Atomic-phase interference devices based on ring-shaped Bose-Einstein condensates: Two ring case

We theoretically investigate the ground-state properties and quantum dynamics of a pair of adjacent ring-shaped Bose-Einstein condensates that are coupled via tunneling. This device, which is the analogue of a symmetric superconducting quantum interference device, is the simplest version of what we term an Atomic-Phase Interference Device (APHID). The two-ring APHID is shown to be sensitive to rotation.Comment: 8 page

Numerical design of streamlined tunnel walls for a two-dimensional transonic test

An analytical procedure is discussed for designing wall shapes for streamlined, nonporous, two-dimensional, transonic wind tunnels. It is based upon currently available 2-D inviscid transonic and boundary layer analysis computer programs. Predicted wall shapes are compared with experimental data obtained from the NASA Langley 6 by 19 inch Transonic Tunnel where the slotted walls were replaced by flexible nonporous walls. Comparisons are presented for the empty tunnel operating at a Mach number of 0.9 and for a supercritical test of an NACA 0012 airfoil at zero lift. Satisfactory agreement is obtained between the analytically and experimentally determined wall shapes

Superfluid Suppression in d-Wave Superconductors due to Disordered Magnetism

The influence of static magnetic correlations on the temperature-dependent superfluid density \rho_s(T) is calculated for d-wave superconductors. In self-consistent calculations, itinerant holes form incommensurate spin density waves (SDW) which coexist with superconductivity. In the clean limit, the density of states is gapped, and \rho_s(T << T_c) is exponentially activated. In inhomogeneously-doped cases, the SDW are disordered and both the density of states and \rho_s(T) obtain forms indistinguishable from those in dirty but pure d-wave superconductors, in accordance with experiments. We conclude that the observed collapse of \rho_s at x\approx 0.35 in underdoped YBCO may plausibly be attributed to the coexistence of SDW and superconductivity.Comment: 6 pages, 5 figures. Expanded discussio

Band structure of Charge Ordered Doped Antiferromagnets

We study the distribution of electronic spectral weight in a doped antiferromagnet with various types of charge order and compare to angle resolved photoemission experiments on lightly doped La$_{2-x}$Sr$_x$CuO$_4$ (LSCO) and electron doped Nd$_{2-x}$Ce$_x$CuO$_{4\pm\delta}$. Calculations on in-phase stripe and bubble phases for the electron doped system are both in good agreement with experiment including in particular the existence of in-gap spectral weight. In addition we find that for in-phase stripes, in contrast to anti-phase stripes, the chemical potential is likely to move with doping. For the hole doped system we find that ``staircase'' stripes which are globally diagonal but locally vertical or horizontal can reproduce the photoemission data whereas pure diagonal stripes cannot. We also calculate the magnetic structure factors of such staircase stripes and find that as the stripe separation is decreased with increased doping these evolve from diagonal to vertical separated by a coexistence region. The results suggest that the transition from horizontal to diagonal stripes seen in neutron scattering on underdoped LSCO may be a crossover between a regime where the typical length of straight stripe segments is longer than the inter-stripe spacing to one where it is shorter and that locally the stripes are always aligned with the Cu-O bonds.Comment: 13 pages, 16 figure

Vacuum polarization of scalar fields near Reissner-Nordstr\"{o}m black holes and the resonance behavior in field-mass dependence

We study vacuum polarization of quantized massive scalar fields $\phi$ in equilibrium at black-hole temperature in Reissner-Nordstr\"{o}m background. By means of the Euclidean space Green's function we analytically derive the renormalized expression $_{H}$ at the event horizon with the area $4\pi r_{+}^{2}$. It is confirmed that the polarization amplitude $_{H}$ is free from any divergence due to the infinite red-shift effect. Our main purpose is to clarify the dependence of $_{H}$ on field mass $m$ in relation to the excitation mechanism. It is shown for small-mass fields with $mr_{+}\ll1$ how the excitation of $_{H}$ caused by finite black-hole temperature is suppressed as $m$ increases, and it is verified for very massive fields with $mr_{+}\gg1$ that $_{H}$ decreases in proportion to $m^{-2}$ with the amplitude equal to the DeWitt-Schwinger approximation. In particular, we find a resonance behavior with a peak amplitude at $mr_{+}\simeq 0.38$ in the field-mass dependence of vacuum polarization around nearly extreme (low-temperature) black holes. The difference between Scwarzschild and nearly extreme black holes is discussed in terms of the mass spectrum of quantum fields dominant near the event horizon.Comment: 24 pages, 1 figure Accepted in PR

