Labelling matrices and index matrices of a graph structure

The concept of graph structure was introduced by E. Sampathkumar in 'Generalised Graph Structures', Bull. Kerala Math. Assoc., Vol 3, No.2, Dec 2006, 65-123. Based on the works of Brouwer, Doob and Stewart, R.H. Jeurissen has ('The Incidence Matrix and Labelings of a Graph', J. Combin. Theory, Ser. B30 (1981), 290-301) proved that the collection of all admissible index vectors and the collection of all labellings for 0 form free F-modules (F is a commutative ring). We have obtained similar results on graph structures in a previous paper. In the present paper, we introduce labelling matrices and index matrices of graph structures and prove that the collection of all admissible index matrices and the collection of all labelling matrices for 0 form free F-modules. We also find their ranks in various cases of bipartition and char F (equal to 2 and not equal to 2)

Order in extremal trajectories

Given a chaotic dynamical system and a time interval in which some quantity takes an unusually large average value, what can we say of the trajectory that yields this deviation? As an example, we study the trajectories of the archetypical chaotic system, the baker's map. We show that, out of all irregular trajectories, a large-deviation requirement selects (isolated) orbits that are periodic or quasiperiodic. We discuss what the relevance of this calculation may be for dynamical systems and for glasses

Interaction Effect in the Kondo Energy of the Periodic Anderson-Hubbard Model

We extend the periodic Anderson model by switching on a Hubbard $U_d$ for the conduction electrons. The nearly integral valent (Kondo) limit of the Anderson--Hubbard model is studied with the Gutzwiller variational method. The new formula for the Kondo energy contains the $U_d$-dependent chemical potential of the Hubbard subsystem in the exponent, and the correlation-induced band narrowing in the prefactor. Both effects tend to suppress the Kondo scale, which can be understood to result from the blocking of hybridization (this behaviour is the opposite of that found for Kondo--Hubbard models). At half-filling, we find a Brinkman--Rice-type transition which leads from a small-gap Kondo insulator to a Mott insulator.Comment: 4 pages (ReVTeX), submitted for publicatio

Destruction of long-range antiferromagnetic order by hole doping

We study the renormalization of the staggered magnetization of a two-dimensional antiferromagnet as a function of hole doping, in the framework of the t-J model. It is shown that the motion of holes generates decay of spin waves into ''particle-hole'' pairs, which causes the destruction of the long-range magnetic order at a small hole concentration. This effect is mainly determined by the coherent motion of holes. The value obtained for the critical hole concentration, of a few percent, is consistent with experimental data for the doped copper oxide high-Tc superconductors.Comment: 12 pages, 2 figure

What Does The Korringa Ratio Measure?

We present an analysis of the Korringa ratio in a dirty metal, emphasizing the case where a Stoner enhancement of the uniform susceptibilty is present. We find that the relaxation rates are significantly enhanced by disorder, and that the inverse problem of determining the bare density of states from a study of the change of the Knight shift and relaxation rates with some parameter, such as pressure, has rather constrained solutions, with the disorder playing an important role. Some preliminary applications to the case of chemical substitution in the Rb$_{3-x}$K$_x$C$_{60}$ family of superconductors is presented and some other relevant systems are mentioned.Comment: 849, Piscataway, New Jersey 08855 24 June 199

Glass Transition of Hard Sphere Systems: Molecular Dynamics and Density Functional Theory

The glass transition of a hard sphere system is investigated within the framework of the density functional theory (DFT). Molecular dynamics (MD) simulations are performed to study dynamical behavior of the system on the one hand and to provide the data to produce the density field for the DFT on the other hand. Energy landscape analysis based on the DFT shows that there appears a metastable (local) free energy minimum representing an amorphous state as the density is increased. This state turns out to become stable, compared with the uniform liquid, at some density, around which we also observe sharp slowing down of the $alpha$ relaxation in MD simulations.Comment: 5 pages, 5 figure

Muon-Spin Rotation Spectra in the Mixed Phase of High-T_c Superconductors : Thermal Fluctuations and Disorder Effects

