52,196 research outputs found
Counting Humps in Motzkin paths
In this paper we study the number of humps (peaks) in Dyck, Motzkin and
Schr\"{o}der paths. Recently A. Regev noticed that the number of peaks in all
Dyck paths of order is one half of the number of super Dyck paths of order
. He also computed the number of humps in Motzkin paths and found a similar
relation, and asked for bijective proofs. We give a bijection and prove these
results. Using this bijection we also give a new proof that the number of Dyck
paths of order with peaks is the Narayana number. By double counting
super Schr\"{o}der paths, we also get an identity involving products of
binomial coefficients.Comment: 8 pages, 2 Figure
Hot Spots on the Fermi Surface of Bi2212: Stripes versus Superstructure
In a recent paper Saini et al. have reported evidence for a pseudogap around
(pi,0) at room temperature in the optimally doped superconductor Bi2212. This
result is in contradiction with previous ARPES measurements. Furthermore they
observed at certain points on the Fermi surface hot spots of high spectral
intensity which they relate to the existence of stripes in the CuO planes. They
also claim to have identified a new electronic band along Gamma-M1 whose one
dimensional character provides further evidence for stripes. We demonstrate in
this Comment that all the measured features can be simply understood by
correctly considering the superstructure (umklapp) and shadow bands which occur
in Bi2212.Comment: 1 page, revtex, 1 encapsulated postscript figure (color
Manin-Olshansky triples for Lie superalgebras
Following V. Drinfeld and G. Olshansky, we construct Manin triples (\fg,
\fa, \fa^*) such that \fg is different from Drinfeld's doubles of \fa for
several series of Lie superalgebras \fa which have no even invariant bilinear
form (periplectic, Poisson and contact) and for a remarkable exception.
Straightforward superization of suitable Etingof--Kazhdan's results guarantee
then the uniqueness of -quantization of our Lie bialgebras. Our examples
give solutions to the quantum Yang-Baxter equation in the cases when the
classical YB equation has no solutions. To find explicit solutions is a
separate (open) problem. It is also an open problem to list (\`a la
Belavin-Drinfeld) all solutions of the {\it classical} YB equation for the
Poisson superalgebras \fpo(0|2n) and the exceptional Lie superalgebra
\fk(1|6) which has a Killing-like supersymmetric bilinear form but no Cartan
matrix
Canonical Charmonium Interpretation for Y(4360) and Y(4660)
In this work, we consider the canonical charmonium assignments for Y(4360)
and Y(4660). Y(4660) is good candidate of state, the
possibility of Y(4360) as a state is studied, and the
charmonium hybrid interpretation of Y(4360) can not be excluded completely. We
evaluate the leptonic widths, E1 transitions, M1 transitions and
the open flavor strong decays of Y(4360) and Y(4660). Experimental tests for
the charmonium assignments are suggested.Comment: 32 pages, 4 figure
Entanglement Entropy and Mutual Information in Bose-Einstein Condensates
In this paper we study the entanglement properties of free {\em
non-relativistic} Bose gases. At zero temperature, we calculate the bipartite
block entanglement entropy of the system, and find it diverges logarithmically
with the particle number in the subsystem. For finite temperatures, we study
the mutual information between the two blocks. We first analytically study an
infinite-range hopping model, then numerically study a set of long-range
hopping models in one-deimension that exhibit Bose-Einstein condensation. In
both cases we find that a Bose-Einstein condensate, if present, makes a
divergent contribution to the mutual information which is proportional to the
logarithm of the number of particles in the condensate in the subsystem. The
prefactor of the logarithmic divergent term is model dependent.Comment: 12 pages, 6 figure
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