16,109 research outputs found
Weighted cohomology of arithmetic groups
M. Goresky, G. Harder, and R. MacPherson defined weighted cohomologies of
arithmetic groups \Gamma in a real group G, with coefficients in certain local
systems, associated to arbitrary upper and lower weight profiles. The author
shows, using essentially local arguments on the reductive Borel-Serre
compactification, that these cohomologies agree with certain weighted L^2
cohomologies defined by J. Franke. When the rank of G is equal to that of a
maximal compact subgroup, this implies that the cohomologies associated to both
upper and lower middle profiles are both isomorphic to L^2 cohomology.Comment: 32 pages, published version, abstract added in migratio
A Statistical Model of Current Loops and Magnetic Monopoles
We formulate a natural model of current loops and magnetic monopoles for
arbitrary planar graphs, which we call the monopole-dimer model, and express
the partition function of this model as a determinant. We then extend the
method of Kasteleyn and Temperley-Fisher to calculate the partition function
exactly in the case of rectangular grids. This partition function turns out to
be a square of the partition function of an emergent monomer-dimer model when
the grid sizes are even. We use this formula to calculate the local monopole
density, free energy and entropy exactly. Our technique is a novel
determinantal formula for the partition function of a model of vertices and
loops for arbitrary graphs.Comment: 17 pages, 5 figures, significant stylistic revisions. In particular,
rewritten with a mathematical audience in mind. Numerous errors fixed. This
is the final published version. Maple program file can be downloaded from the
link on the right of this pag
Heavy Scalar, Vector and Axial-Vector Mesons in Hot and Dense Nuclear Medium
In this work we shall investigate the mass modifications of scalar mesons
,vector mesons
and axial-vector mesons at finite density and
temperature of the nuclear medium. The above mesons are modified in the nuclear
medium through themodification of quark and gluon condensates. We shall find
the medium modification of quark and gluon condensates within chiral SU(3)
model through the medium modification of scalar-isoscalar fields and
at finite density and temperature. These medium modified quark and
gluon condensates will further be used through QCD sum rules for the evaluation
of in-medium properties of above mentioned scalar, vector and axial vector
mesons. We shall also discuss the effects of density and temperature of the
nuclear medium on the scattering lengths of above scalar, vector and
axial-vector mesons. The study of the medium modifications of above mesons may
be helpful for understanding their production rates in heavy-ion collision
experiments. The results of present investigations of medium modifications of
scalar, vector and axial-vector mesons at finite density and temperature can be
verified in the Compressed Baryonic Matter (CBM) experiment of FAIR facility at
GSI, Germany.Comment: 35 pages, 11 figure
Full Current Statistics for a Disordered Open Exclusion Process
We consider the nonabelian sandpile model defined on directed trees by Ayyer,
Schilling, Steinberg and Thi\'ery (Commun. Math. Phys, 2013) and restrict it to
the special case of a one-dimensional lattice of sites which has open
boundaries and disordered hopping rates. We focus on the joint distribution of
the integrated currents across each bond simultaneously, and calculate its
cumulant generating function exactly. Surprisingly, the process conditioned on
seeing specified currents across each bond turns out to be a renormalised
version of the same process. We also remark on a duality property of the large
deviation function. Lastly, all eigenvalues and both Perron eigenvectors of the
tilted generator are determined.Comment: 14 pages, minor clarification
A finite variant of the Toom Model
We present results for a finite variant of the one-dimensional Toom model
with closed boundaries. We show that the steady state distribution is not of
product form, but is nonetheless simple. In particular, we give explicit
formulas for the densities and some nearest neighbour correlation functions. We
also give exact results for eigenvalues and multiplicities of the transition
matrix using the theory of -trivial monoids in joint work with A.
Schilling, B. Steinberg and N. M. Thi\'ery.Comment: Journal of Physics: Conference Series stylefile, 8 pages, 1 figure;
minor changes and clarification
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