Thermal Entanglement for Interacting Spin-1/2 Systems and its Quantum Criticality

In this work, we investigate the thermal entanglement for interacting spin systems , by varying the parameters of temperature T, direction and magnetic field B. PACS numbers: 03.67.Mn, 03.65.Ud, 05.30.Cd, 73.43.Nq     

Field Equations of Arbitrary Spin in Space-time with Torsion

A two spinor lagrangian formulation of field equations for massive particle of arbitrary spin is proposed in a curved space-time with torsion. The interaction between fields and torsion is expressed by generalizing the situation of the Dirac equation. The resulting field equations are different (except for the spin-1/2 case) from those obtained by promoting the covariant derivatives of the torsion free equations to include torsion. The non linearity of the equations, that is induced by torsion, can be interpreted as a self-interaction of the particle. The spin-1 and spin-3/2 cases are studied with some details by translating into tensor form. There result the Proca and Rarita-Schwinger field equations with torsion, respectively. PACS numbers: 03.65.Pm; 04.20.Cv; 04.20.Fy.     

Spinning Particles in Spacetimes with Torsion

A novel analysis of the Mathisson-Papapetrou-Dixon equations is presented employing mathematical tools that do not rely on the torsion free geometries used in previous literature. A system of differential algebraic equations that can be used to describe the motion of spinning particles in an arbitrary geometry is derived. The curvature in these equations can involve non-Riemannian contributions. Subsequently, this particular system of equations can accommodate modification to geodesic motion from both scalar fields and the spin of the particle. PACS: 02.40.Hw, 04.20.Cv, 04.40.Nr     

Finitary Topos for Locally Finite,Causal and Quantal Vacuum Einstein Gravity

The pentalogy (Mallios, A. and Raptis, I. (2001). International Journal of Theoretical Physics 40, 1885; Mallios, A. and Raptis, I. (2002). International Journal of Theoretical Physics 41, 1857; Mallios, A. and Raptis, I. (2003).International Journal of Theoretical Physics 42, 1479; Mallios, A. and Raptis, I. (2004). ‘paper-book’/research monograph); I. Raptis (2005). International Journal of Theoretical Physics (to appear)is brought to its categorical climax by organizing the curved finitary spacetime sheaves of quantumcausal sets involved therein, on which a finitary (:locally finite), singularity-free, background manifold independent and geometrically prequantized version of the gravitational vacuum Einstein field equations were seen to hold, into a topos structure . We show that the category of finitary differential triads is a finitary instance of an elementary topos proper in the original sense dueto Lawvere and Tierney. We present in the light of Abstract Differential Geometry (ADG) a Grothendieck-type of generalization of Sorkin’s finitary substitutes of continuous spacetime manifoldtopologies, the latter’s topological refinement inverse systems of locally finite coverings and their associated coarse graining sieves, the upshot being that is also a finitary example of a Grothendieck topos. In the process, we discover that the subobject classifier Ω _fcq of is a Heyting algebra type of object, thus we infer that the internal logic of our finitary topos is intuitionistic, as expected. We also introduce the new notion of ‘finitary differential geometric morphism’ which, as befits ADG, gives a differential geometric slant to Sorkin’s purely topological acts of refinement (:coarse graining). Based on finitary differential geometric morphisms regarded as natural transformations of the relevant sheaf categories, we observe that the functorial ADG-theoretic version of the principle of general covariance of GeneralRelativity is preserved under topological refinement. The paper closes with a thorough discussion of four future routes we could take in order to further develop our topos-theoretic perspective on ADG-gravity along certain categorical trends in current quantum gravity research. PACS numbers: 04.60.-m, 04.20.Gz, 04.20.-q Posted at the General Relativity and Quantum Cosmology (gr-qc) electronic archive (www.arXiv.org), as: gr-qc/0507100.     

High-frequency perturbations of coupled gravitational and electromagnetic fields in a weakly ionized dust

Wavelike perturbations of a system consisting of a gravitational and an electromagnetic field and a dust with a small ionized component are studied. By using the spin coefficient formalism we expand the perturbations of the various quantities characterizing the system into asymptotic series. The whole dynamics of high-frequency waves is shown to be governed by four propagation equations for the expansion coefficients of the tetrad components and of perturbations of the Weyl tensor and Maxwell tensor in each order of the expansion. The perturbations of all the other variables can be derived without integration. The propagation equations are explicitly derived and discussed in the zeroth-order (geometrical optics) and in the first-order approximation. The influence of dust and plasma on the propagation is considered in the first-order equations.     

