14,466 research outputs found
Complete bond-operator theory of the two-chain spin ladder
The discovery of the almost ideal, two-chain spin-ladder material
(C_5H_12N)_2CuBr_4 has once again focused attention on this most fundamental
problem in low-dimensional quantum magnetism. Within the bond-operator
framework, three qualitative advances are introduced which extend the theory to
all finite temperatures and magnetic fields in the gapped regime. This
systematic description permits quantitative and parameter-free experimental
comparisons, which are presented for the specific heat, and predictions for
thermal renormalization of the triplet magnon excitations.Comment: 12 pages, 10 figure
Two population models with constrained migrations
We study two models of population with migration. We assume that we are given
infinitely many islands with the same number r of resources, each individual
consuming one unit of resources. On an island lives an individual whose
genealogy is given by a critical Galton-Watson tree. If all the resources are
consumed, any newborn child has to migrate to find new resources. In this
sense, the migrations are constrained, not random. We will consider first a
model where resources do not regrow, so the r first born individuals remain on
their home island, whereas their children migrate. In the second model, we
assume that resources regrow, so only r people can live on an island at the
same time, the supernumerary ones being forced to migrate. In both cases, we
are interested in how the population spreads on the islands, when the number of
initial individuals and available resources tend to infinity. This mainly
relies on computing asymptotics for critical random walks and functionals of
the Brownian motion.Comment: 38 pages, 12 figure
A model for coagulation with mating
We consider in this work a model for aggregation, where the coalescing
particles initially have a certain number of potential links (called arms)
which are used to perform coagulations. There are two types of arms, male and
female, and two particles may coagulate only if one has an available male arm,
and the other has an available female arm. After a coagulation, the used arms
are no longer available. We are interested in the concentrations of the
different types of particles, which are governed by a modification of
Smoluchowski's coagulation equation -- that is, an infinite system of nonlinear
differential equations. Using generating functions and solving a nonlinear PDE,
we show that, up to some critical time, there is a unique solution to this
equation. The Lagrange Inversion Formula allows in some cases to obtain
explicit solutions, and to relate our model to two recent models for limited
aggregation. We also show that, whenever the critical time is infinite, the
concentrations converge to a state where all arms have disappeared, and the
distribution of the masses is related to the law of the size of some two-type
Galton-Watson tree. Finally, we consider a microscopic model for coagulation:
we construct a sequence of Marcus-Lushnikov processes, and show that it
converges, before the critical time, to the solution of our modified
Smoluchowski's equation.Comment: 30 page
Vertical and Diagonal Stripes in the Extended Hubbard Model
We extend previous real-space Hartree-Fock studies of static stripe stability
to determine the phase diagram of the Hubbard model with anisotropic
nearest-neighbor hopping t, by varying the on-site Coulomb repulsion U and
investigating locally stable structures for representative hole doping levels
x=1/8 and x=1/6. We also report the changes in stability of these stripes in
the extended Hubbard model due to next-neighbor hopping t' and to a
nearest-neighbor Coulomb interaction V.Comment: 4 pages, 2 figure
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