Fractionalization in a square-lattice model with time-reversal symmetry

We propose a two-dimensional time-reversal invariant system of essentially non-interacting electrons on a square lattice that exhibits configurations with fractional charges e/2. These are vortex-like topological defects in the dimerization order parameter describing spatial modulation in the electron hopping amplitudes. Charge fractionalization is established by a simple counting argument, analytical calculation within the effective low-energy theory, and by an exact numerical diagonalization of the lattice Hamiltonian. We comment on the exchange statistics of fractional charges and possible realizations of the system.Comment: 4 pages, 3 figures, RevTex 4. (v2) improved discussion of lattice effects and confinement; clearer figure

Polynomial Interpretation of Multipole Vectors

Copi, Huterer, Starkman and Schwarz introduced multipole vectors in a tensor context and used them to demonstrate that the first-year WMAP quadrupole and octopole planes align at roughly the 99.9% confidence level. In the present article the language of polynomials provides a new and independent derivation of the multipole vector concept. Bezout's Theorem supports an elementary proof that the multipole vectors exist and are unique (up to rescaling). The constructive nature of the proof leads to a fast, practical algorithm for computing multipole vectors. We illustrate the algorithm by finding exact solutions for some simple toy examples, and numerical solutions for the first-year WMAP quadrupole and octopole. We then apply our algorithm to Monte Carlo skies to independently re-confirm the estimate that the WMAP quadrupole and octopole planes align at the 99.9% level.Comment: Version 1: 6 pages. Version 2: added uniqueness proof to Corollary 2; added proper citation (to Starkman et al.) for Open Question; other minor improvement

Dynamics and structure of an aging binary colloidal glass

We study aging in a colloidal suspension consisting of micron-sized particles in a liquid. This system is made glassy by increasing the particle concentration. We observe samples composed of particles of two sizes, with a size ratio of 1:2.1 and a volume fraction ratio 1:6, using fast laser scanning confocal microscopy. This technique yields real-time, three-dimensional movies deep inside the colloidal glass. Specifically, we look at how the size, motion and structural organization of the particles relate to the overall aging of the glass. Particles move in spatially heterogeneous cooperative groups. These mobile regions tend to be richer in small particles, and these small particles facilitate the motion of nearby particles of both sizes.Comment: 7 pages; submitted to Phys. Rev. E. Revised with 1 new figure, improved tex

1911 Old Home Week Sheet Music

Original sheet music from the 1911 Brockport Old Home Week Celebration.https://digitalcommons.brockport.edu/local_books/1004/thumbnail.jp

Ringing the eigenmodes from compact manifolds

We present a method for finding the eigenmodes of the Laplace operator acting on any compact manifold. The procedure can be used to simulate cosmic microwave background fluctuations in multi-connected cosmological models. Other applications include studies of chaotic mixing and quantum chaos.Comment: 11 pages, 8 figures, IOP format. To be published in the proceedings of the Cleveland Cosmology and Topology Workshop 17-19 Oct 1997. Submitted to Class. Quant. Gra

Divine Competition: Religious Organisations and Service Provision in India

This paper examines religious and non-religious service provision by religious organisations in India. We present a stylized Hotelling-style model in which two religious organisations differentiate hemselves on the strength of religious beliefs in order to compete in attracting adherents. We show in the model two central predictions: first,that the organisations will differentiate themselves on the strength of religious beliefs. Second, that in equilibrium, economic inequality makes the organisations increase their provision of non-religious services. To test this, we present unique primary survey dataon the economics of religion, collected by us between 2006 and 2010 from 568 Hindu, Muslim, Christian, Sikh and Jain religious organisations spread across 7 Indian states. We use these data to demonstrate that the organisations have substantially increasedtheir provision of non-religious services. We also provide quantitative evidence based oneconometric testing to highlight that religious organisations are differenting themselves on the strength of religious beliefs with respect to other organisations, and are also providing higher education and health services as economic inequality increases in India

Divine competition: Religious organizations and service provision in India

This paper examines religious and non-religious service provision by religious organisations in India. We present a stylized Hotelling-style model in which two religious organisations differentiate hemselves on the strength of religious beliefs in order to compete in attracting adherents. We show in the model two central predictions: first,that the organisations will differentiate themselves on the strength of religious beliefs. Second, that in equilibrium, economic inequality makes the organisations increase their provision of non-religious services. To test this, we present unique primary survey dataon the economics of religion, collected by us between 2006 and 2010 from 568 Hindu, Muslim, Christian, Sikh and Jain religious organisations spread across 7 Indian states. We use these data to demonstrate that the organisations have substantially increasedtheir provision of non-religious services. We also provide quantitative evidence based oneconometric testing to highlight that religious organisations are differenting themselves on the strength of religious beliefs with respect to other organisations, and are also providing higher education and health services as economic inequality increases in India