688 research outputs found
Arithmetic area for m planar Brownian paths
We pursue the analysis made in [1] on the arithmetic area enclosed by m
closed Brownian paths. We pay a particular attention to the random variable
S{n1,n2, ...,n} (m) which is the arithmetic area of the set of points, also
called winding sectors, enclosed n1 times by path 1, n2 times by path 2, ...,nm
times by path m. Various results are obtained in the asymptotic limit
m->infinity. A key observation is that, since the paths are independent, one
can use in the m paths case the SLE information, valid in the 1-path case, on
the 0-winding sectors arithmetic area.Comment: 12 pages, 2 figure
The Local Time Distribution of a Particle Diffusing on a Graph
We study the local time distribution of a Brownian particle diffusing along
the links on a graph. In particular, we derive an analytic expression of its
Laplace transform in terms of the Green's function on the graph. We show that
the asymptotic behavior of this distribution has non-Gaussian tails
characterized by a nontrivial large deviation function.Comment: 8 pages, two figures (included
Statistics of reduced words in locally free and braid groups: Abstract studies and application to ballistic growth model
We study numerically and analytically the average length of reduced
(primitive) words in so-called locally free and braid groups. We consider the
situations when the letters in the initial words are drawn either without or
with correlations. In the latter case we show that the average length of the
reduced word can be increased or lowered depending on the type of correlation.
The ideas developed are used for analytical computation of the average number
of peaks of the surface appearing in some specific ballistic growth modelComment: 29 pages, LaTeX, 7 separated Postscript figures (available on
request), submitted to J. Phys. (A): Math. Ge
Radiation budget estimates over Africa and surrounding oceans: inter-annual comparisons
International audienceThree independent datasets of Radiation Budget at the top of the atmosphere (TOA) spanning two decades are compared: the Scanner Narrow Field of View data (from ERBE, ScaRaB, and CERES instruments, 1985â2005), the ERBS Nonscanner Wide Field of View data (1985â1998) and the simulated broadband fluxes from the International Satellite Cloud Climatology Project (ISCCP-FD, 1983â2004). The analysis concerns the shortwave (SW) reflected flux, the longwave (LW) emitted flux and the net flux at the Top Of the Atmosphere (TOA) over Africa and the surrounding oceans (45° Sâ45° N/60° Wâ60° E), a region particularly impacted by climate variability. For each month, local anomalies are computed with reference to the average over this large region, and their differences between the 2002â2005 and 1985â1989 periods are analysed. These anomalies are relative values and are mostly independent on the absolute observed trends (about 2.5 Wm-2 per decade) which may be affected by possible calibration drifts. Large inter-annual variations are observed locally. Over a part of the South East Atlantic (35°â10° S/10° Wâ10° E), including the marine low cloud area off Angola, there is a decrease of the yearly means of net flux estimated to 2.2, 3 and 6 Wm-2 respectively for the Scanner, Nonscanner and ISCPP-FD data. Over a narrow strip of the Sahel Zone, the net flux increases by about 5 Wm-2
Brownian Motion in wedges, last passage time and the second arc-sine law
We consider a planar Brownian motion starting from at time and
stopped at and a set of semi-infinite
straight lines emanating from . Denoting by the last time when is
reached by the Brownian motion, we compute the probability law of . In
particular, we show that, for a symmetric and even values, this law can
be expressed as a sum of or functions. The original
result of Levy is recovered as the special case . A relation with the
problem of reaction-diffusion of a set of three particles in one dimension is
discussed
Localization effects in a periodic quantum graph with magnetic field and spin-orbit interaction
A general technique for the study of embedded quantum graphs with magnetic
fields and spin-orbit interaction is presented. The analysis is used to
understand the contribution of Rashba constant to the extreme localization
induced by magnetic field in the T3 shaped quantum graph. We show that this
effect is destroyed at generic values of the Rashba constant. On the other
hand, for certain combinations of the Rashba constant and the magnetic
parameters another series of infinitely degenerate eigenvalues appears.Comment: 25 pages, typos corrected, references extende
Scars on quantum networks ignore the Lyapunov exponent
We show that enhanced wavefunction localization due to the presence of short
unstable orbits and strong scarring can rely on completely different
mechanisms. Specifically we find that in quantum networks the shortest and most
stable orbits do not support visible scars, although they are responsible for
enhanced localization in the majority of the eigenstates. Scarring orbits are
selected by a criterion which does not involve the classical Lyapunov exponent.
We obtain predictions for the energies of visible scars and the distributions
of scarring strengths and inverse participation ratios.Comment: 5 pages, 2 figure
Algebraic and arithmetic area for planar Brownian paths
The leading and next to leading terms of the average arithmetic area enclosed by independent closed Brownian planar paths, with
a given length and starting from and ending at the same point, is
calculated. The leading term is found to be
and the -winding sector arithmetic area inside the paths is subleading
in the asymptotic regime. A closed form expression for the algebraic area
distribution is also obtained and discussed.Comment: 8 pages, 2 figure
Scattering theory on graphs
We consider the scattering theory for the Schr\"odinger operator
-\Dc_x^2+V(x) on graphs made of one-dimensional wires connected to external
leads. We derive two expressions for the scattering matrix on arbitrary graphs.
One involves matrices that couple arcs (oriented bonds), the other involves
matrices that couple vertices. We discuss a simple way to tune the coupling
between the graph and the leads. The efficiency of the formalism is
demonstrated on a few known examples.Comment: 21 pages, LaTeX, 10 eps figure
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