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D. Lenz
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D. Lenz

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Mathematics - Functional Analysis (10)
Mathematics - Spectral Theory (10)
Mathematics - Dynamical Systems (9)
Mathematics - Mathematical Physics (8)
Astrophysics of Galaxies (8)
Mathematical Physics (8)
Nuclear Experiment (7)
Physics - Instrumentation and Detectors (5)
High Energy Physics - Experiment (5)
Mathematics - Probability (5)
Mathematics - Metric Geometry (3)
Mathematics - Combinatorics (2)
Mathematics - Analysis of PDEs (2)
Mathematics - Category Theory (2)
Instrumentation and Methods for Astrophysics (2)
Mathematics - Group Theory (2)
Physics - Data Analysis; Statistics and Probability (1)
Cosmology and Nongalactic Astrophysics (1)
Physics - Soft Condensed Matter (1)
Earth and Planetary Astrophysics (1)
Mathematics - Operator Algebras (1)
Mathematics - Number Theory (1)

Publications Authored By D. Lenz

The goal of this expository article is a fairly self-contained account of some averaging processes of functions along sequences of the form $(\alpha^n x)^{}_{n\in\mathbb{N}}$, where $\alpha$ is a fixed real number with $| \alpha | > 1$ and $x\in\mathbb{R}$ is arbitrary. Such sequences appear in a multitude of situations including the spectral theory of inflation systems in aperiodic order. Due to the connection with uniform distribution theory, the results will mostly be metric in nature, which means that they hold for Lebesgue-almost every $x\in\mathbb{R}$. Read More

We consider graphs associated to Delone sets in Euclidean space. Such graphs arise in various ways from tilings. Here, we provide a unified framework. Read More

Measurement of the Galactic neutral atomic hydrogen (HI) column density, NHI, and brightness temperatures, Tb, is of high scientific value for a broad range of astrophysical disciplines. In the past two decades, one of the most-used legacy HI datasets has been the Leiden/Argentine/Bonn Survey (LAB). We release the HI 4$\pi$ survey (HI4PI), an all-sky database of Galactic HI, which supersedes the LAB survey. Read More

We study the diffraction and dynamical properties of translation bounded weakly almost periodic measures. We prove that the dynamical hull of a weakly almost periodic measure is a weakly almost periodic dynamical system with unique minimal component given by the hull of the strongly almost periodic component of the measure. In particular the hull is minimal if and only if the measure is strongly almost periodic and the hull is always measurably conjugate to a torus and has pure point spectrum with continuous eigenfunctions. Read More

The HI halo clouds of the Milky Way, and in particular the intermediate-velocity clouds (IVCs), are thought to be connected to Galactic fountain processes. Observations of fountain clouds are important for understanding the role of matter recycling and accretion onto the Galactic disk and subsequent star formation. Here, we quantify the amount of molecular gas in the Galactic halo. Read More

In this article, we present a new method to treat uniqueness of form extensions in a rather general setting including various magnetic Schr\"odinger forms. The method is based on the theory of ordered Hilbert spaces and the concept of domination of semigroups. We review this concept in an abstract setting and give a characterization in terms of the associated forms. Read More

We study dynamical systems $(X,G,m)$ with a compact metric space $X$ and a locally compact, $\sigma$-compact, abelian group $G$. We show that such a system has discrete spectrum if and only if a certain space average over the metric is a Bohr almost periodic function. In this way, this average over the metric plays for general dynamical systems a similar role as the autocorrelation measure plays in the study of aperiodic order for special dynamical systems based on point sets. Read More

The Cryogenic Underground Observatory for Rare Events (CUORE) is a ton-scale cryogenic experiment designed to search for neutrinoless double-beta decay of $^{130}$Te and other rare events. The CUORE detector consists of 988 TeO$_2$ bolometers operated underground at 10 mK in a dilution refrigerator at the Laboratori Nazionali del Gran Sasso. Candidate events are identified through a precise measurement of their energy. Read More

