Bi-Lipschitz geometry of weighted homogeneous surface singularities

We show that a weighted homogeneous complex surface singularity is metrically conical (i.e., bi-Lipschitz equivalent to a metric cone) only if its two lowest weights are equal. We also give an example of a pair of weighted homogeneous complex surface singularities that are topologically equivalent but not bi-Lipschitz equivalent.Comment: 5 pages. Added result that nonhomogeneous cyclic quotients are not conica

Generalization of Quantum Error Correction via the Heisenberg Picture

We show that the theory of operator quantum error correction can be naturally generalized by allowing constraints not only on states but also on observables. The resulting theory describes the correction of algebras of observables (and may therefore suitably be called ``operator algebra quantum error correction''). In particular, the approach provides a framework for the correction of hybrid quantum-classical information and it does not require the state to be entirely in one of the corresponding subspaces or subsystems. We discuss applications to quantum teleportation and to the study of information flows in quantum interactions.Comment: 5 pages, preprint versio

Energy Loss from Reconnection with a Vortex Mesh

Experiments in superfluid 4He show that at low temperatures, energy dissipation from moving vortices is many orders of magnitude larger than expected from mutual friction. Here we investigate other mechanisms for energy loss by a computational study of a vortex that moves through and reconnects with a mesh of small vortices pinned to the container wall. We find that such reconnections enhance energy loss from the moving vortex by a factor of up to 100 beyond that with no mesh. The enhancement occurs through two different mechanisms, both involving the Kelvin oscillations generated along the vortex by the reconnections. At relatively high temperatures the Kelvin waves increase the vortex motion, leading to more energy loss through mutual friction. As the temperature decreases, the vortex oscillations generate additional reconnection events between the moving vortex and the wall, which decrease the energy of the moving vortex by transfering portions of its length to the pinned mesh on the wall.Comment: 9 pages, 10 figure

Using Classical Probability To Guarantee Properties of Infinite Quantum Sequences

We consider the product of infinitely many copies of a spin-$1\over 2$ system. We construct projection operators on the corresponding nonseparable Hilbert space which measure whether the outcome of an infinite sequence of $\sigma^x$ measurements has any specified property. In many cases, product states are eigenstates of the projections, and therefore the result of measuring the property is determined. Thus we obtain a nonprobabilistic quantum analogue to the law of large numbers, the randomness property, and all other familiar almost-sure theorems of classical probability.Comment: 7 pages in LaTe

Formation of long-lived, scarlike modes near avoided resonance crossings in optical microcavities

We study the formation of long-lived states near avoided resonance crossings in open systems. For three different optical microcavities (rectangle, ellipse, and semi-stadium) we provide numerical evidence that these states are localized along periodic rays, resembling scarred states in closed systems. Our results shed light on the morphology of long-lived states in open mesoscopic systems.Comment: 4 pages, 5 figures (in reduced quality), to appear in Phys. Rev. Let

3C 295, a cluster and its cooling flow at z=0.46

We present ROSAT HRI data of the distant and X-ray luminous (L_x(bol)=2.6^ {+0.4}_{-0.2} 10^{45}erg/sec) cluster of galaxies 3C 295. We fit both a one-dimensional and a two-dimensional isothermal beta-model to the data, the latter one taking into account the effects of the point spread function (PSF). For the error analysis of the parameters of the two-dimensional model we introduce a Monte-Carlo technique. Applying a substructure analysis, by subtracting a cluster model from the data, we find no evidence for a merger, but we see a decrement in emission South-East of the center of the cluster, which might be due to absorption. We confirm previous results by Henry & Henriksen(1986) that 3C 295 hosts a cooling flow. The equations for the simple and idealized cooling flow analysis presented here are solely based on the isothermal beta-model, which fits the data very well, including the center of the cluster. We determine a cooling flow radius of 60-120kpc and mass accretion rates of dot{M}=400-900 Msun/y, depending on the applied model and temperature profile. We also investigate the effects of the ROSAT PSF on our estimate of dot{M}, which tends to lead to a small overestimate of this quantity if not taken into account. This increase of dot{M} (10-25%) can be explained by a shallower gravitational potential inferred by the broader overall profile caused by the PSF, which diminishes the efficiency of mass accretion. We also determine the total mass of the cluster using the hydrostatic approach. At a radius of 2.1 Mpc, we estimate the total mass of the cluster (M{tot}) to be (9.2 +/- 2.7) 10^{14}Msun. For the gas to total mass ratio we get M{gas}/M{tot} =0.17-0.31, in very good agreement with the results for other clusters of galaxies, giving strong evidence for a low density universe.Comment: 26 pages, 7 figures, accepted for publication in Ap

Quantum Glassiness

Describing matter at near absolute zero temperature requires understanding a system's quantum ground state and the low energy excitations around it, the quasiparticles, which are thermally populated by the system's contact to a heat bath. However, this paradigm breaks down if thermal equilibration is obstructed. This paper presents solvable examples of quantum many-body Hamiltonians of systems that are unable to reach their ground states as the environment temperature is lowered to absolute zero. These examples, three dimensional generalizations of quantum Hamiltonians proposed for topological quantum computing, 1) have no quenched disorder, 2) have solely local interactions, 3) have an exactly solvable spectrum, 4) have topologically ordered ground states, and 5) have slow dynamical relaxation rates akin to those of strong structural glasses.Comment: 4 page

Electronic Structure of Cu_(1-x)Ni_xRh_2S_4 and CuRh_2Se_4: Band Structure Calculations, X-ray Photoemission and Fluorescence Measurements

The electronic structure of spinel-type Cu_(1-x)Ni_xRh_2S_4 (x = 0.0, 0.1, 0.3, 0.5, 1.0) and CuRh_2Se_4 compounds has been studied by means of X-ray photoelectron and fluorescent spectroscopy. Cu L_3, Ni L_3, S L_(2,3) and Se M_(2,3) X-ray emission spectra (XES) were measured near thresholds at Beamline 8.0 of the Lawrence Berkeley Laboratory's Advanced Light Source. XES measurements of the constituent atoms of these compounds, reduced to the same binding energy scale, are found to be in excellent agreement with XPS valence bands. The calculated XES spectra which include dipole matrix elements show that the partial density of states reproduce experimental spectra quite well. States near the Fermi level (E_F) have strong Rh d and S(Se) p character in all compounds. In NiRh_2S_4 the Ni 3d states contribute strongly at E_F, whereas in both Cu compounds the Cu 3d bands are only ~1 eV wide and centered ~2.5 eV below E_F, leaving very little 3d character at E_F. The density of states at the Fermi level is less in NiRh_2S_4 than in CuRh_2S_4. This difference may contribute to the observed decrease, as a function of Ni concentration, in the superconducting transition temperature in Cu_(1-x)Ni_xRh_2S_4. The density of states of the ordered alloy Cu_(1/2)Ni_(1/2)Rh_2S_4 shows behavior that is more ``split-band''-like than ``rigid band''-like.Comment: 7 pages of text, 11 trailing figures, updated to fix faulty postscript in Fig.