Soliton topology versus discrete symmetry in optical lattices

We address the existence of vortex solitons supported by azimuthally modulated lattices and reveal how the global lattice discrete symmetry has fundamental implications on the possible topological charges of solitons. We set a general ``charge rule'' using group-theory techniques, which holds for all lattices belonging to a given symmetry group. Focusing in the case of Bessel lattices allows us to derive also a overall stability rule for the allowed vortex solitons.Comment: 4 pages, 3 figures. To appear in Phys. Rev. Let

Hard sphere crystallization gets rarer with increasing dimension

We recently found that crystallization of monodisperse hard spheres from the bulk fluid faces a much higher free energy barrier in four than in three dimensions at equivalent supersaturation, due to the increased geometrical frustration between the simplex-based fluid order and the crystal [J.A. van Meel, D. Frenkel, and P. Charbonneau, Phys. Rev. E 79, 030201(R) (2009)]. Here, we analyze the microscopic contributions to the fluid-crystal interfacial free energy to understand how the barrier to crystallization changes with dimension. We find the barrier to grow with dimension and we identify the role of polydispersity in preventing crystal formation. The increased fluid stability allows us to study the jamming behavior in four, five, and six dimensions and compare our observations with two recent theories [C. Song, P. Wang, and H. A. Makse, Nature 453, 629 (2008); G. Parisi and F. Zamponi, Rev. Mod. Phys, in press (2009)].Comment: 15 pages, 5 figure

Addition theorems for spin spherical harmonics. I Preliminaries

We develop a systematic approach to deriving addition theorems for, and some other bilocal sums of, spin spherical harmonics. In this first part we establish some necessary technical results. We discuss the factorization of orbital and spin degrees of freedom in certain products of Clebsch-Gordan coefficients, and obtain general explicit results for the matrix elements in configuration space of tensor products of arbitrary rank of the position and angular-momentum operators. These results are the basis of the addition theorems for spin spherical harmonics obtained in part II

Analytic, Group-Theoretic Density Profiles for Confined, Correlated N-Body Systems

Confined quantum systems involving $N$ identical interacting particles are to be found in many areas of physics, including condensed matter, atomic and chemical physics. A beyond-mean-field perturbation method that is applicable, in principle, to weakly, intermediate, and strongly-interacting systems has been set forth by the authors in a previous series of papers. Dimensional perturbation theory was used, and in conjunction with group theory, an analytic beyond-mean-field correlated wave function at lowest order for a system under spherical confinement with a general two-body interaction was derived. In the present paper, we use this analytic wave function to derive the corresponding lowest-order, analytic density profile and apply it to the example of a Bose-Einstein condensate.Comment: 15 pages, 2 figures, accepted by Physics Review A. This document was submitted after responding to a reviewer's comment

Condensation of Ideal Bose Gas Confined in a Box Within a Canonical Ensemble

We set up recursion relations for the partition function and the ground-state occupancy for a fixed number of non-interacting bosons confined in a square box potential and determine the temperature dependence of the specific heat and the particle number in the ground state. A proper semiclassical treatment is set up which yields the correct small-T-behavior in contrast to an earlier theory in Feynman's textbook on Statistical Mechanics, in which the special role of the ground state was ignored. The results are compared with an exact quantum mechanical treatment. Furthermore, we derive the finite-size effect of the system.Comment: 18 pages, 8 figure

Sex Differences in the Perceived Dominance and Prestige of Women With and Without Cosmetics

Human social status has long been of interest to evolutionary and social psychologists. The question of who gets to control resources and be a leader has garnered a lot of attention from these and other fields, and this thesis examines evidence for there being two different mechanisms of achieving high status, and their correlates. The mechanisms are 1) Dominance: being aggressive, manipulative and forcing others to follow you, and 2) Prestige: possessing qualities which make others freely follow you. Chapter 1 is an introductory chapter in which I explain selection pressures, group formation, and the need for social hierarchies; I then describe the two proposed methods of attaining social status and how facial characteristics can give clues as to an individual’s social status. In Chapter 2, my first experimental chapter, I examined how faces created to appear either high in dominance or high in prestige were judged with respect to those traits as well as personality characteristics. Taking this further, in Chapter 3, I looked at how natural variation in real faces would reflect differences in other- and self-perceived ratings of dominance and prestige. Chapter 4 served to examine whether, given a set of words related to social status, I would find differences in what words were placed into dominant or prestige categories. Findings within these chapters are consistent with dominance and prestige being separable methods of attaining high status, from differences in facial appearance (Chapter 2 and 3), to personality characteristics (Chapter 2), to word usage (Chapter 4). Once I had established that these were two distinct routes to achieving high status, I chose to focus on dominance in Chapter 5 and explored the conceptual relationships between dominance and facial expressions. I found that manipulating perceptions of dominance affected how intense expressions of anger, sadness, and fear were perceived (Chapter 5). As there has been a paucity of research in the area of women’s social status, in Chapter 6, I went on to explore what effects cosmetics use in women would have on their perceived social status. I found differences in how men and women perceived women wearing cosmetics, which again points to a distinction between dominance and prestige. My thesis then presents a broad view of the two different mechanisms for attaining high status. Using new methods not otherwise used in exploring dominance and prestige I was able to explore correlates and indicators, as well as perceptions of both strategies. These findings will allow us to determine who might be capable of attaining social status, which of the two methods they might use, as well as what implicit associations we hold about each. They will also open doors for future research into the two strategies, and even help interpret previous research, as many previous studies simply relate to high status and do not distinguish between dominance and prestige