It is well known that, given an equivariant and continuous (in a suitable sense) family of selfadjoint operators in a Hilbert space over a minimal dynamical system, the spectrum of all operators from that family coincides. As shown recently similar results also hold for suitable families of non-selfadjoint operators in $\ell^p (\ZM)$. Here, we generalize this to a large class of bounded linear operator families on Banach-space valued $\ell^p$-spaces over countable discrete groups. Read More

We prove a quantitative uncertainty principle at low energies for the Laplacian on fairly general weighted graphs with a uniform explicit control of the constants in terms of geometric quantities. A major step consists in establishing lower bounds for Dirichlet eigenvalues in terms of the geometry. Read More

We construct model sets arising from cut and project schemes in Euclidean spaces whose associated Delone dynamical systems have positive toplogical entropy. The construction works both with windows that are proper and with windows that have empty interior. In a probabilistic construction, the entropy almost surely turns out to be proportional to the measure of the boundary of the window. Read More

Data gridding is a common task in astronomy and many other science disciplines. It refers to the resampling of irregularly sampled data to a regular grid. We present cygrid, a library module for the general purpose programming language Python. Read More

Authors: J. Kerp1, D. Lenz2, T. Roehser3
Affiliations: 1Argelander-Institut fuer Astronomie, Bonn University, 2Argelander-Institut fuer Astronomie, Bonn University, 3Argelander-Institut fuer Astronomie, Bonn University

A recent discovery of two stellar clusters associated with the diffuse high-latitude cloud HRK 81.4-77.8 has important implications for star formation in the Galactic halo. Read More

Affiliations: 1Argelander-Institut fuer Astronomie, 2Argelander-Institut fuer Astronomie, 3Argelander-Institut fuer Astronomie, 4Argelander-Institut fuer Astronomie, 5Argelander-Institut fuer Astronomie, 6Max-Planck-Institut fuer Radioastronomie

The subsequent coalescence of low--mass halos over cosmic time is thought to be the major formation channel of massive spiral galaxies like the Milky Way and the Andromeda Galaxy (M31). The gaseous halo of a massive galaxy is considered to be the reservoir of baryonic matter persistently fueling the star formation in the disk. Because of its proximity, M31 is the ideal object for studying the structure of the halo gas in great detail. Read More

We investigate data from the Galactic Effelsberg--Bonn HI Survey (EBHIS), supplemented with data from the third release of the Galactic All Sky Survey (GASS III) observed at Parkes. We explore the all sky distribution of the local Galactic HI gas with $|v_{\rm LSR}| < 25 $ kms$^{-1}$ on angular scales of 11' to 16'. Unsharp masking (USM) is applied to extract small scale features. Read More

Various spectral notions have been employed to grasp the structure of point sets, in particular non-periodic ones. In this article, we present them in a unified setting and explain the relations between them. For the sake of readability, we use Delone sets in Euclidean space as our main object class, and give generalisations in the form of further examples and remarks. Read More

Because isolated high-velocity clouds (HVCs) are found at great distances from the Galactic radiation field and because they have subsolar metallicities, there have been no detections of dust in these structures. A key problem in this search is the removal of foreground dust emission. Using the Effelsberg-Bonn HI Survey and the Planck far-infrared data, we investigate a bright, cold, and clumpy HVC. Read More

The Effelsberg-Bonn HI Survey (EBHIS) is a new 21-cm survey performed with the 100-m telescope at Effelsberg. It covers the whole northern sky out to a redshift of z~0.07 and comprises HI line emission from the Milky Way and the Local Volume. Read More

Affiliations: 1Bielefeld, 2Jena, 3Jena

We show that binary Toeplitz flows can be interpreted as Delone dynamical systems induced by model sets and analyse the quantitative relations between the respective system parameters. This has a number of immediate consequences for the theory of model sets. In particular, we use our results in combination with special examples of irregular Toeplitz flows from the literature to demonstrate that irregular proper model sets may be uniquely ergodic and do not need to have positive entropy. Read More

