Salem numbers and arithmetic hyperbolic groups

In this paper we prove that there is a direct relationship between Salem numbers and translation lengths of hyperbolic elements of arithmetic hyperbolic groups that are determined by a quadratic form over a totally real number field. As an application we determine a sharp lower bound for the length of a closed geodesic in a noncompact arithmetic hyperbolic n-orbifold for each dimension n. We also discuss a "short geodesic conjecture", and prove its equivalence with "Lehmer's conjecture" for Salem numbers.Comment: The exposition in version 3 is more compact; this shortens the paper: 26 pages now instead of 37. A discussion on Lehmer's problem has been added in Section 1.2. Final version, to appear is Trans. AM

InP/Ga0.47In0.53As monolithic, two-junction, three-terminal tandem solar cells

The work presented has focussed on increasing the efficiency of InP-based solar cells through the development of a high-performance InP/Ga(0.47)In(0.53)As two-junction, three-terminal monolithic tandem cell. Such a tandem is particularly suited to space applications where a radiation-hard top cell (i.e., InP) is required. Furthermore, the InP/Ga(0.47)In(0.53)As materials system is lattice matched and offers a top cell/bottom cell bandgap differential (0.60 eV at 300 K) suitable for high tandem cell efficiencies under AMO illumination. A three-terminal configuration was chosen since it allows for independent power collection from each subcell in the monolithic stack, thus minimizing the adverse impact of radiation damage on the overall tandem efficiency. Realistic computer modeling calculations predict an efficiency boost of 7 to 11 percent from the Ga(0.47)In(0.53)As bottom cell under AMO illumination (25 C) for concentration ratios in the 1 to 1000 range. Thus, practical AMO efficiencies of 25 to 32 percent appear possible with the InP/Ga(0.47)In(0.53)As tandem cell. Prototype n/p/n InP/Ga(0.47)In(0.53)As monolithic tandem cells were fabricated and tested successfully. Using an aperture to define the illuminated areas, efficiency measurements performed on a non-optimized device under standard global illumination conditions (25 C) with no antireflection coating (ARC) give 12.2 percent for the InP top cell and 3.2 percent for the Ga(0.47)In(0.53)As bottom cell, yielding an overall tandem efficiency of 15.4 percent. With an ARC, the tandem efficiency could reach approximately 22 percent global and approximately 20 percent AMO. Additional details regarding the performance of individual InP and Ga(0.47)In(0.53)As component cells, fabrication and operation of complete tandem cells and methods for improving the tandem cell performance, are also discussed

s-wave Superconductivity Phase Diagram in the Inhomogeneous Two-Dimensional Attractive Hubbard Model

We study s-wave superconductivity in the two-dimensional square lattice attractive Hubbard Hamiltonian for various inhomogeneous patterns of interacting sites. Using the Bogoliubov-de Gennes (BdG) mean field approximation, we obtain the phase diagram for inhomogeneous patterns in which the on-site attractive interaction U_i between the electrons takes on two values, U_i=0 and -U/(1-f) (with f the concentration of non-interacting sites) as a function of average electron occupation per site n, and study the evolution of the phase diagram as f varies. In certain regions of the phase diagram, inhomogeneity results in a larger zero temperature average pairing amplitude (order parameter) and also a higher superconducting (SC) critical temperature T_c, relative to a uniform system with the same mean interaction strength (U_i=-U on all sites). These effects are observed for stripes, checkerboard, and even random patterns of the attractive centers, suggesting that the pattern of inhomogeneity is unimportant. The phase diagrams also include regions where superconductivity is obliterated due to the formation of various charge ordered phases. The enhancement of T_{c} due to inhomogeneity is robust as long as the electron doping per site n is less than twice the fraction of interacting sites [2(1-f)] regardless of the pattern. We also show that for certain inhomogeneous patterns, when n = 2(1-f), increasing temperature can work against the stability of existing charge ordered phases for large f and as a result, enhance T_{c}.Comment: 16 pages, 11 figure

Measurement of the Hyperfine Structure and Isotope Shifts of the 3s23p2 3P2 to 3s3p3 3Do3 Transition in Silicon

The hyperfine structure and isotope shifts of the 3s23p2 3P2 to 3s3p3 3Do3 transition in silicon have been measured. The transition at 221.7 nm was studied by laser induced fluorescence in an atomic Si beam. For 29Si, the hyperfine A constant for the 3s23p2 3P2 level was determined to be -160.1+-1.3 MHz (1 sigma error), and the A constant for the 3s3p3 3Do3 level is -532.9+-0.6 MHz. This is the first time that these constants were measured. The isotope shifts (relative to the abundant isotope 28Si) of the transition were determined to be 1753.3+-1.1 MHz for 29Si and 3359.9+-0.6 MHz for 30Si. This is an improvement by about two orders of magnitude over a previous measurement. From these results we are able to predict the hyperfine structure and isotope shift of the radioactive 31Si atom, which is of interest in building a scalable quantum computer

