13,608 research outputs found

### Diffusivity in one-dimensional generalized Mott variable-range hopping models

We consider random walks in a random environment which are generalized
versions of well-known effective models for Mott variable-range hopping. We
study the homogenized diffusion constant of the random walk in the
one-dimensional case. We prove various estimates on the low-temperature
behavior which confirm and extend previous work by physicists.Comment: Published in at http://dx.doi.org/10.1214/08-AAP583 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org

### Recurrence and transience for long-range reversible random walks on a random point process

We consider reversible random walks in random environment obtained from
symmetric long--range jump rates on a random point process. We prove almost
sure transience and recurrence results under suitable assumptions on the point
process and the jump rate function. For recurrent models we obtain almost sure
estimates on effective resistances in finite boxes. For transient models we
construct explicit fluxes with finite energy on the associated electrical
network.Comment: 34 page

### Synchronization in fiber lasers arrays

We consider an array of fiber lasers coupled through the nearest neighbors.
The model is a generalized nonlinear Schroedinger equation where the usual
Laplacian is replaced by the graph Laplacian. For a graph with no symmetries,
we show that there is no resonant transfer of energy between the different
eigenmodes. We illustrate this and confirm our result on a simple graph. This
shows that arrays of fiber ring lasers can be made temporally coherent

### Invariance principle for Mott variable range hopping and other walks on point processes

We consider a random walk on a homogeneous Poisson point process with energy
marks. The jump rates decay exponentially in the A-power of the jump length and
depend on the energy marks via a Boltzmann--like factor. The case A=1
corresponds to the phonon-induced Mott variable range hopping in disordered
solids in the regime of strong Anderson localization. We prove that for almost
every realization of the marked process, the diffusively rescaled random walk,
with arbitrary start point, converges to a Brownian motion whose diffusion
matrix is positive definite, and independent of the environment. Finally, we
extend the above result to other point processes including diluted lattices.Comment: 47 pages, minor corrections, submitte

### Two tone response of radiofrequency signals using the voltage output of a Superconducting Quantum Interference Filter

In the presence of weak time harmonic electromagnetic fields, Superconducting
Quantum Interference Filters (SQIFs) show the typical behavior of non linear
mixers. The SQIFs are manufactured from high-T_c grain boundary Josephson
junctions and operated in active microcooler. The dependence of dc voltage
output V_dc vs. static external magnetic field B is non-periodic and consists
of a well pronounced unique dip at zero field, with marginal side modulations
at higher fields. We have successfully exploited the parabolic shape of the
voltage dip around B=0 to mix quadratically two external time harmonic
rf-signals, at frequencies f_1 and f_2 below the Josephson frequency f_J, and
detect the corresponding mixing signal at f_1-f_2. When the mixing takes place
on the SQIF current-voltage characteristics the component at 2f_2 - f_1 is
present. The experiments suggest potential applications of a SQIF as a
non-linear mixing device, capable to operate at frequencies from dc to few GHz
with a large dynamic range.Comment: 10 pages, 3 Figures, submitted to J. Supercond. (as proceeding of the
HTSHFF Symposium, June 2006, Cardiff

### Fractional Fokker-Planck Equation for Ultraslow Kinetics

Several classes of physical systems exhibit ultraslow diffusion for which the
mean squared displacement at long times grows as a power of the logarithm of
time ("strong anomaly") and share the interesting property that the probability
distribution of particle's position at long times is a double-sided
exponential. We show that such behaviors can be adequately described by a
distributed-order fractional Fokker-Planck equations with a power-law
weighting-function. We discuss the equations and the properties of their
solutions, and connect this description with a scheme based on continuous-time
random walks

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