There is a recently discovered connection between the spectral theory of Schr\"o-dinger operators whose potentials exhibit aperiodic order and that of Laplacians associated with actions of groups on regular rooted trees, as Grigorchuk's group of intermediate growth. We give an overview of corresponding results, such as different spectral types in the isotropic and anisotropic cases, including Cantor spectrum of Lebesgue measure zero and absence of eigenvalues. Moreover, we discuss the relevant background as well as the combinatorial and dynamical tools that allow one to establish the afore-mentioned connection. Read More

We present a simple observation showing that the heat kernel on a locally finite graph behaves for short times $t$ roughly like $t^d$, where $d$ is the combinatorial distance. This is very different from the classical Varadhan type behavior on manifolds. Moreover, this also gives that short time behavior and global behavior of the heat kernel are governed by two different metrics whenever the degree of the graph is not uniformly bounded. Read More

The classical theory of invariant means, which plays an important role in the theory of paradoxical decompositions, is based upon what are usually termed `pseudogroups'. Such pseudogroups are in fact concrete examples of the Boolean inverse monoids which give rise to etale topological groupoids under non-commutative Stone duality. We accordingly initiate the theory of invariant means on arbitrary Boolean inverse monoids. Read More

We consider diffraction of Delone sets in Euclidean space. We show that the set of Bragg peaks with high intensity is always Meyer (if it is relatively dense). We use this to provide a new characterization for Meyer sets in terms of positive and positive definite measures. Read More

We study spectral properties of the Laplacians on Schreier graphs arising from Grigorchuk's group acting on the boundary of the infinite binary tree. We establish a connection between the action of $G$ on its space of Schreier graphs and a subshift associated to a non-primitive substitution and relate the Laplacians on the Schreier graphs to discrete Schroedinger operators with aperiodic order. We use this relation to prove that the spectrum of the anisotropic Laplacians is a Cantor set of Lebesgue measure zero. Read More

We consider equivariant continuous families of discrete one-dimensional operators over arbitrary dynamical systems. We introduce the concept of a pseudo-ergodic element of a dynamical system. We then show that all operators associated to pseudo-ergodic elements have the same spectrum and that this spectrum agrees with their essential spectrum. Read More

We study global properties of Dirichlet forms such as uniqueness of the Dirichlet extension, stochastic completeness and recurrence. We characterize these properties by means of vanishing of a boundary term in Green's formula for functions from suitable function spaces and suitable operators arising from extensions of the underlying form. We first present results in the framework of general Dirichlet forms on $\sigma$-finite measure spaces. Read More

Given the current and past star-formation in the Milky Way in combination with the limited gas supply, the re-fuelling of the reservoir of cool gas is an important aspect of Galactic astrophysics. The infall of \ion{H}{i} halo clouds can, among other mechanisms, contribute to solving this problem. We study the intermediate-velocity cloud IVC135+54 and its spatially associated high-velocity counterpart to look for signs of a past or ongoing interaction. Read More

We study a special class of graphs with a strong transience feature called uniform transience. We characterize uniform transience via a Feller-type property and via validity of an isoperimetric inequality. We then give a further characterization via equality of the Royden boundary and the harmonic boundary and show that the Dirichlet problem has a unique solution for such graphs. Read More

We put forward the concept of measure graphs. These are (possibly uncountable) graphs equipped with an action of a groupoid and a measure invariant under this action. Examples include periodic graphs, fractal graphs, graphings and percolation graphs. Read More

We discuss the application of various concepts from the theory of topological dynamical systems to Delone sets and tilings. We consider in particular, the maximal equicontinuous factor of a Delone dynamical system, the proximality relation and the enveloping semigroup of such systems. Read More

We consider diffusion on discrete measure spaces as encoded by Markovian semigroups arising from weighted graphs. We study whether the graph is uniquely determined if the diffusion is given up to order isomorphism. If the graph is recurrent then the complete graph structure and the measure space are determined (up to an overall scaling). Read More

