Compressibility of a two-dimensional extended Hubbard model

The compressibility of an extended $d-p$ Hubbard model is investigated by the Roth's two-pole approximation. Using the factorization procedure proposed by Beenen and Edwards, superconductivity with singlet $d_{x^2-y^2}$-wave pairing is also considered. Within this framework, the effects of $d-p$ hybridization and Coulomb interaction $U$ on the compressibility are studied carefully. It has been found that the compressibility diverges and then it becomes negative near the half-filling. Within Roth's method, it has been verified that an important contribution for the negative compressibility comes from the spin-correlation term $$ present in Roth's band shift. This correlation function plays an important role due to its high doping dependence. Also, its effects in the band shift and consequently in the compressibility are pronounced near the half-filling. The numerical results show that the hybridization acts in the sense of suppressing the negative compressibility near half-filling. Finally, the possibility of a connection between the negative compressibility and the phase separation is also discussed.Comment: 3 pages, 1 figure, accepted for publication in Physica

Role of Hybridization in the Superconducting Properties of an Extended d−pd-p Hubbard Model: a Detailed Numerical Study

The Roth's two-pole approximation has been used by the present authors to study the effects of the hybridization in the superconducting properties of a strongly correlated electron system. The model used is the extended Hubbard model which includes the $d-p$ hybridization, the $p$-band and a narrow $d$-band. The present work is an extension a previous reference [Intern. Journ. of Modern Phys. B, Vol. 18 No. 2 (2004) 241]. Nevertheless, some important correlation functions necessary to estimate the Roth's band shift, are included together with the temperature $T$ and the Coulomb interaction $U$ to describe the superconductivity. The superconducting order parameter of a cuprate system, is obtained following Beenen and Edwards formalism. Here, we investigate in detail the change of the order parameter associated to temperature, Coulomb interaction and Roth's band shift effects on superconductivity. The phase diagram with $T_c$ versus the total occupation numbers $n_T$, shows the difference respect to the previous work.Comment: 4 pages, 1 figure, accept to be published in Physica

Turmalinas en la pegmatita granítica de Li-Cs-Ta del Grupo Namacotche, Mozambique: cristalquímica y origen

The field work, backscattered electron images and detailed microanalyses of three generations of tourmaline from the Namacotche LCT pegmatites allows de distinction between the compositional magmatic and hydrothermal tourmalines. The generation 1 occurs in the outer intermediate zone of the pegmatite. It consists of zoned crystals with an oscillatory inner core of foitite and schorl, an outer core of schorl and an Fe-rich fluor-elbaite rim. Unzoned Fe-rich fluor-elbaite crystals occur in the inner intermediate zone of the pegmatite. All the crystals are derived by fractionation of a (Al, Li, B)-rich pegmatite melt. However, the rim of zoned crystals and some compositions of unzoned crystals show evidence of hydrothermal fluids, as they plot outside the fractionation trends. The zoned fluor-elbaite crystals of the generation 2 are from the inner intermediate zone of the pegmatite. They have a pink core and a green rim. The rim has higher YFe2+, Na, F contents YFe2+/(YFe2++Licalc.) value and lower Si, YAl, Licalc. and X-site vacancy contents, X-vacancy/(Na+X-vacancy) value than the core. Both zones are hydrothermal. The rim is an overgrowth. The fluor-elbaite gemmy crystals of the generation 3 occur in sheared breccia blasts and clasts with a cookeite matrix. They depend mainly on the fluid-rich hydrothermal environment of low temperatures (280-150ºC). Some from the cycle a may result from the dissolution of magmatic tourmaline crystals of the generation 1 from the sheared outer and inner intermediate zones of the pegmatite due to reaction with late fluids in chemical disequilibrium, followed by growth of tourmaline with low temperature hydrothermal fluids. The evolution from the cycle a to the cycle b and to the cycle c of the generation 3 implies that the hydrothermal reacting fluids were undergoing fractionation and becoming richer in Li and poorer in Fe2+ during the late hydrothermal crystallization of the pegmatites.El trabajo de campo, las imágenes de electrones retrodispersados y microanálisis detallados de tres generaciones de turmalina de las pegmatitas LCT de Namacotche permiten distinguir entre las turmalinas magmáticas y las hidrotermales. La generación 1 aparece en la zona intermedia exterior de la pegmatita. Consiste en cristales zonados con un núcleo interno oscilante de foitita y esquisto, un núcleo externo de esquisto y un borde de fluor-elbaita rico en Fe. En la zona intermedia interior de la pegmatita aparecen cristales no zonados de fluor-elbaita ricos en Fe. Todos los cristales derivan del fraccionamiento de un fundido pegmatítico rico en Al, Li y B. Sin embargo, el borde de los cristales zonados y algunas composiciones de cristales no zonados muestran evidencias de fluidos hidrotermales, ya que trazan fuera de las tendencias de fraccionamiento. Los cristales zonados de fluor-elbaita de la generación 2 proceden de la zona intermedia interna de la pegmatita. Tienen un núcleo rosa y un borde verde. El borde tiene mayor contenido en YFe2+, Na, F (YFe2+/(YFe2++Licalc.)) y menor contenido en Si, YAl, Licalc. y vacantes X, vacantes X/(Na+X-vacantes) que el núcleo. Ambas zonas son hidrotermales. El borde es un sobrecrecimiento. Los cristales geminados de fluor-elbaita de la generación 3 aparecen en clastos de brechas cizalladas y en clastos con matriz de cookeita. Dependen principalmente del ambiente hidrotermal rico en fluidos de bajas temperaturas (280-150ºC). Algunos del ciclo a pueden ser el resultado de la disolución de cristales magmáticos de turmalina de la generación 1 de las zonas cizalladas externa e interna intermedia de la pegmatita debido a la reacción con fluidos tardíos en desequilibrio químico, seguida del crecimiento de la turmalina con fluidos hidrotermales de baja temperatura. La evolución del ciclo a al ciclo b y al ciclo c de la generación 3 implica que los fluidos hidrotermales reaccionantes estaban sufriendo fraccionamiento y haciéndose más ricos en Li y más pobres en Fe2+ durante la cristalización hidrotermal tardía de las pegmatitas

