Pairing in Inhomogeneous Superconductors

Starting from a t-J model, we introduce inhomogeneous terms to mimic stripes. We find that if the inhomogeneous terms break the SU(2) spin symmetry the binding between holes is tremendously enhanced in the thermodynamic limit. In any other model (including homogeneous models) the binding in the thermodynamic limit is small or neglible. By including these inhomogeneous terms we can reproduce experimental neutron scattering data. We also discuss the connection of the resulting inhomogeneity-induced superconductivity to recent experimental evidence for a linear relation between magnetic incommensurability and the superconducting transition temperature, as a function of doping.Comment: 4 pages, 2 figure

BCS-to-BEC crossover from the exact BCS solution

The BCS-to-BEC crossover, as well as the nature of Cooper pairs, in a superconducting and Fermi superfluid medium is studied from the exact ground state wavefunction of the reduced BCS Hamiltonian. As the strength of the interaction increases, the ground state continuously evolves from a mixed-system of quasifree fermions and pair resonances (BCS), to pair resonances and quasibound molecules (pseudogap), and finally to a system of quasibound molecules (BEC). A single unified scenario arises where the Cooper-pair wavefunction has a unique functional form. Several exact analytic expressions, such as the binding energy and condensate fraction, are derived. We compare our results with recent experiments in ultracold atomic Fermi gases.Comment: 5 pages, 4 figures. Revised version with one figure adde

Inhomogeneity-Induced Superconductivity?

A t-J-like model for inhomogeneous superconductivity of cuprate oxides is presented, in which local anisotropic magnetic terms are essential. We show that this model predicts pairing, consistent with experiments, and argue how the macroscopic phase-coherent state gradually grows upon lowering of the temperature. We show that appropriate inhomogeneities are essential in order to have significant pair binding in the thermodynamic limit. Particularly, {\it local} breaking of SU(2) spin symmetry is an efficient mechanism for inducing pairing of two holes, as well as explaining the magnetic scattering properties. We also discuss the connection of the resulting inhomogeneity-induced superconductivity to recent experimental evidence for a linear relation between magnetic incommensurability and the superconducting transition temperature, as a function of doping.Comment: 4 pages, REVTEX, 4 jpeg figures. To appear in Europhys. Let

Latitudinal variation of the solar photospheric intensity

We have examined images from the Precision Solar Photometric Telescope (PSPT) at the Mauna Loa Solar Observatory (MLSO) in search of latitudinal variation in the solar photospheric intensity. Along with the expected brightening of the solar activity belts, we have found a weak enhancement of the mean continuum intensity at polar latitudes (continuum intensity enhancement $\sim0.1 - 0.2$ corresponding to a brightness temperature enhancement of $\sim2.5{\rm K}$). This appears to be thermal in origin and not due to a polar accumulation of weak magnetic elements, with both the continuum and CaIIK intensity distributions shifted towards higher values with little change in shape from their mid-latitude distributions. Since the enhancement is of low spatial frequency and of very small amplitude it is difficult to separate from systematic instrumental and processing errors. We provide a thorough discussion of these and conclude that the measurement captures real solar latitudinal intensity variations.Comment: 24 pages, 8 figs, accepted in Ap

Geometry of Discrete Quantum Computing

Conventional quantum computing entails a geometry based on the description of an n-qubit state using 2^{n} infinite precision complex numbers denoting a vector in a Hilbert space. Such numbers are in general uncomputable using any real-world resources, and, if we have the idea of physical law as some kind of computational algorithm of the universe, we would be compelled to alter our descriptions of physics to be consistent with computable numbers. Our purpose here is to examine the geometric implications of using finite fields Fp and finite complexified fields Fp^2 (based on primes p congruent to 3 mod{4}) as the basis for computations in a theory of discrete quantum computing, which would therefore become a computable theory. Because the states of a discrete n-qubit system are in principle enumerable, we are able to determine the proportions of entangled and unentangled states. In particular, we extend the Hopf fibration that defines the irreducible state space of conventional continuous n-qubit theories (which is the complex projective space CP{2^{n}-1}) to an analogous discrete geometry in which the Hopf circle for any n is found to be a discrete set of p+1 points. The tally of unit-length n-qubit states is given, and reduced via the generalized Hopf fibration to DCP{2^{n}-1}, the discrete analog of the complex projective space, which has p^{2^{n}-1} (p-1)\prod_{k=1}^{n-1} (p^{2^{k}}+1) irreducible states. Using a measure of entanglement, the purity, we explore the entanglement features of discrete quantum states and find that the n-qubit states based on the complexified field Fp^2 have p^{n} (p-1)^{n} unentangled states (the product of the tally for a single qubit) with purity 1, and they have p^{n+1}(p-1)(p+1)^{n-1} maximally entangled states with purity zero.Comment: 24 page