We study muon-spin rotation (muSR) spectra in the mixed phase of highly anisotropic layered superconductors, specifically Bi_2+xSr_2-xCaCu_2O_8+delta (BSCCO), by modeling the fluid and solid phases of pancake vortices using liquid-state and density functional methods. The role of thermal fluctuations in causing motional narrowing of muSR lineshapes is quantified in terms of a first-principles theory of the flux-lattice melting transition. The effects of random point pinning are investigated using a replica treatment of liquid state correlations and a replicated density functional theory. Our results indicate that motional narrowing in the pure system, although substantial, cannot account for the remarkably small linewidths obtained experimentally at relatively high fields and low temperatures. We find that satisfactory agreement with the muSR data for BSCCO in this regime can be obtained through the ansatz that this ``phase'' is characterized by frozen short-range positional correlations reflecting the structure of the liquid just above the melting transition. This proposal is consistent with recent suggestions of a ``pinned liquid'' or ``glassy'' state of pancake vortices in the presence of pinning disorder. Our results for the high-temperature liquid phase indicate that measurable linewidths may be obtained in this phase as a consequence of density inhomogeneities induced by the pinning disorder. The results presented here comprise a unified, first-principles theoretical treatment of muSR spectra in highly anisotropic layered superconductors in terms of a controlled set of approximations.Comment: 50 pages Latex file, including 10 postscript figure

Vortex in a d-wave superconductor at low temperatures

A systematic perturbation theory is developed to describe the magnetic field-induced subdominant $s$- and $d_{xy}$-wave order parameters in the mixed state of a $d_{x^2-y^2}$-wave superconductor, enabling us to obtain, within weak-coupling BCS theory, analytic results for the free energy of a d-wave superconductor in an applied magnetic field H_{c1}\ltsim H\ll H_{c2} from $T_c$ down to very low temperatures. Known results for a single isolated vortex in the Ginzburg-Landau regime are recovered, and the behavior at low temperatures for the subdominant component is shown to be qualitatively different. In the case of subdominant $d_{xy}$ pair component, superfluid velocity gradients and an orbital Zeeman effect are shown to compete in determining the vortex state, but for realistic field strengths the latter appears to be irrelevant. On this basis, we argue that recent predictions of a low-temperature phase transition in connection with recent thermal conductivity measurements are unlikely to be correct.Comment: 20 RevTEX pages, 6 EPS figures; considerably expanded versio

Model for Glass Transition in a Binary fluid from a Mode Coupling approach

We consider the Mode Coupling Theory (MCT) of Glass transition for a Binary fluid. The Equations of Nonlinear Fluctuating Hydrodynamics are obtained with a proper choice of the slow variables corresponding to the conservation laws. The resulting model equations are solved in the long time limit to locate the dynamic transition. The transition point from our model is considerably higher than predicted in existing MCT models for binary systems. This is in agreement with what is seen in Computer Simulation of binary fluids. fluids.Comment: 9 Pages, 3 Figure

Effective Actions and Phase Fluctuations in d-wave Superconductors

We study effective actions for order parameter fluctuations at low temperature in layered d-wave superconductors such as the cuprates. The order parameter lives on the bonds of a square lattice and has two amplitude and two phase modes associated with it. The low frequency spectral weights for amplitude and relative phase fluctuations is determined and found to be subdominant to quasiparticle contributions. The Goldstone phase mode and its coupling to density fluctuations in charged systems is treated in a gauge-invariant manner. The Gaussian phase action is used to study both the $c$-axis Josephson plasmon and the more conventional in-plane plasmon in the cuprates. We go beyond the Gaussian theory by deriving a coarse-grained quantum XY model, which incorporates important cutoff effects overlooked in previous studies. A variational analysis of this effective model shows that in the cuprates, quantum effects of phase fluctuations are important in reducing the zero temperature superfluid stiffness, but thermal effects are small for $T << T_c$.Comment: Some numerical estimates corrected and figures changed. to appear in PRB, Sept.1 (2000