Quantum number projection at finite temperature via thermofield dynamics

Applying the thermo field dynamics, we reformulate exact quantum number projection in the finite-temperature Hartree-Fock-Bogoliubov theory. Explicit formulae are derived for the simultaneous projection of particle number and angular momentum, in parallel to the zero-temperature case. We also propose a practical method for the variation-after-projection calculation, by approximating entropy without conflict with the Peierls inequality. The quantum number projection in the finite-temperature mean-field theory will be useful to study effects of quantum fluctuations associated with the conservation laws on thermal properties of nuclei.Comment: 27 pages, using revtex4, to be published in PR

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

Off-Diagonal Geometric Phases

We investigate the adiabatic evolution of a set of non-degenerate eigenstates of a parameterized Hamiltonian. Their relative phase change can be related to geometric measurable quantities that extend the familiar concept of Berry phase to the evolution of more than one state. We present several physical systems where these concepts can be applied, including an experiment on microwave cavities for which off-diagonal phases can be determined from published data.Comment: 5 pages 2 figures - RevTeX. Revised version including geometrical interpretatio

Rotational Symmetry of Classical Orbits, Arbitrary Quantization of Angular Momentum and the Role of Gauge Field in Two-Dimensional Space

We study the quantum-classical correspondence in terms of coherent wave functions of a charged particle in two-dimensional central-scalar-potentials as well as the gauge field of a magnetic flux in the sense that the probability clouds of wave functions are well localized on classical orbits. For both closed and open classical orbits, the non-integer angular-momentum quantization with the level-space of angular momentum being greater or less than $\hbar$ is determined uniquely by the same rotational symmetry of classical orbits and probability clouds of coherent wave functions, which is not necessarily $2\pi$-periodic. The gauge potential of a magnetic flux impenetrable to the particle cannot change the quantization rule but is able to shift the spectrum of canonical angular momentum by a flux-dependent value, which results in a common topological phase for all wave functions in the given model. The quantum mechanical model of anyon proposed by Wilczek (Phys. Rev. Lette. 48, 1144) becomes a special case of the arbitrary-quantization.Comment: 6 pages, 5 figure

Representation-theoretic derivation of the Temperley-Lieb-Martin algebras

Explicit expressions for the Temperley-Lieb-Martin algebras, i.e., the quotients of the Hecke algebra that admit only representations corresponding to Young diagrams with a given maximum number of columns (or rows), are obtained, making explicit use of the Hecke algebra representation theory. Similar techniques are used to construct the algebras whose representations do not contain rectangular subdiagrams of a given size.Comment: 12 pages, LaTeX, to appear in J. Phys.

Lower job satisfaction among workers migrating within Europe: A gender paradox

Intra-European migrants reported lower job satisfaction levels than native workers, in three rounds of the European Social Survey. This deficit was also experienced by their descendants (the second generation), despite the latter generation achieving native levels of household income. At least some part of these lower levels of job satisfaction was associated with a clustering into lower-productivity industries. There are striking gender differences in experiences: among men the first generation is just as likely to be satisfied with their jobs as the ‘native’ population, whilst it is the second generation who are less likely to achieve job satisfaction. For women, both generations experienced a deficit in job satisfaction. This may reflect changing expectations of work among men, and integration for women, across generations, and contrasts with the convergence in earnings over time. The country of origin, within Europe, did not seem to be associated with levels of job satisfaction

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

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

Instanton vibrations of the 3-Skyrmion

The Atiyah-Drinfeld-Hitchin-Manin matrix corresponding to a tetrahedrally symmetric 3-instanton is calculated. Some small variations of the matrix correspond to vibrations of the instanton-generated 3-Skyrmion. These vibrations are decomposed under tetrahedral symmetry and this decomposition is compared to previous knowledge of the 3-Skyrmion vibration spectrum.Comment: 10 pages, LaTeX, no figures, PRD version with longer introduction and minor change

Butterfly-like spectra and collective modes of antidot superlattices in magnetic fields

We calculate the energy band structure for electrons in an external periodic potential combined with a perpendicular magnetic field. Electron-electron interactions are included within a Hartree approximation. The calculated energy spectra display a considerable degree of self-similarity, just as the ``Hofstadter butterfly.'' However, screening affects the butterfly, most importantly the bandwidths oscillate with magnetic field in a characteristic way. We also investigate the dynamic response of the electron system in the far-infrared (FIR) regime. Some of the peaks in the FIR absorption spectra can be interpreted mainly in semiclassical terms, while others originate from inter(sub)band transitions.Comment: 4 pages with 2 embeded eps figures. Uses revtex, multicol and graphicx styles. Accepted for publication in PRB Brief Report