1,910 research outputs found
Optimal target search on a fast folding polymer chain with volume exchange
We study the search process of a target on a rapidly folding polymer (`DNA')
by an ensemble of particles (`proteins'), whose search combines 1D diffusion
along the chain, Levy type diffusion mediated by chain looping, and volume
exchange. A rich behavior of the search process is obtained with respect to the
physical parameters, in particular, for the optimal search.Comment: 4 pages, 3 figures, REVTe
The fractional Schr\"{o}dinger operator and Toeplitz matrices
Confining a quantum particle in a compact subinterval of the real line with
Dirichlet boundary conditions, we identify the connection of the
one-dimensional fractional Schr\"odinger operator with the truncated Toeplitz
matrices. We determine the asymptotic behaviour of the product of eigenvalues
for the -stable symmetric laws by employing the Szeg\"o's strong limit
theorem. The results of the present work can be applied to a recently proposed
model for a particle hopping on a bounded interval in one dimension whose
hopping probability is given a discrete representation of the fractional
Laplacian.Comment: 10 pages, 2 figure
Area Distribution of Elastic Brownian Motion
We calculate the excursion and meander area distributions of the elastic
Brownian motion by using the self adjoint extension of the Hamiltonian of the
free quantum particle on the half line. We also give some comments on the area
of the Brownian motion bridge on the real line with the origin removed. We will
stress on the power of self adjoint extension to investigate different possible
boundary conditions for the stochastic processes.Comment: 18 pages, published versio
Phase space measure concentration for an ideal gas
We point out that a special case of an ideal gas exhibits concentration of
the volume of its phase space, which is a sphere, around its equator in the
thermodynamic limit. The rate of approach to the thermodynamic limit is
determined. Our argument relies on the spherical isoperimetric inequality of
L\'{e}vy and Gromov.Comment: 15 pages, No figures, Accepted by Modern Physics Letters
The Lagrange and Markov spectra from the dynamical point of view
This text grew out of my lecture notes for a 4-hours minicourse delivered on
October 17 \& 19, 2016 during the research school "Applications of Ergodic
Theory in Number Theory" -- an activity related to the Jean-Molet Chair project
of Mariusz Lema\'nczyk and S\'ebastien Ferenczi -- realized at CIRM, Marseille,
France. The subject of this text is the same of my minicourse, namely, the
structure of the so-called Lagrange and Markov spectra (with an special
emphasis on a recent theorem of C. G. Moreira).Comment: 27 pages, 6 figures. Survey articl
Generalised extreme value statistics and sum of correlated variables
We show that generalised extreme value statistics -the statistics of the k-th
largest value among a large set of random variables- can be mapped onto a
problem of random sums. This allows us to identify classes of non-identical and
(generally) correlated random variables with a sum distributed according to one
of the three (k-dependent) asymptotic distributions of extreme value
statistics, namely the Gumbel, Frechet and Weibull distributions. These
classes, as well as the limit distributions, are naturally extended to real
values of k, thus providing a clear interpretation to the onset of Gumbel
distributions with non-integer index k in the statistics of global observables.
This is one of the very few known generalisations of the central limit theorem
to non-independent random variables. Finally, in the context of a simple
physical model, we relate the index k to the ratio of the correlation length to
the system size, which remains finite in strongly correlated systems.Comment: To appear in J.Phys.
Phase transitions driven by L\'evy stable noise: exact solutions and stability analysis of nonlinear fractional Fokker-Planck equations
Phase transitions and effects of external noise on many body systems are one
of the main topics in physics. In mean field coupled nonlinear dynamical
stochastic systems driven by Brownian noise, various types of phase transitions
including nonequilibrium ones may appear. A Brownian motion is a special case
of L\'evy motion and the stochastic process based on the latter is an
alternative choice for studying cooperative phenomena in various fields.
Recently, fractional Fokker-Planck equations associated with L\'evy noise have
attracted much attention and behaviors of systems with double-well potential
subjected to L\'evy noise have been studied intensively. However, most of such
studies have resorted to numerical computation. We construct an {\it
analytically solvable model} to study the occurrence of phase transitions
driven by L\'evy stable noise.Comment: submitted to EP
B\"acklund transformation for non-relativistic Chern-Simons vortices
A B\"acklund transformation yielding the static non-relativistic Chern-Simons
vortices of Jackiw and Pi is presented.Comment: 7 pages plain Te
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