Dark Energy Model with Canonical Scalar Field and Non-Linear Born–Infeld Type Scalar Field

In this paper, we propose the non-linear Born–Infeld scalar field and canonical scalar field dark energy models with the potential , which admits late time de Sitter attractor solution. The attractor solution corresponds to an equation of state ω_φ → − 1 and a cosmic density parameter Ω_φ → 1, which are important features for a dark energy model that can meet the current observations. dark energy; canonical scalar field, non-linear Born–Infeld type scalar field, attractor solution. PACS number(s):98.80.-k; 98.80.Cq; 98.80.Es.     

Orthocomplementation and Compound Systems

In their 1936 founding paper on quantum logic, Birkhoff and von Neumann postulated that the lattice describing the experimental propositions concerning a quantum system is orthocomplemented. We prove that this postulate fails for the lattice _sep describing a compound system consisting of so called separated quantum systems. By separated we mean two systems prepared in different “rooms” of the lab, and before any interaction takes place. In that case, the state of the compound system is necessarily a product state. As a consequence, Dirac’s superposition principle fails, and therefore _sep cannot satisfy all Piron’s axioms. In previous works, assuming that _sep is orthocomplemented, it was argued that _sep is not orthomodular and fails to have the covering property. Here we prove that _sep cannot admit an orthocomplementation. Moreover, we propose a natural model for _sep which has the covering property. PACS: 03.65.Ta, 03.65.Ca     

Vector Measures on the Logic of <Emphasis Type="Italic">J</Emphasis>-projections of a Krein Space

Let be a Hilbert space with an inner product . In Jajte, R., and Paszkiewicz, A. (1978, Vector measure on the closed subspaces of a Hilbert space, Studia Mathematica 63, 229–251), the -measure on the logic of all orthogonal projections on H was studied. We examine the -measure on the hyperbolic logic of all J-projections on a Krein space. PACS: 03.65.Ta, 03.65.Db, 03.65.Ca.     

What is a mean gravitational field?

The equations of General Relativity are non-linear. This makes their averaging non-trivial. The notion of mean gravitational field is defined and it is proven that this field obeys the equations of General Relativity if the unaveraged field does. The workings of the averaging procedure on Maxwells field and on perfect fluids in curved space-times are also discussed. It is found that Maxwells equations are still verified by the averaged quantities but that the equation of state for other kinds of matter generally changes upon average. In particular, it is proven that the separation between matter and gravitational field is not scale-independent. The same result can be interpreted by introducing a stress-energy tensor for a mean-vacuum. Possible applications to cosmology are discussed. Finally, the work presented in this article also suggests that the signature of the metric might be scale-dependent too.Received: 16 October 2003, Published online: 15 March 2004PACS: 04.20.Cv Fundamental problems and general formalism 04.40.Nr Einstein-Maxwell spacetimes, spacetimes with fluids, radiation or classical fields - 95.35. + d Dark matter (stellar, interstellar, galactic, and cosmological)     

An Algebra of Deformation Quantization for Star-Exponentials on Complex Symplectic Manifolds

The cotangent bundle T ^* X to a complex manifold X is classically endowed with the sheaf of k-algebras of deformation quantization, where k := is a subfield of . Here, we construct a new sheaf of k-algebras which contains as a subalgebra and an extra central parameter t. We give the symbol calculus for this algebra and prove that quantized symplectic transformations operate on it. If P is any section of order zero of , we show that is well defined in .     

Quantum Computational Semantics on Fock Space

In the Fock space semantics, meanings of sentences are identified with density operators of the (unsymmetrized) Fock space based on the Hilbert space ℂ². Generally, the meaning of a sentence is smeared over different sectors of . The standard quantum computational semantics is a limit case of the Fock space semantics, where the meaning of any sentence α only “lives” in one sector of , which is determined by the logical complexity of α. We prove that the global Fock space semantics and the standard quantum computational semantics characterize the same logic. PACS: 03.67.Lx.     

Complete spectroscopy in high-spin cranking calculations

Exact and approximate quantum numbers of the cranked Nilsson-Strutinsky (CNS) formalism are exploited to calculate excited bands in fixed configurations with the energy of the individual bands minimized with respect to deformation for all spin values. The formalism is applied to ⁵⁹Cu, where all bands which appear important in the decay out of the superdeformed band are calculated.Received: 14 November 2002, Published online: 17 February 2004PACS: 21.10.Ma Level density - 21.60.Cs Shell model - 23.20.Lv transitions and level energies - 27.50. + e C. Andreoiu: Present address: Department of Physics, University of Guelph, Guelph, Ontario, Canada N1G 2W1.     

