Interplay of charge, spin, orbital and lattice correlations in colossal magnetoresistance manganites

We derive a realistic microscopic model for doped colossal magnetoresistance manganites, which includes the dynamics of charge, spin, orbital and lattice degrees of freedom on a quantum mechanical level. The model respects the SU(2) spin symmetry and the full multiplet structure of the manganese ions within the cubic lattice. Concentrating on the hole doped domain ( 0≤x≤0.5) we study the influence of the electron-lattice interaction on spin and orbital correlations by means of exact diagonalisation techniques. We find that the lattice can cause a considerable suppression of the coupling between spin and orbital degrees of freedom and show how changes in the magnetic correlations are reflected in dynamic phonon correlations. In addition, our calculation gives detailed insights into orbital correlations and demonstrates the possibility of complex orbital states. Received 4 September 2002 / Received in final form 8 November 2002 Published online 31 December 2002     

Comprehensive study on the formation of polyelectrolyte complexes from (quaternized) poly[2‐(dimethylamino)ethyl methacrylate] and poly(2‐acrylamido‐2‐methylpropane sodium sulfonate)

Polyelectrolyte complexes (PECs) have been prepared from well‐defined (quaternized) poly[2‐(dimethylamino)ethyl methacrylate] (PDMAEMA) and high molecular weight poly(2‐acrylamido‐2‐methylpropane sodium sulfonate) (PAMPSNa) after a thorough study of their viscometric properties. The effect of pH and quaternization degree of PDMAEMA on PECs stoichiometry has been examined. PEC‐based materials have been characterized in terms of thermal stability, equilibrium swelling degree, and free/bound water composition. The stoichiometry and swellability of the physically crosslinked hydrogels obtained from fully quaternized PDMAEMA/PAMPSNa complexes do not depend on pH. In contrast, PECs made of non quaternized PDMAEMA and PAMPSNa are highly affected by pH, and could reversibly disintegrate at pH ≥ 9. Partially quaternized PDMAEMA/PAMPSNa PECs exhibit intermediate properties and form stable loose structures in the whole investigated pH range. Finally, stable dispersions of PECs nanoparticles have been successfully produced from dilute solutions of the complementary polyelectrolytes. The nanoparticle average diameter as determined by dynamic light scattering proved to depend on the molar fraction of DMAEMA‐based subunits and on the initial polyelectrolyte concentration. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5468–5479, 2006     

Non-gravitating scalars and spacetime compactification

We discuss role of partially gravitating scalar fields, scalar fields whose energy–momentum tensors vanish for a subset of dimensions, in dynamical compactification of a given set of dimensions. We show that the resulting spacetime exhibits a factorizable geometry consisting of usual four-dimensional spacetime with full Poincaré invariance times a manifold of extra dimensions whose size and shape are determined by the scalar field dynamics. Depending on the strength of its coupling to the curvature scalar, the vacuum expectation value (VEV) of the scalar field may or may not vanish. When its VEV is zero the higher-dimensional spacetime is completely flat and there is no compactification effect at all. On the other hand, when its VEV is nonzero the extra dimensions get spontaneously compactified. The compactification process is such that a bulk cosmological constant is utilized for curving the extra dimensions.     

Entropy of Bogoliubov automorphisms of the canonical anticommutation relations

We compute the entropyh _A ( _U ) in the sense of Connes, Narnhofer and Thirring of Bogoliubov automorphisms _U of the CAR-algebra with respect to invariant quasifree states _A with 0A1 having pure point spectrum.Supported in part by a grant from the National Science Foundation     

Integration on then th power of a hyperbolic space in terms of invariants under diagonal action of isometries (Lorentz transformations)

The integral of a function over then'th power of hyperbolicd-dimensional spaceH is decomposed into integration along each orbit under diagonal action onH ⁿ of the isometry groupG onH, followed by integration over the orbit space, parametrized in terms of a complete set of invariants. The Jacobian entering in this last integral is expressed explicitly in terms of certain determinants. When viewingH as a half-hyperboloid in _d+1 ,G is induced by the homogeneous Lorentz groupO (1,d) acting on _d+1 .