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

Patient problems encountered by psychiatric nurses

Thesis (M.S.)--Boston Universit

Separate and Unequal: Trade and Human Rights Regimes

human development, human rights