806 research outputs found
Exponents and bounds for uniform spanning trees in d dimensions
Uniform spanning trees are a statistical model obtained by taking the set of
all spanning trees on a given graph (such as a portion of a cubic lattice in d
dimensions), with equal probability for each distinct tree. Some properties of
such trees can be obtained in terms of the Laplacian matrix on the graph, by
using Grassmann integrals. We use this to obtain exact exponents that bound
those for the power-law decay of the probability that k distinct branches of
the tree pass close to each of two distinct points, as the size of the lattice
tends to infinity.Comment: 5 pages. v2: references added. v3: closed form results can be
extended slightly (thanks to C. Tanguy). v4: revisions, and a figure adde
Radiation effects on silicon second quarterly progress report, sep. 1 - nov. 30, 1964
Electron spin resonance measurements on P-doped silicon - vacancy phosphorus defec
Full counting statistics of chaotic cavities with many open channels
Explicit formulas are obtained for all moments and for all cumulants of the
electric current through a quantum chaotic cavity attached to two ideal leads,
thus providing the full counting statistics for this type of system. The
approach is based on random matrix theory, and is valid in the limit when both
leads have many open channels. For an arbitrary number of open channels we
present the third cumulant and an example of non-linear statistics.Comment: 4 pages, no figures; v2-added references; typos correcte
Rotor interaction in the annulus billiard
Introducing the rotor interaction in the integrable system of the annulus
billiard produces a variety of dynamical phenomena, from integrability to
ergodicity
On the duality relation for correlation functions of the Potts model
We prove a recent conjecture on the duality relation for correlation
functions of the Potts model for boundary spins of a planar lattice.
Specifically, we deduce the explicit expression for the duality of the n-site
correlation functions, and establish sum rule identities in the form of the
M\"obius inversion of a partially ordered set. The strategy of the proof is by
first formulating the problem for the more general chiral Potts model. The
extension of our consideration to the many-component Potts models is also
given.Comment: 17 pages in RevTex, 5 figures, submitted to J. Phys.
Properties of dense partially random graphs
We study the properties of random graphs where for each vertex a {\it
neighbourhood} has been previously defined. The probability of an edge joining
two vertices depends on whether the vertices are neighbours or not, as happens
in Small World Graphs (SWGs). But we consider the case where the average degree
of each node is of order of the size of the graph (unlike SWGs, which are
sparse). This allows us to calculate the mean distance and clustering, that are
qualitatively similar (although not in such a dramatic scale range) to the case
of SWGs. We also obtain analytically the distribution of eigenvalues of the
corresponding adjacency matrices. This distribution is discrete for large
eigenvalues and continuous for small eigenvalues. The continuous part of the
distribution follows a semicircle law, whose width is proportional to the
"disorder" of the graph, whereas the discrete part is simply a rescaling of the
spectrum of the substrate. We apply our results to the calculation of the
mixing rate and the synchronizability threshold.Comment: 14 pages. To be published in Physical Review
Radiation effects on silicon solar cells Final report, Dec. 1, 1961 - Dec. 31, 1962
Displacement defects in silicon solar cells by high energy electron irradiation using electron spin resonance, galvanometric, excess carrier lifetime, and infrared absorption measurement
Maximum principle and mutation thresholds for four-letter sequence evolution
A four-state mutation-selection model for the evolution of populations of
DNA-sequences is investigated with particular interest in the phenomenon of
error thresholds. The mutation model considered is the Kimura 3ST mutation
scheme, fitness functions, which determine the selection process, come from the
permutation-invariant class. Error thresholds can be found for various fitness
functions, the phase diagrams are more interesting than for equivalent
two-state models. Results for (small) finite sequence lengths are compared with
those for infinite sequence length, obtained via a maximum principle that is
equivalent to the principle of minimal free energy in physics.Comment: 25 pages, 16 figure
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