550 research outputs found
The Unequal Twins - Probability Distributions Aren't Everything
It is the common lore to assume that knowing the equation for the probability
distribution function (PDF) of a stochastic model as a function of time tells
the whole picture defining all other characteristics of the model. We show that
this is not the case by comparing two exactly solvable models of anomalous
diffusion due to geometric constraints: The comb model and the random walk on a
random walk (RWRW). We show that though the two models have exactly the same
PDFs, they differ in other respects, like their first passage time (FPT)
distributions, their autocorrelation functions and their aging properties
From deterministic dynamics to kinetic phenomena
We investigate a one-dimenisonal Hamiltonian system that describes a system
of particles interacting through short-range repulsive potentials. Depending on
the particle mean energy, , the system demonstrates a spectrum of
kinetic regimes, characterized by their transport properties ranging from
ballistic motion to localized oscillations through anomalous diffusion regimes.
We etsablish relationships between the observed kinetic regimes and the
"thermodynamic" states of the system. The nature of heat conduction in the
proposed model is discussed.Comment: 4 pages, 4 figure
Dynamical heat channels
We consider heat conduction in a 1D dynamical channel. The channel consists
of a group of noninteracting particles, which move between two heat baths
according to some dynamical process. We show that the essential thermodynamic
properties of the heat channel can be evaluated from the diffusion properties
of the underlying particles. Emphasis is put on the conduction under anomalous
diffusion conditions. \\{\bf PACS number}: 05.40.+j, 05.45.ac, 05.60.cdComment: 4 figure
Molecular motor with a build-in escapement device
We study dynamics of a classical particle in a one-dimensional potential,
which is composed of two periodic components, that are time-independent, have
equal amplitudes and periodicities. One of them is externally driven by a
random force and thus performs a diffusive-type motion with respect to the
other. We demonstrate that here, under certain conditions, the particle may
move unidirectionally with a constant velocity, despite the fact that the
random force averages out to zero. We show that the physical mechanism
underlying such a phenomenon resembles the work of an escapement-type device in
watches; upon reaching certain level, random fluctuations exercise a locking
function creating the points of irreversibility in particle's trajectories such
that the particle gets uncompensated displacements. Repeated (randomly) in each
cycle, this process ultimately results in a random ballistic-type motion. In
the overdamped limit, we work out simple analytical estimates for the
particle's terminal velocity. Our analytical results are in a very good
agreement with the Monte Carlo data.Comment: 7 pages, 4 figure
L\'evy walks
Random walk is a fundamental concept with applications ranging from quantum
physics to econometrics. Remarkably, one specific model of random walks appears
to be ubiquitous across many fields as a tool to analyze transport phenomena in
which the dispersal process is faster than dictated by Brownian diffusion. The
L\'{e}vy walk model combines two key features, the ability to generate
anomalously fast diffusion and a finite velocity of a random walker. Recent
results in optics, Hamiltonian chaos, cold atom dynamics, bio-physics, and
behavioral science demonstrate that this particular type of random walks
provides significant insight into complex transport phenomena. This review
provides a self-consistent introduction to L\'{e}vy walks, surveys their
existing applications, including latest advances, and outlines further
perspectives.Comment: 50 page
Probing anomalous relaxation by coherent multidimensional optical spectroscopy
We propose to study the origin of algebraic decay of two-point correlation
functions observed in glasses, proteins, and quantum dots by their nonlinear
response to sequences of ultrafast laser pulses. Power-law spectral
singularities and temporal relaxation in two-dimensional correlation
spectroscopy (2DCS) signals are predicted for a continuous time random walk
model of stochastic spectral jumps in a two level system with a power-law
distribution of waiting times . Spectroscopic
signatures of stationary ensembles for and aging effects in
nonstationary ensembles with are identified
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