(Co)cyclic (Co)homology of Bialgebroids: An Approach via (Co)monads

For a (co)monad T _l on a category , an object X in , and a functor , there is a (co)simplex in . The aim of this paper is to find criteria for para-(co)cyclicity of Z ^*. Our construction is built on a distributive law of T _l with a second (co)monad T _r on , a natural transformation , and a morphism in . The (symmetrical) relations i and w need to satisfy are categorical versions of Kaygun’s axioms of a transposition map. Motivation comes from the observation that a (co)ring T over an algebra R determines a distributive law of two (co)monads and on the category of R-bimodules. The functor Π can be chosen such that is the cyclic R-module tensor product. A natural transformation is given by the flip map and a morphism is constructed whenever T is a (co)module algebra or coring of an R-bialgebroid. The notion of a stable anti-Yetter-Drinfel’d module over certain bialgebroids, the so-called  ×  _R -Hopf algebras, is introduced. In the particular example when T is a module coring of a  ×  _R -Hopf algebra and X is a stable anti-Yetter-Drinfel’d -module, the para-cyclic object Z _* is shown to project to a cyclic structure on . For a -Galois extension , a stable anti-Yetter-Drinfel’d -module T _S is constructed, such that the cyclic objects and are isomorphic. This extends a theorem by Jara and Ştefan for Hopf Galois extensions. As an application, we compute Hochschild and cyclic homologies of a groupoid with coefficients in a stable anti-Yetter-Drinfel’d module, by tracing it back to the group case. In particular, we obtain explicit expressions for (coinciding relative and ordinary) Hochschild and cyclic homologies of a groupoid. The latter extends results of Burghelea on cyclic homology of groups.     

Dynamical Differential Equations Compatible with Rational <Emphasis Type="Italic">qKZ</Emphasis> Equations

For the Lie algebra _N we introduce a system of differential operators called the dynamical operators. We prove that the dynamical differential operators commute with the _N rational quantized Knizhnik–Zamolodchikov difference operators. We describe the transformations of the dynamical operators under the natural action of the _N Weyl group.Mathematics Subject Classifications (2000). 17B37, 17B80, 81R10.     

Plane Symmetric Inhomogeneous Cosmological Models with a Perfect Fluid in General Relativity

In this paper we investigate a class of solutions of Einstein equations for the plane- symmetric perfect fluid case with shear and vanishing acceleration. If these solutions have shear, they must necessarily be non-static. We examine the integrable cases of the field equations systematically. Among the cases with shear we find three classes of solutions. PACS No.: 04.20.-q.     

Inhomogeneous dark energy and cosmological acceleration

We study the evolution of an inhomogeneous fluid with self-similarity of the second kind and anisotropic pressure. We found a class of solution to the Einstein field equations by assuming an equation of state where the radial pressure of the fluid is proportional to its energy density () and that the fluid moves along time-like geodesics. The equation of state combined with the self-similarity of second kind implies ω = −1. The energy conditions, geometrical and physical properties of the solutions are studied. We have found that, for the self-similar parameter , the solution represents an accelerated cosmological model ending in a Big Rip stage.     

Perturbative Solutions of the Extended Constraint Equations in General Relativity

The extended constraint equations arise as a special case of the conformal constraint equations that are satisfied by an initial data hypersurface in an asymptotically simple space-time satisfying the vacuum conformal Einstein equations developed by H. Friedrich. The extended constraint equations consist of a quasi-linear system of partial differential equations for the induced metric, the second fundamental form and two other tensorial quantities defined on , and are equivalent to the usual constraint equations that satisfies as a space-like hypersurface in a space-time satisfying Einstein’s vacuum equation. This article develops a method for finding perturbative, asymptotically flat solutions of the extended constraint equations in a neighbourhood of the flat solution on Euclidean space. This method is fundamentally different from the ‘classical’ method of Lichnerowicz and York that is used to solve the usual constraint equations.     

On the Global Wellposedness to the 3-D Incompressible Anisotropic Navier-Stokes Equations

Corresponding to the wellposedness result [2] for the classical 3-D Navier-Stokes equations (NS _ν) with initial data in the scaling invariant Besov space, here we consider a similar problem for the 3-D anisotropic Navier-Stokes equations (ANS _ν), where the vertical viscosity is zero. In order to do so, we first introduce the Besov-Sobolev type spaces, and Then with initial data in the scaling invariant space we prove the global wellposedness for (ANS _ν) provided the norm of initial data is small enough compared to the horizontal viscosity. In particular, this result implies the global wellposedness of (ANS _ν) with high oscillatory initial data (1.2).