Brief of Corporate Law Professors as Amici Curie in Support of Respondents

The Supreme Court has looked to the rights of corporate shareholders in determining the rights of union members and non-members to control political spending, and vice versa. The Court sometimes assumes that if shareholders disapprove of corporate political expression, they can easily sell their shares or exercise control over corporate spending. This assumption is mistaken. Because of how capital is saved and invested, most individual shareholders cannot obtain full information about corporate political activities, even after the fact, nor can they prevent their savings from being used to speak in ways with which they disagree. Individual shareholders have no “opt out” rights or practical ability to avoid subsidizing corporate political expression with which they disagree. Nor do individuals have the practical option to refrain from putting their savings into equity investments, as doing so would impose damaging economic penalties and ignore conventional financial guidance for individual investors

Cluster-based density-functional approach to quantum transport through molecular and atomic contacts

We present a cluster-based density-functional approach to model charge transport through molecular and atomic contacts. The electronic structure of the contacts is determined in the framework of density functional theory, and the parameters needed to describe transport are extracted from finite clusters. A similar procedure, restricted to nearest-neighbor interactions in the electrodes, has been presented by Damle et al. [Chem. Phys. 281, 171 (2002)]. Here, we show how to systematically improve the description of the electrodes by extracting bulk parameters from sufficiently large metal clusters. In this way we avoid problems arising from the use of nonorthogonal basis functions. For demonstration we apply our method to electron transport through Au contacts with various atomic-chain configurations and to a single-atom contact of Al.Comment: 18 pages, 13 figure

Exact eigenspectrum of the symmetric simple exclusion process on the complete, complete bipartite, and related graphs

We show that the infinitesimal generator of the symmetric simple exclusion process, recast as a quantum spin-1/2 ferromagnetic Heisenberg model, can be solved by elementary techniques on the complete, complete bipartite, and related multipartite graphs. Some of the resulting infinitesimal generators are formally identical to homogeneous as well as mixed higher spins models. The degeneracies of the eigenspectra are described in detail, and the Clebsch-Gordan machinery needed to deal with arbitrary spin-s representations of the SU(2) is briefly developed. We mention in passing how our results fit within the related questions of a ferromagnetic ordering of energy levels and a conjecture according to which the spectral gaps of the random walk and the interchange process on finite simple graphs must be equal.Comment: Final version as published, 19 pages, 4 figures, 40 references given in full forma

Structural estimation of labor adjustment costs with temporally disaggregated data

Estimating labor adjustment costs is plagued by a variety of errors, many arising from data limitations. Most researchers have assumed that adjustment decisions are made at the firm level, that adjustment happens at the frequency at which a firm is observed (typically annually or quarterly), and that adjustment costs are incurred on net changes in employment. In this paper, I estimate a dynamic optimization model of labor adjustment of establishments based on data that permit 1) specifying any desired adjustment frequency, 2) estimating the model based on net and on gross employment flows and 3) allowing for simultaneous hirings and separations. The unit of observation is an establishment. Results for adjustment costs depend crucially on the model specification. Only a monthly adjustment model yields cost parameters in a reasonable range, while estimates from quarterly and annual adjustment models imply negative (adjustment implies a gain rather than a loss) or excessive adjustment costs. Estimating the model on net employment changes implies hiring and separation costs of around four annual median salaries, while the model on gross changes implies costs on the order of 1.7 annual median salaries. Adjustment costs differ significantly between small and large establishments. However, a dynamic model performs only marginally better than a static model with respect to out-of-sample predictions