Cluster Perturbation Theory for Hubbard models

Cluster perturbation theory is a technique for calculating the spectral weight of Hubbard models of strongly correlated electrons, which combines exact diagonalizations on small clusters with strong-coupling perturbation theory at leading order. It is exact in both the strong- and weak-coupling limits and provides a good approximation to the spectral function at any wavevector. Following the paper by S\'en\'echal et al. (Phys. Rev. Lett. {\bf 84}, 522 (2000)), we provide a more complete description and derivation of the method. We illustrate some of its capabilities, in particular regarding the effect of doping, the calculation of ground state energy and double occupancy, the disappearance of the Fermi surface in the $t-t'$ Hubbard model, and so on. The method is applicable to any model with on-site repulsion only.Comment: 11 pages, 10 figures (RevTeX 4

Phase transitions with four-spin interactions

Using an extended Lee-Yang theorem and GKS correlation inequalities, we prove, for a class of ferromagnetic multi-spin interactions, that they will have a phase transition(and spontaneous magnetization) if, and only if, the external field $h=0$ (and the temperature is low enough). We also show the absence of phase transitions for some nonferromagnetic interactions. The FKG inequalities are shown to hold for a larger class of multi-spin interactions

A lower bound for the mass of a random Gaussian lattice

We give a criterion that the two point function for a Gaussian lattice with random mass decay exponentially. The proof uses a random walk representation which may be of interest in other contexts.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46517/1/220_2005_Article_BF01940332.pd

Strong-Coupling Expansion for the Hubbard Model

A strong-coupling expansion for models of correlated electrons in any dimension is presented. The method is applied to the Hubbard model in $d$ dimensions and compared with numerical results in $d=1$. Third order expansion of the Green function suffices to exhibit both the Mott metal-insulator transition and a low-temperature regime where antiferromagnetic correlations are strong. It is predicted that some of the weak photoemission signals observed in one-dimensional systems such as $SrCuO_2$ should become stronger as temperature increases away from the spin-charge separated state.Comment: 4 pages, RevTex, 3 epsf figures include

Rigorous results on superconducting ground states for attractive extended Hubbard models

We show that the exact ground state for a class of extended Hubbard models including bond-charge, exchange, and pair-hopping terms, is the Yang "eta-paired" state for any non-vanishing value of the pair-hopping amplitude, at least when the on-site Coulomb interaction is attractive enough and the remaining physical parameters satisfy a single constraint. The ground state is thus rigorously superconducting. Our result holds on a bipartite lattice in any dimension, at any band filling, and for arbitrary electron hopping.Comment: 12 page

A Unifying Gravity Framework for Dispersal

Most organisms disperse at some life-history stage, but different research traditions to study dispersal have evolved in botany, zoology, and epidemiology. In this paper, we synthesize concepts, principles, patterns, and processes in dispersal across organisms. We suggest a consistent conceptual framework for dispersal, which utilizes generalized gravity models. This framework will facilitate communication among research traditions, guide the development of dispersal models for theoretical and applied ecology, and enable common representation across taxonomic groups, encapsulating processes at the source and destination of movement, as well as during the intervening relocation process, while allowing each of these stages in the dispersal process to be addressed separately and in relevant detail. For different research traditions, certain parts of the dispersal process are less studied than others (e.g., seed release processes in plants and termination of dispersal in terrestrial and aquatic animals). The generalized gravity model can serve as a unifying framework for such processes, because it captures the general conceptual and formal components of any dispersal process, no matter what the relevant biological timescale involved. We illustrate the use of the framework with examples of passive (a plant), active (an animal), and vectored (a fungus) dispersal, and point out promising applications, including studies of dispersal mechanisms, total dispersal kernels, and spatial population dynamics

A Unifying Gravity Framework for Dispersal

Most organisms disperse at some life-history stage, but different research traditions to study dispersal have evolved in botany, zoology, and epidemiology. In this paper, we synthesize concepts, principles, patterns, and processes in dispersal across organisms. We suggest a consistent conceptual framework for dispersal, which utilizes generalized gravity models. This framework will facilitate communication among research traditions, guide the development of dispersal models for theoretical and applied ecology, and enable common representation across taxonomic groups, encapsulating processes at the source and destination of movement, as well as during the intervening relocation process, while allowing each of these stages in the dispersal process to be addressed separately and in relevant detail. For different research traditions, certain parts of the dispersal process are less studied than others (e.g., seed release processes in plants and termination of dispersal in terrestrial and aquatic animals). The generalized gravity model can serve as a unifying framework for such processes, because it captures the general conceptual and formal components of any dispersal process, no matter what the relevant biological timescale involved. We illustrate the use of the framework with examples of passive (a plant), active (an animal), and vectored (a fungus) dispersal, and point out promising applications, including studies of dispersal mechanisms, total dispersal kernels, and spatial population dynamics

The immune cell landscape in kidneys of patients with lupus nephritis.

Lupus nephritis is a potentially fatal autoimmune disease for which the current treatment is ineffective and often toxic. To develop mechanistic hypotheses of disease, we analyzed kidney samples from patients with lupus nephritis and from healthy control subjects using single-cell RNA sequencing. Our analysis revealed 21 subsets of leukocytes active in disease, including multiple populations of myeloid cells, T cells, natural killer cells and B cells that demonstrated both pro-inflammatory responses and inflammation-resolving responses. We found evidence of local activation of B cells correlated with an age-associated B-cell signature and evidence of progressive stages of monocyte differentiation within the kidney. A clear interferon response was observed in most cells. Two chemokine receptors, CXCR4 and CX3CR1, were broadly expressed, implying a potentially central role in cell trafficking. Gene expression of immune cells in urine and kidney was highly correlated, which would suggest that urine might serve as a surrogate for kidney biopsies

Binding of molecules to DNA and other semiflexible polymers

A theory is presented for the binding of small molecules such as surfactants to semiflexible polymers. The persistence length is assumed to be large compared to the monomer size but much smaller than the total chain length. Such polymers (e.g. DNA) represent an intermediate case between flexible polymers and stiff, rod-like ones, whose association with small molecules was previously studied. The chains are not flexible enough to actively participate in the self-assembly, yet their fluctuations induce long-range attractive interactions between bound molecules. In cases where the binding significantly affects the local chain stiffness, those interactions lead to a very sharp, cooperative association. This scenario is of relevance to the association of DNA with surfactants and compact proteins such as RecA. External tension exerted on the chain is found to significantly modify the binding by suppressing the fluctuation-induced interaction.Comment: 15 pages, 7 figures, RevTex, the published versio