Local Lattice Instability and Superconductivity in La1.85_{1.85}Sr0.15_{0.15}Cu1−x_{1-x}Mx_xO4_4 (M=Mn, Ni, and Co)

Local lattice structures of La$_{1.85}$Sr$_{0.15}$Cu$_{1-x}$M$_x$O$_4$ (M=Mn, Ni, and Co) single crystals are investigated by polarized extended x-ray absorption fine structure (EXAFS). The local lattice instability at low temperature is described by in-plane Cu-O bond splitting. We find that substitution of Mn for Cu causes little perturbation of local lattice instability while Ni and Co substitution strongly suppresses the instability. The suppression of superconductivity by Cu-site substitution is related to the perturbation of lattice instability, indicating that local lattice instability (polaron) plays an important role in superconductivity

Wigner crystal and bubble phases in graphene in the quantum Hall regime

Graphene, a single free-standing sheet of graphite with honeycomb lattice structure, is a semimetal with carriers that have linear dispersion. A consequence of this dispersion is the absence of Wigner crystallization in graphene, since the kinetic and potential energies both scale identically with the density of carriers. We study the ground state of graphene in the presence of a strong magnetic field focusing on states with broken translational symmetry. Our mean-field calculations show that at integer fillings a uniform state is preferred, whereas at non-integer filling factors Wigner crystal states (with broken translational symmetry) have lower energy. We obtain the phase diagram of the system. We find that it is qualitatively similar to that of quantum Hall systems in semiconductor heterostructures. Our analysis predicts that non-uniform states, including Wigner crystal state, will occur in graphene in the presence of a magnetic field and will lead to anisotropic transport in high Landau levels.Comment: New references added; 9 pages, 9 figures, (paper with high-resolution images is available at http://www.physics.iupui.edu/yogesh/graphene.pdf

Geometry and Representations of the Quantum Supergroup OSPq(1|2n)

The quantum supergroup OSPq(1|2n) is studied systematically. A Haar functional is constructed, and an algebraic version of the Peter - Weyl theory is extended to this quantum supergroup. Quantum homogeneous superspaces and quantum homogeneous supervector bundles are defined following the strategy of Connes' theory. Parabolic induction is developed by employing the quantum homogeneous supervector bundles. Quantum Frobenius reciprocity and a generalized Borel - Weil theorem are established for the induced representations.Comment: Latex, 20 page

Solving Functional Constraints by Variable Substitution

Functional constraints and bi-functional constraints are an important constraint class in Constraint Programming (CP) systems, in particular for Constraint Logic Programming (CLP) systems. CP systems with finite domain constraints usually employ CSP-based solvers which use local consistency, for example, arc consistency. We introduce a new approach which is based instead on variable substitution. We obtain efficient algorithms for reducing systems involving functional and bi-functional constraints together with other non-functional constraints. It also solves globally any CSP where there exists a variable such that any other variable is reachable from it through a sequence of functional constraints. Our experiments on random problems show that variable elimination can significantly improve the efficiency of solving problems with functional constraints