Approximation by point potentials in a magnetic field

We discuss magnetic Schrodinger operators perturbed by measures from the generalized Kato class. Using an explicit Krein-like formula for their resolvent, we prove that these operators can be approximated in the strong resolvent sense by magnetic Schrodinger operators with point potentials. Since the spectral problem of the latter operators is solvable, one in fact gets an alternative way to calculate discrete spectra; we illustrate it by numerical calculations in the case when the potential is supported by a circle.Comment: 16 pages, 2 eps figures, submitted to J. Phys.

Lower bounds for nodal sets of eigenfunctions

We prove lower bounds for the Hausdorff measure of nodal sets of eigenfunctions.Comment: To appear in Communications in Mathematical Physics; revised to include two additional references and update bibliographic informatio

Lower bounds for nodal sets of Dirichlet and Neumann eigenfunctions

Let \phi\ be a Dirichlet or Neumann eigenfunction of the Laplace-Beltrami operator on a compact Riemannian manifold with boundary. We prove lower bounds for the size of the nodal set {\phi=0}.Comment: 7 page

Spin Gap in the Single Spin-1/2 Chain Cuprate Sr1.9_{1.9}Ca0.1_{0.1}CuO3_3

We report $^{63}$Cu nuclear magnetic resonance and muon spin rotation measurements on the S=1/2 antiferromagnetic Heisenberg spin chain compound Sr$_{1.9}$Ca$_{0.1}$CuO$_3$. An exponentially decreasing spin-lattice relaxation rate 1/T$_1$ indicates the opening of a spin gap. This behavior is very similar to what has been observed for the cognate zigzag spin chain compound Sr$_{0.9}$Ca$_{0.1}$CuO$_2$, and confirms that the occurrence of a spin gap upon Ca doping is independent of the interchain exchange coupling $J'$. Our results therefore generally prove the appearance of a spin gap in an antiferromagnetic Heisenberg spin chain induced by a local bond disorder of the intrachain exchange coupling $J$. A low temperature upturn of 1/T$_1$ evidences growing magnetic correlations. However, zero field muon spin rotation measurements down to 1.5 K confirm the absence of magnetic order in this compound which is most likely suppressed by the opening of the spin gap.Comment: 5 pages, 4 figure

Heat kernels on curved cones

A functorial derivation is presented of a heat-kernel expansion coefficient on a manifold with a singular fixed point set of codimension two. The existence of an extrinsic curvature term is pointed out.Comment: 4p.,sign errors corrected and a small addition,uses JyTeX,MUTP/94/0

Magnetoelectric coupling in a frustrated spinel studied using high-field scanning probe microscopy

Below its N\'eel temperature, the frustrated magnet CdCr$_2$O$_4$ exhibits an antiferromagnetic spin-spiral ground state. Such states can give rise to a sizable magnetoelectric coupling. In this report, we measure the electric polarization induced in single-crystalline CdCr$_2$O$_4$ by a large applied magnetic field. Because the detection of a macroscopic polarization is hindered by the structural domains in the tetragonal spin-spiral phase, we have pioneered an alternative method of measuring polarization induced by high magnetic fields, using electrostatic force microscopy. This method enables us to measure polarization from nanometer sized areas of the sample surface, as well as imaging how to charge inhomogeneities change with magnetic field.Comment: 5 pages, 3 figure

CeRuPO: A rare example of a Ferromagnetic Kondo lattice

We have determined the physical ground state properties of the compounds CeRuPO and CeOsPO by means of magnetic susceptibility chi(T), specific heat C(T), electrical resistivity rho(T), and thermopower S(T) measurements. chi(T) reveals a trivalent 4f1 cerium state in both compounds. For CeRuPO a pronounced decrease of rho(T) below 50K indicates the onset of coherent Kondo scattering which is confirmed by enhanced S(T). The temperature and magnetic field dependence of chi(T) and C(T) evidence ferromagnetic (FM) order at TC=15K. Thus, CeRuPO seems to be one of the rare example of a FM Kondo lattice. In contrast, CeOsPO shows antiferromagnetic order at TN=4.4K despite only minor changes in lattice parameters and electronic configuration. Additional 31P NMR results support these scenarios. LSDA+U calculations evidence a quasi two dimensional electronic band structure, reflecting a strong covalent bonding within the CeO and RuP layers and a weak ionic like bonding between the layers.Comment: accepted in Phys. Rev. B, high quality figures: http://www.cpfs.mpg.de/~krellner

Parametrizations of density matrices

This article gives a brief overview of some recent progress in the characterization and parametrization of density matrices of finite dimensional systems. We discuss in some detail the Bloch-vector and Jarlskog parametrizations and mention briefly the coset parametrization. As applications of the Bloch parametrization we discuss the trace invariants for the case of time dependent Hamiltonians and in some detail the dynamics of three-level systems. Furthermore, the Bloch vector of two-qubit systems as well as the use of the polarization operator basis is indicated. As the main application of the Jarlskog parametrization we construct density matrices for composite systems. In addition, some recent related articles are mentioned without further discussion.Comment: 31 pages. v2: 32 pages, Abstract and Introduction rewritten and Conclusion section added, references adde

Common effect of chemical and external pressures on the magnetic properties of RECoPO (RE = La, Pr)

We report a detailed investigation of RECoPO (RE = La, Pr) and LaCoAsO materials performed by means of muon spin spectroscopy. Zero-field measurements show that the electrons localized on the Pr$^{3+}$ ions do not play any role in the static magnetic properties of the compounds. Magnetism at the local level is indeed fully dominated by the weakly-itinerant ferromagnetism from the Co sublattice only. The increase of the chemical pressure triggered by the different ionic radii of La$^{3+}$ and Pr$^{3+}$, on the other hand, plays a crucial role in enhancing the value of the magnetic critical temperature and can be mimicked by the application of external hydrostatic pressure up to 24 kbar. A sharp discontinuity in the local magnetic field at the muon site in LaCoPO at around 5 kbar suggests a sizeable modification in the band structure of the material upon increasing pressure. This scenario is qualitatively supported by \emph{ab-initio} density-functional theory calculations.Comment: 13 pages, 10 figure