A Statistical Mechanical Problem in Schwarzschild Spacetime

We use Fermi coordinates to calculate the canonical partition function for an ideal gas in a circular geodesic orbit in Schwarzschild spacetime. To test the validity of the results we prove theorems for limiting cases. We recover the Newtonian gas law subject only to tidal forces in the Newtonian limit. Additionally we recover the special relativistic gas law as the radius of the orbit increases to infinity. We also discuss how the method can be extended to the non ideal gas case.Comment: Corrected an equation misprint, added four references, and brief comments on the system's center of mass and the thermodynamic limi

Thin deformable mirrors for a reconfigurable space telescope

As part of a small satellite technology demonstration that will utilize autonomous assembly, reconfiguration, and docking technology to form the primary mirror for the mission’s telescope payload, the mirror segments are required to modify and control their shape, in order to allow for imaging in different configurations. This paper focuses on the development of 10 cm diameter active lightweight mirrors. The current mirror design, control scheme, and fabrication methods are described, as well as experimental results on initial samples. The data demonstrates that the mirrors are capable of at least 100 microns of displacement during operation, and that fabrication on polished molds can result in high quality reflective surfaces

Coupling between planes and chains in YBa2Cu3O7 : a possible solution for the order parameter controversy

We propose to explain the contradictory experimental evidence about the symmetry of the order parameter in $YBa_{2}Cu_{3}O_{7}$ by taking into account the coupling between planes and chains. This leads to an anticrossing of the plane and chain band. We include an attractive pairing interaction within the planes and a repulsive one between planes and chains, leading to opposite signs for the order parameter on planes and chains, and to nodes of the gap because of the anticrossing. Our model blends s-wave and d-wave features, and provides a natural explanation for all the contradictory experimentsComment: 13 pages, revtex, 2 uucoded figure

Quantum dots in magnetic fields: thermal response of broken symmetry phases

We investigate the thermal properties of circular semiconductor quantum dots in high magnetic fields using finite temperature Hartree-Fock techniques. We demonstrate that for a given magnetic field strength quantum dots undergo various shape phase transitions as a function of temperature, and we outline possible observable consequences.Comment: In Press, Phys. Rev. B (2001

Composite Fermion Description of Correlated Electrons in Quantum Dots: Low Zeeman Energy Limit

We study the applicability of composite fermion theory to electrons in two-dimensional parabolically-confined quantum dots in a strong perpendicular magnetic field in the limit of low Zeeman energy. The non-interacting composite fermion spectrum correctly specifies the primary features of this system. Additional features are relatively small, indicating that the residual interaction between the composite fermions is weak. \footnote{Published in Phys. Rev. B {\bf 52}, 2798 (1995).}Comment: 15 pages, 7 postscript figure

Particle Dark Matter Constraints from the Draco Dwarf Galaxy

It is widely thought that neutralinos, the lightest supersymmetric particles, could comprise most of the dark matter. If so, then dark halos will emit radio and gamma ray signals initiated by neutralino annihilation. A particularly promising place to look for these indicators is at the center of the local group dwarf spheroidal galaxy Draco, and recent measurements of the motion of its stars have revealed it to be an even better target for dark matter detection than previously thought. We compute limits on WIMP properties for various models of Draco's dark matter halo. We find that if the halo is nearly isothermal, as the new measurements indicate, then current gamma ray flux limits prohibit much of the neutralino parameter space. If Draco has a moderate magnetic field, then current radio limits can rule out more of it. These results are appreciably stronger than other current constraints, and so acquiring more detailed data on Draco's density profile becomes one of the most promising avenues for identifying dark matter.Comment: 13 pages, 6 figure

Density-functional theory of quantum wires and dots in a strong magnetic field

We study the competition between the exchange and the direct Coulomb interaction near the edge of a two-dimensional electron gas in a strong magnetic field using density-functional theory in a local approximation for the exchange-energy functional. Exchange is shown to play a significant role in reducing the spatial extent of the compressible edge channel regions obtained from an electrostatic description. The transition from the incompressible edge channels of the Hartree-Fock picture to the broad, compressible strips predicted by electrostatics occurs within a narrow and experimentally accessible range of confinement strengths.Comment: 24 pages latex and 10 postscript figures in self extracting fil

Black Holes from Cosmic Rays: Probes of Extra Dimensions and New Limits on TeV-Scale Gravity

If extra spacetime dimensions and low-scale gravity exist, black holes will be produced in observable collisions of elementary particles. For the next several years, ultra-high energy cosmic rays provide the most promising window on this phenomenon. In particular, cosmic neutrinos can produce black holes deep in the Earth's atmosphere, leading to quasi-horizontal giant air showers. We determine the sensitivity of cosmic ray detectors to black hole production and compare the results to other probes of extra dimensions. With n \ge 4 extra dimensions, current bounds on deeply penetrating showers from AGASA already provide the most stringent bound on low-scale gravity, requiring a fundamental Planck scale M_D > 1.3 - 1.8 TeV. The Auger Observatory will probe M_D as large as 4 TeV and may observe on the order of a hundred black holes in 5 years. We also consider the implications of angular momentum and possible exponentially suppressed parton cross sections; including these effects, large black hole rates are still possible. Finally, we demonstrate that even if only a few black hole events are observed, a standard model interpretation may be excluded by comparison with Earth-skimming neutrino rates.Comment: 30 pages, 18 figures; v2: discussion of gravitational infall, AGASA and Fly's Eye comparison added; v3: Earth-skimming results modified and strengthened, published versio

Yukawa couplings in intersecting D-brane models

We compute the Yukawa couplings among chiral fields in toroidal Type II compactifications with wrapping D6-branes intersecting at angles. Those models can yield realistic standard model spectrum living at the intersections. The Yukawa couplings depend both on the Kahler and open string moduli but not on the complex structure. They arise from worldsheet instanton corrections and are found to be given by products of complex Jacobi theta functions with characteristics. The Yukawa couplings for a particular intersecting brane configuration yielding the chiral spectrum of the MSSM are computed as an example. We also show how our methods can be extended to compute Yukawa couplings on certain classes of elliptically fibered CY manifolds which are mirror to complex cones over del Pezzo surfaces. We find that the Yukawa couplings in intersecting D6-brane models have a mathematical interpretation in the context of homological mirror symmetry. In particular, the computation of such Yukawa couplings is related to the construction of Fukaya's category in a generic symplectic manifold.Comment: 47 pages, using JHEP3.cls, 11 figures. Typos and other minor corrections. References adde

Spontaneous Coherence and Collective Modes in Double-Layer Quantum Dot Systems

We study the ground state and the collective excitations of parabolically-confined double-layer quantum dot systems in a strong magnetic field. We identify parameter regimes where electrons form maximum density droplet states, quantum-dot analogs of the incompressible states of the bulk integer quantum Hall effect. In these regimes the Hartree-Fock approximation and the time-dependent Hartree-Fock approximations can be used to describe the ground state and collective excitations respectively. We comment on the relationship between edge excitations of dots and edge magneto-plasmon excitations of bulk double-layer systems.Comment: 20 pages (figures included) and also available at http://fangio.magnet.fsu.edu/~jhu/Paper/qdot_cond.ps, replaced to fix figure