Bloch electron in a magnetic field and the Ising model

The spectral determinant det(H-\epsilon I) of the Azbel-Hofstadter Hamiltonian H is related to Onsager's partition function of the 2D Ising model for any value of magnetic flux \Phi=2\pi P/Q through an elementary cell, where P and Q are coprime integers. The band edges of H correspond to the critical temperature of the Ising model; the spectral determinant at these (and other points defined in a certain similar way) is independent of P. A connection of the mean of Lyapunov exponents to the asymptotic (large Q) bandwidth is indicated.Comment: 4 pages, 1 figure, REVTE

On semiclassical dispersion relations of Harper-like operators

We describe some semiclassical spectral properties of Harper-like operators, i.e. of one-dimensional quantum Hamiltonians periodic in both momentum and position. The spectral region corresponding to the separatrices of the classical Hamiltonian is studied for the case of integer flux. We derive asymptotic formula for the dispersion relations, the width of bands and gaps, and show how geometric characteristics and the absence of symmetries of the Hamiltonian influence the form of the energy bands.Comment: 13 pages, 8 figures; final version, to appear in J. Phys. A (2004

Sampling of Borehole WL-3A through -12 in Support of the Vadose Zone Transport Field Study

This report presents the results of the fiscal year 2001 core sampling effort conducted to support the Vadose Zone Transport Field Study

Bethe ansatz for the Harper equation: Solution for a small commensurability parameter

The Harper equation describes an electron on a 2D lattice in magnetic field and a particle on a 1D lattice in a periodic potential, in general, incommensurate with the lattice potential. We find the distribution of the roots of Bethe ansatz equations associated with the Harper equation in the limit as alpha=1/Q tends to 0, where alpha is the commensurability parameter (Q is integer). Using the knowledge of this distribution we calculate the higher and lower boundaries of the spectrum of the Harper equation for small alpha. The result is in agreement with the semiclassical argument, which can be used for small alpha.Comment: 17 pages including 5 postscript figures, Latex, minor changes, to appear in Phys.Rev.

A Catalog of Geologic Data for the Hanford Site

This report catalogs the existing geologic data that can be found in various databases, published and unpublished reports, and in individuals' technical files. The scope of this catalog is primarily on the 100, 200, and 300 Areas, with a particular emphasis on the 200 Areas. Over 2,922 wells are included in the catalog. Nearly all of these wells (2,459) have some form of driller's or geologist's log. Archived samples are available for 1,742 wells. Particle size data are available from 1,078 wells and moisture data are available from 356 wells. Some form of chemical property data is available from 588 wells. However, this catalog is by no means complete. Numerous individuals have been involved in various geologic-related studies of the Hanford Site. The true extent of unpublished data retained in their technical files is unknown. However, this data catalog is believed to represent the majority (>90%) of the geologic data that is currently retrievable

Decorrelation of a class of Gibbs particle processes and asymptotic properties of U-statistics

We study a stationary Gibbs particle process with deterministically bounded particles on Euclidean space defined in terms of an activity parameter and non-negative interaction potentials of finite range. Using disagreement percolation we prove exponential decay of the correlation functions, provided a dominating Boolean model is subcritical. We also prove this property for the weighted moments of a U-statistic of the process. Under the assumption of a suitable lower bound on the variance, this implies a central limit theorem for such U-statistics of the Gibbs particle process. A byproduct of our approach is a new uniqueness result for Gibbs particle processes

Essential spectra of difference operators on \sZ^n-periodic graphs

Let (\cX, \rho) be a discrete metric space. We suppose that the group \sZ^n acts freely on $X$ and that the number of orbits of $X$ with respect to this action is finite. Then we call $X$ a \sZ^n-periodic discrete metric space. We examine the Fredholm property and essential spectra of band-dominated operators on $l^p(X)$ where $X$ is a \sZ^n-periodic discrete metric space. Our approach is based on the theory of band-dominated operators on \sZ^n and their limit operators. In case $X$ is the set of vertices of a combinatorial graph, the graph structure defines a Schr\"{o}dinger operator on $l^p(X)$ in a natural way. We illustrate our approach by determining the essential spectra of Schr\"{o}dinger operators with slowly oscillating potential both on zig-zag and on hexagonal graphs, the latter being related to nano-structures

