconds.Comment: 14 pages, Latex, 3 figures. One figure is also available at
http://www.glue.umd.edu/~klimov/seq_I_H.html, to be published in Physical
Review Letter
Two refreshing views of Fluctuation Theorems through Kinematics Elements and Exponential Martingale
In the context of Markov evolution, we present two original approaches to
obtain Generalized Fluctuation-Dissipation Theorems (GFDT), by using the
language of stochastic derivatives and by using a family of exponential
martingales functionals. We show that GFDT are perturbative versions of
relations verified by these exponential martingales. Along the way, we prove
GFDT and Fluctuation Relations (FR) for general Markov processes, beyond the
usual proof for diffusion and pure jump processes. Finally, we relate the FR to
a family of backward and forward exponential martingales.Comment: 41 pages, 7 figures; version2: 45 pages, 7 figures, minor revisions,
new results in Section
Work and heat fluctuations in two-state systems: a trajectory thermodynamics formalism
Two-state models provide phenomenological descriptions of many different
systems, ranging from physics to chemistry and biology. We investigate work
fluctuations in an ensemble of two-state systems driven out of equilibrium
under the action of an external perturbation. We calculate the probability
density P(W) that a work equal to W is exerted upon the system along a given
non-equilibrium trajectory and introduce a trajectory thermodynamics formalism
to quantify work fluctuations in the large-size limit. We then define a
trajectory entropy S(W) that counts the number of non-equilibrium trajectories
P(W)=exp(S(W)/kT) with work equal to W. A trajectory free-energy F(W) can also
be defined, which has a minimum at a value of the work that has to be
efficiently sampled to quantitatively test the Jarzynski equality. Within this
formalism a Lagrange multiplier is also introduced, the inverse of which plays
the role of a trajectory temperature. Our solution for P(W) exactly satisfies
the fluctuation theorem by Crooks and allows us to investigate
heat-fluctuations for a protocol that is invariant under time reversal. The
heat distribution is then characterized by a Gaussian component (describing
small and frequent heat exchange events) and exponential tails (describing the
statistics of large deviations and rare events). For the latter, the width of
the exponential tails is related to the aforementioned trajectory temperature.
Finite-size effects to the large-N theory and the recovery of work
distributions for finite N are also discussed. Finally, we pay particular
attention to the case of magnetic nanoparticle systems under the action of a
magnetic field H where work and heat fluctuations are predicted to be
observable in ramping experiments in micro-SQUIDs.Comment: 28 pages, 14 figures (Latex
- …