469 research outputs found
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
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
On the spectrum of the Laplace operator of metric graphs attached at a vertex -- Spectral determinant approach
We consider a metric graph made of two graphs
and attached at one point. We derive a formula relating the
spectral determinant of the Laplace operator
in terms of the spectral
determinants of the two subgraphs. The result is generalized to describe the
attachment of graphs. The formulae are also valid for the spectral
determinant of the Schr\"odinger operator .Comment: LaTeX, 8 pages, 7 eps figures, v2: new appendix, v3: discussions and
ref adde
Random Operator Approach for Word Enumeration in Braid Groups
We investigate analytically the problem of enumeration of nonequivalent
primitive words in the braid group B_n for n >> 1 by analysing the random word
statistics and the target space on the basis of the locally free group
approximation. We develop a "symbolic dynamics" method for exact word
enumeration in locally free groups and bring arguments in support of the
conjecture that the number of very long primitive words in the braid group is
not sensitive to the precise local commutation relations. We consider the
connection of these problems with the conventional random operator theory,
localization phenomena and statistics of systems with quenched disorder. Also
we discuss the relation of the particular problems of random operator theory to
the theory of modular functionsComment: 36 pages, LaTeX, 4 separated Postscript figures, submitted to Nucl.
Phys. B [PM
Prophylactic properties of biofloc- or Nile tilapia-conditioned water against Vibrio parahaemolyticus infection of whiteleg shrimp (Penaeus vannamei)
Isolates of Vibrio parahaemolyticus (VpAHPND) that carry a plasmid encoding two Pir-like toxins cause acute hepatopancreatic necrosis disease (AHPND), a disease that has caused devastating economic losses to the shrimp industry, particularly in Asia. However, lower prevalence of AHPND infection has been associated with farms that operate with biofloc or lower salinity culture water. Therefore, the aim of this present study was to investigate the effects of biofloc and Nile tilapia (Oreochromis niloticus)-conditioned water prepared at different culture water salinities on survival of whiteleg shrimp (Penaeus vannamei) bath-challenged experimentally with VpAHPND. First, groups of shrimp were bath-challenged with VpAHPND in clear 15 ppt seawater (CW) or in the presence of a pre-cultured biofloc at 25%, 50% and 100% (v/v). Survival during 96 h post-challenge was significantly greater in groups cultured in 50% and 100% biofloc (p
Functionals of the Brownian motion, localization and metric graphs
We review several results related to the problem of a quantum particle in a
random environment.
In an introductory part, we recall how several functionals of the Brownian
motion arise in the study of electronic transport in weakly disordered metals
(weak localization).
Two aspects of the physics of the one-dimensional strong localization are
reviewed : some properties of the scattering by a random potential (time delay
distribution) and a study of the spectrum of a random potential on a bounded
domain (the extreme value statistics of the eigenvalues).
Then we mention several results concerning the diffusion on graphs, and more
generally the spectral properties of the Schr\"odinger operator on graphs. The
interest of spectral determinants as generating functions characterizing the
diffusion on graphs is illustrated.
Finally, we consider a two-dimensional model of a charged particle coupled to
the random magnetic field due to magnetic vortices. We recall the connection
between spectral properties of this model and winding functionals of the planar
Brownian motion.Comment: Review article. 50 pages, 21 eps figures. Version 2: section 5.5 and
conclusion added. Several references adde
Zeta functions of quantum graphs
In this article we construct zeta functions of quantum graphs using a contour
integral technique based on the argument principle. We start by considering the
special case of the star graph with Neumann matching conditions at the center
of the star. We then extend the technique to allow any matching conditions at
the center for which the Laplace operator is self-adjoint and finally obtain an
expression for the zeta function of any graph with general vertex matching
conditions. In the process it is convenient to work with new forms for the
secular equation of a quantum graph that extend the well known secular equation
of the Neumann star graph. In the second half of the article we apply the zeta
function to obtain new results for the spectral determinant, vacuum energy and
heat kernel coefficients of quantum graphs. These have all been topics of
current research in their own right and in each case this unified approach
significantly expands results in the literature.Comment: 32 pages, typos corrected, references adde
Natural nanoparticules against cancer: mature dendritic cell-derived exosomes
Deep insight on Natural nanoparticules against cancer: mature dendritic cell-derived exosomes
Scattering theory on graphs (2): the Friedel sum rule
We consider the Friedel sum rule in the context of 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 generalize the Smith formula for graphs.
We give several examples of graphs where the state counting method given by the
Friedel sum rule is not working. The reason for the failure of the Friedel sum
rule to count the states is the existence of states localized in the graph and
not coupled to the leads, which occurs if the spectrum is degenerate and the
number of leads too small.Comment: 20 pages, LaTeX, 6 eps figure
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