Size Gap for Zero Temperature Black Holes in Semiclassical Gravity

We show that a gap exists in the allowed sizes of all zero temperature static spherically symmetric black holes in semiclassical gravity when only conformally invariant fields are present. The result holds for both charged and uncharged black holes. By size we mean the proper area of the event horizon. The range of sizes that do not occur depends on the numbers and types of quantized fields that are present. We also derive some general properties that both zero and nonzero temperature black holes have in all classical and semiclassical metric theories of gravity.Comment: 4 pages, ReVTeX, no figure

Spontaneous superconductivity and optical properties of high-Tc cuprates

We suggest that the high temperature superconductivity in cuprate compounds may emerge due to interaction between copper-oxygen layers mediated by in-plane plasmons. The strength of the interaction is determined by the c-axis geometry and by the ab-plane optical properties. Without making reference to any particular in-plane mechanism of superconductivity, we show that the interlayer interaction favors spontaneous appearance of the superconductivity in the layers. At a qualitative level the model describes correctly the dependence of the transition temperature on the interlayer distance, and on the number of adjacent layers in multilayered homologous compounds. Moreover, the model has a potential to explain (i) a mismatch between the optimal doping levels for critical temperature and superconducting density and (ii) a universal scaling relation between the dc-conductivity, the superfluid density, and the superconducting transition temperature.Comment: 4.4 pages, 2 figures; v2 matches the published version (clarifying remarks and references are added

Quantum Cosmological Relational Model of Shape and Scale in 1-d

Relational particle models are useful toy models for quantum cosmology and the problem of time in quantum general relativity. This paper shows how to extend existing work on concrete examples of relational particle models in 1-d to include a notion of scale. This is useful as regards forming a tight analogy with quantum cosmology and the emergent semiclassical time and hidden time approaches to the problem of time. This paper shows furthermore that the correspondence between relational particle models and classical and quantum cosmology can be strengthened using judicious choices of the mechanical potential. This gives relational particle mechanics models with analogues of spatial curvature, cosmological constant, dust and radiation terms. A number of these models are then tractable at the quantum level. These models can be used to study important issues 1) in canonical quantum gravity: the problem of time, the semiclassical approach to it and timeless approaches to it (such as the naive Schrodinger interpretation and records theory). 2) In quantum cosmology, such as in the investigation of uniform states, robustness, and the qualitative understanding of the origin of structure formation.Comment: References and some more motivation adde

Superposition Formulas for Darboux Integrable Exterior Differential Systems

In this paper we present a far-reaching generalization of E. Vessiot's analysis of the Darboux integrable partial differential equations in one dependent and two independent variables. Our approach provides new insights into this classical method, uncovers the fundamental geometric invariants of Darboux integrable systems, and provides for systematic, algorithmic integration of such systems. This work is formulated within the general framework of Pfaffian exterior differential systems and, as such, has applications well beyond those currently found in the literature. In particular, our integration method is applicable to systems of hyperbolic PDE such as the Toda lattice equations, 2 dimensional wave maps and systems of overdetermined PDE.Comment: 80 page report. Updated version with some new sections, and major improvements to other

Deterministic creation, pinning, and manipulation of quantized vortices in a Bose-Einstein condensate

We experimentally and numerically demonstrate deterministic creation and manipulation of a pair of oppositely charged singly quantized vortices in a highly oblate Bose-Einstein condensate (BEC). Two identical blue-detuned, focused Gaussian laser beams that pierce the BEC serve as repulsive obstacles for the superfluid atomic gas; by controlling the positions of the beams within the plane of the BEC, superfluid flow is deterministically established around each beam such that two vortices of opposite circulation are generated by the motion of the beams, with each vortex pinned to the \emph{in situ} position of a laser beam. We study the vortex creation process, and show that the vortices can be moved about within the BEC by translating the positions of the laser beams. This technique can serve as a building block in future experimental techniques to create, on-demand, deterministic arrangements of few or many vortices within a BEC for precise studies of vortex dynamics and vortex interactions.Comment: 9 pages, 7 figure