Quantum-Mechanical Position Operator and Localization in Extended Systems

We introduce a fundamental complex quantity, $z_{L}$, which allows us to discriminate between a conducting and non-conducting thermodynamic phase in extended quantum systems. Its phase can be related to the expectation value of the position operator, while its modulus provides an appropriate definition of a localization length. The expressions are valid for {\it any} fractional particle filling. As an illustration we use $z_{L}$ to characterize insulator to ``superconducting'' and Mott transitions in one-dimensional lattice models with infinite on-site Coulomb repulsion at quarter filling.Comment: 4 pages, REVTEX, 1 ps figure

The dimerized phase of ionic Hubbard models

We derive an effective Hamiltonian for the ionic Hubbard model at half filling, extended to include nearest-neighbor repulsion. Using a spin-particle transformation, the effective model is mapped onto simple spin-1 models in two particular cases. Using another spin-particle transformation, a slightly modified model is mapped into an SU(3) antiferromagnetic Heisenberg model whose exact ground state is known to be spontaneously dimerized. From the effective models several properties of the dimerized phase are discussed, like ferroelectricity and fractional charge excitations. Using bosonization and recent developments in the theory of macroscopic polarization, we show that the polarization is proportional to the charge of the elementary excitations

Striped superconductors in the extended Hubbard model

We present a minimal model of a doped Mott insulator that simultaneously supports antiferromagnetic stripes and d-wave superconductivity. We explore the implications for the global phase diagram of the superconducting cuprates. At the unrestricted mean-field level, the various phases of the cuprates, including weak and strong pseudogap phases, and two different types of superconductivity in the underdoped and the overdoped regimes, find a natural interpretation. We argue that on the underdoped side, the superconductor is intrinsically inhomogeneous -- striped coexistence of of superconductivity and magnetism -- and global phase coherence is achieved through Josephson-like coupling of the superconducting stripes. On the overdoped side, the state is overall homogeneous and the superconductivity is of the classical BCS type.Comment: 5 pages, 3 eps figures. Effect of t' on stripe filling + new references are adde

Identifying Ultra-Cool Dwarfs at Low Galactic Latitudes: A Southern Candidate Catalogue

We present an Ultra-Cool Dwarf (UCD) catalogue compiled from low southern Galactic latitudes and mid-plane, from a cross-correlation of the 2MASS and SuperCOSMOS surveys. The catalogue contains 246 members identified from 5042 sq. deg. within 220 deg. <= l <= 360 deg. and 0 deg. < l <= 30 deg., for |b| <= 15 deg. Sixteen candidates are spectroscopically confirmed in the near-IR as UCDs with spectral types from M7.5V to L9. Our catalogue selection method is presented enabling UCDs from ~M8V to the L-T transition to be selected down to a 2MASS limiting magnitude of Ks ~= 14.5 mag. This method does not require candidates to have optical detections for catalogue inclusion. An optimal set of optical/near-IR and reduced proper-motion selection criteria have been defined that includes: an Rf and Ivn photometric surface gravity test, a dual Rf-band variability check, and an additional photometric classification scheme to selectively limit contaminants. We identify four candidates as possible companions to nearby Hipparcos stars -- observations are needed to identify these as potential benchmark UCD companions. We also identify twelve UCDs within a possible distance 20 pc, three are previously unknown of which two are estimated within 10 pc, complimenting the nearby volume-limited census of UCDs. An analysis of the catalogue spatial completeness provides estimates for distance completeness over three UCD MJ ranges, while Monte-Carlo simulations provide an estimate of catalogue areal completeness at the 75 per cent level. We estimate a UCD space density of Rho (total) = (6.41+-3.01)x10^3/pc^3 over the range of 10.5 <= MJ ~< 14.9, similar to values measured at higher Galactic latitudes (|b| ~> 10 deg.) in the field population and obtained from more robust spectroscopically confirmed UCD samples.Comment: MNRAS accepted April 2012. Contains 30 figures and 11 tables. Tables 2 and 6 to be published in full and on-line only. The on-line tables can also be obtained by contacting the author