Properties of charge density waves in La2−x_{2-x}Bax_{x}CuO4_4

We report a comprehensive x-ray scattering study of charge density wave (stripe) ordering in $\rm La_{2-x}Ba_xCuO_4 (x \approx 1/8)$, for which the superconducting $T_c$ is greatly suppressed. Strong superlattice reflections corresponding to static ordering of charge stripes were observed in this sample. The structural modulation at the lowest temperature was deduced based on the intensity of over 70 unique superlattice positions surveyed. We found that the charge order in this sample is described with one-dimensional charge density waves, which have incommensurate wave-vectors (0.23, 0, 0.5) and (0, 0.23, 0.5) respectively on neighboring $\rm CuO_2$ planes. The structural modulation due to the charge density wave order is simply sinusoidal, and no higher harmonics were observed. Just below the structural transition temperature, short-range charge density wave correlation appears, which develops into a large scale charge ordering around 40 K, close to the spin density wave ordering temperature. However, this charge ordering fails to grow into a true long range order, and its correlation length saturates at $\sim 230\AA$, and slightly decreases below about 15 K, which may be due to the onset of two-dimensional superconductivity.Comment: 11 pages, 9 figure

Magic identities for conformal four-point integrals

We propose an iterative procedure for constructing classes of off-shell four-point conformal integrals which are identical. The proof of the identity is based on the conformal properties of a subintegral common for the whole class. The simplest example are the so-called `triple scalar box' and `tennis court' integrals. In this case we also give an independent proof using the method of Mellin--Barnes representation which can be applied in a similar way for general off-shell Feynman integrals.Comment: 13 pages, 12 figures. New proof included with neater discussion of contact terms. Typo correcte

Time evolution of a quantum many-body system: transition from integrability to ergodicity in thermodynamic limit

Numerical evidence is given for non-ergodic (non-mixing) behavior, exhibiting ideal transport, of a simple non-integrable many-body quantum system in the thermodynamic limit, namely kicked $t-V$ model of spinless fermions on a ring. However, for sufficiently large kick parameters $t$ and $V$ we recover quantum ergodicity, and normal transport, which can be described by random matrix theory.Comment: 4 pages in RevTex (6 figures in PostScript included

Delocalization in Coupled Luttinger Liquids with Impurities

We study effects of quenched disorder on coupled two-dimensional arrays of Luttinger liquids (LL) as a model for stripes in high-T_c compounds. In the framework of a renormalization-group analysis, we find that weak inter-LL charge-density-wave couplings are always irrelevant as opposed to the pure system. By varying either disorder strength, intra- or inter-LL interactions, the system can undergo a delocalization transition between an insulator and a novel strongly anisotropic metallic state with LL-like transport. This state is characterized by short-ranged charge-density-wave order, the superconducting order is quasi long-ranged along the stripes and short-ranged in the transversal direction.Comment: 6 pages, 5 figures, substantially extended and revised versio

Charge Dynamics in Cuprate Superconductors

In this lecture we present some interesting issues that arise when the dynamics of the charge carriers in the CuO$_2$ planes of the high temperature superconductors is considered. Based on the qualitative picture of doping, set by experiments and some previous calculations, we consider the strength of various inter and intra-cell charge transfer susceptibilities, the question of Coulomb screening and charge collective modes. The starting point is the usual p-d model extended by the long range Coulomb (LRC) interaction. Within this model it is possible to examine the case in which the LRC forces frustrate the electronic phase separation, the instability which is present in the model without an LRC interaction. While the static dielectric function in such systems is negative down to arbitrarily small wavevectors, the system is not unstable. We consider the dominant electronic charge susceptibilities and possible consequences for the lattice properties.Comment: 14 pages, 15 figures, latex, to be published in "From Quantum Mechanics to Technology", Lecture Notes in Physics, Springe

Anisotropy in the helicity modulus of a quantum 3D XY-model: application to YBCO

We present a variational study of the helicity moduli of an anisotropic quantum three-dimensional (3D) XY-model of YBCO in superconducting state. It is found that both the ab-plane and the c-axis helicity moduli, which are proportional to the inverse square of the corresponding magnetic field penetration depth, vary with temperature T as T to the fourth power in the zero temperature limit. Moreover, the c-axis helicity modulus drops with temperature much faster than the ab-plane helicity modulus because of the weaker Josephson couplings along the c-axis compared to those along the ab-plane. These findings are in disagreement with the experiments on high quality samples of YBCO.Comment: 9 pages, 1 figur