Polynomial Realization of sℓq(2)s\ell_q(2) and Fusion Rules at Exceptional Values of qq

Representations of the $s\ell_q(2)$ algebra are constructed in the space of polynomials of real (complex) variable for $q^N=1$. The spin addition rule based on eigenvalues of Casimir operator is illustrated on few simplest cases and conjecture for general case is formulated

A Vector Supersymmetry in Noncommutative U(1) Gauge Theory with the Slavnov Term

We consider noncommutative U(1) gauge theory with the additional term, involving a scalar field lambda, introduced by Slavnov in order to cure the infrared problem. we show that this theory, with an appropriate space-like axial gauge-fixing, wxhibits a linear vector supersymmetry similar to the one present in the 2-dimensional BF model. This vector supersymmetry implies that all loop corrections are independent of the $\lambda AA$-vertex and thereby explains why Slavnov found a finite model for the same gauge-fixing.Comment: 18 pages, 3 figures; v2 Acknowledgments adde

Continuity of Optimal Control Costs and its application to Weak KAM Theory

We prove continuity of certain cost functions arising from optimal control of affine control systems. We give sharp sufficient conditions for this continuity. As an application, we prove a version of weak KAM theorem and consider the Aubry-Mather problems corresponding to these systems.Comment: 23 pages, 1 figures, added explanations in the proofs of the main theorem and the exampl

On the use of a single site approximation to describe correlation in pure metals

The magnetic properties of pure transition-like metals are discussed within the single site approximation, to take into account the electron correlation. The metal is described by two hybridized bands one of which includes the Coulomb correlation. Our results indicate that ferromagnetism follows from adequate values of the correlation and hybridization.Comment: 2 pages and 2 figure

On the consistency of the three-dimensional noncommutative supersymmetric Yang-Mills theory

We study the one-loop quantum corrections to the U(N) noncommutative supersymmetric Yang-Mills theory in three spacetime dimensions (NCSYM$_3$). We show that the cancellation of the dangerous UV/IR infrared divergences only takes place in the fundamental representation of the gauge group. Furthermore, in the one-loop approximation, the would be subleading UV and UV/IR infrared divergences are shown to vanish.Comment: 8 pages and 2 figure

Exchange couplings in the magnetic molecular cluster Mn12Ac

The magnetic properties of the molecular cluster Mn12Ac are due to the four Mn3+ ions which have spins S=3/2 and the eight Mn4+ ions with spins S=2. These spins are coupled by superexchange mechanism. We determine the four exchange couplings assuming a Heisenberg-type interaction between the ions. We use exact diagonalization of the spin Hamiltonian by a Lanczos algorithm and we adjust the couplings to reproduce the magnetization curve of Mn12Ac. We also impose the constraint of reproducing a gap of 35K between a S=10 ground state and a first excited state with S=9. We predict that there is an excited level with S=8 at 37K above the ground state, only slightly above the S=9 excited state which lies at 35K and the next excited state is a S=9 multiplet at 67K above the S=10 ground state.Comment: 15 pages, 6 figures, submitted to Phys Rev B, corrected a misTeX: values of J1, J2 have changed, refs update