Piezoelectricity: Quantized Charge Transport Driven by Adiabatic Deformations

We study the (zero temperature) quantum piezoelectric response of Harper-like models with broken inversion symmetry. The charge transport in these models is related to topological invariants (Chern numbers). We show that there are arbitrarily small periodic modulations of the atomic positions that lead to nonzero charge transport for the electrons.Comment: Latex, letter. Replaced version with minor change in style. 1 fi

Ferroelectric and Incipient Ferroelectric Properties of a Novel Sr_(9-x)PbxCe2Ti2O36 (x=0-9) Ceramic System

Sr_(9-x)PbxCe2Ti12O36 system is derived from the perovskite SrTiO3 and its chemical formula can be written as (Sr_(1-y)Pby)0.75Ce0.167TiO3. We investigated dielectric response of Sr_(9-x)PbxCe2Ti12O36 ceramics (x = 0-9) between 100 Hz and 100 THz at temperatures from 10 to 700 K using low- and high-frequency dielectric, microwave (MW), THz and infrared spectroscopy. We revealed that Sr9Ce2Ti12O36 is an incipient ferroelectric with the R-3c trigonal structure whose relative permittivity e' increases from 167 at 300 K and saturates near 240 below 30 K. The subsequent substitution of Sr by Pb enhances e' to several thousands and induces a ferroelectric phase transition to monoclinic Cc phase for x>=3. Its critical temperature Tc linearly depends on the Pb concentration and reaches 550 K for x=9. The phase transition is of displacive type. The soft mode frequency follows the Barrett formula in samples with x=3. The MW dispersion is lacking and quality factor Q is high in samples with low Pb concentration, although the permittivity is very high in some cases. However, due to the lattice softening, the temperature coefficient of the permittivity is rather high. The best MW quality factor was observed for x=1: Q*f=5800 GHz and e'=250. Concluding, the dielectric properties of Sr_(9- x)PbxCe2Ti12O36 are similar to those of Ba_(1-x)SrxTiO3 so that this system can be presumably used as an alternative for MW devices or capacitors.Comment: subm. to Chem. Mate

Cell shape analysis of random tessellations based on Minkowski tensors

To which degree are shape indices of individual cells of a tessellation characteristic for the stochastic process that generates them? Within the context of stochastic geometry and the physics of disordered materials, this corresponds to the question of relationships between different stochastic models. In the context of image analysis of synthetic and biological materials, this question is central to the problem of inferring information about formation processes from spatial measurements of resulting random structures. We address this question by a theory-based simulation study of shape indices derived from Minkowski tensors for a variety of tessellation models. We focus on the relationship between two indices: an isoperimetric ratio of the empirical averages of cell volume and area and the cell elongation quantified by eigenvalue ratios of interfacial Minkowski tensors. Simulation data for these quantities, as well as for distributions thereof and for correlations of cell shape and volume, are presented for Voronoi mosaics of the Poisson point process, determinantal and permanental point processes, and Gibbs hard-core and random sequential absorption processes as well as for Laguerre tessellations of polydisperse spheres and STIT- and Poisson hyperplane tessellations. These data are complemented by mechanically stable crystalline sphere and disordered ellipsoid packings and area-minimising foam models. We find that shape indices of individual cells are not sufficient to unambiguously identify the generating process even amongst this limited set of processes. However, we identify significant differences of the shape indices between many of these tessellation models. Given a realization of a tessellation, these shape indices can narrow the choice of possible generating processes, providing a powerful tool which can be further strengthened by density-resolved volume-shape correlations.Comment: Chapter of the forthcoming book "Tensor Valuations and their Applications in Stochastic Geometry and Imaging" in Lecture Notes in Mathematics edited by Markus Kiderlen and Eva B. Vedel Jense