Trees of finite cone type have appeared in various contexts. In particular, they come up as simplified models of regular tessellations of the hyperbolic plane. The spectral theory of the associated Laplacians can thus be seen as induced by geometry. Read More

The OLYMPUS experiment was designed to measure the ratio between the positron-proton and electron-proton elastic scattering cross sections, with the goal of determining the contribution of two-photon exchange to the elastic cross section. Two-photon exchange might resolve the discrepancy between measurements of the proton form factor ratio, $\mu_p G^p_E/G^p_M$, made using polarization techniques and those made in unpolarized experiments. OLYMPUS operated on the DORIS storage ring at DESY, alternating between 2. Read More

We consider an arbitrary selfadjoint operator on a separable Hilbert space. To this operator we construct an expansion in generalized eigenfunctions in which the original Hilbert space is decomposed as a direct integral of Hilbert spaces consisting of general eigenfunctions. This automatically gives a Plancherel type formula. Read More

We consider weighted graphs with an infinite set of vertices. We show that boundedness of all functions of finite energy can be seen as a notion of `relative compactness' for such graphs and study sufficient and necessary conditions for this property in terms of various metrics. We then equip graphs satisfying this property with a finite measure and investigate the associated Laplacian and its semigroup. Read More

We study Schr\"odinger operators on $\R$ with measures as potentials. Choosing a suitable subset of measures we can work with a dynamical system consisting of measures. We then relate properties of this dynamical system with spectral properties of the associated operators. Read More

It is well-known that the dynamical spectrum of an ergodic measure dynamical system is related to the diffraction measure of a typical element of the system. This situation includes ergodic subshifts from symbolic dynamics as well as ergodic Delone dynamical systems, both via suitable embeddings. The connection is rather well understood when the spectrum is pure point, where the two spectral notions are essentially equivalent. Read More

We establish several new relations between the discrete transition operator, the continuous Laplacian and the averaging operator associated with combinatorial and metric graphs. It is shown that these operators can be expressed through each other using explicit expressions. In particular, we show that the averaging operator is closely related with the solutions of the associated wave equation. Read More

We develop the theory of distributive inverse semigroups as the analogue of distributive lattices without top element and prove that they are in a duality with those etale groupoids having a spectral space of identities, where our spectral spaces are not necessarily compact. We prove that Boolean inverse semigroups can be characterized as those distributive inverse semigroups in which every prime filter is an ultrafilter; we also provide a topological characterization in terms of Hausdorffness. We extend the notion of the patch topology to distributive inverse semigroups and prove that every distributive inverse semigroup has a Booleanization. Read More

Authors: GERDA Collaboration, K. -H. Ackermann, M. Agostini, M. Allardt, M. Altmann, E. Andreotti, A. M. Bakalyarov, M. Balata, I. Barabanov, M. Barnabe Heider, N. Barros, L. Baudis, C. Bauer, N. Becerici-Schmidt, E. Bellotti, S. Belogurov, S. T. Belyaev, G. Benato, A. Bettini, L. Bezrukov, T. Bode, V. Brudanin, R. Brugnera, D. Budjas, A. Caldwell, C. Cattadori, A. Chernogorov, O. Chkvorets, F. Cossavella, A. D`Andragora, E. V. Demidova, A. Denisov, A. di Vacri, A. Domula, V. Egorov, R. Falkenstein, A. Ferella, K. Freund, F. Froborg, N. Frodyma, A. Gangapshev, A. Garfagnini, J. Gasparro, S. Gazzana, R. Gonzalez de Orduna, P. Grabmayr, V. Gurentsov, K. Gusev, K. K. Guthikonda, W. Hampel, A. Hegai, M. Heisel, S. Hemmer, G. Heusser, W. Hofmann, M. Hult, L. V. Inzhechik, L. Ioannucci, J. Janicsko Csalty, J. Jochum, M. Junker, R. Kankanyan, S. Kianovsky, T. Kihm, J. Kiko, I. V. Kirpichnikov, A. Kirsch, A. Klimenko, M. Knapp, K. T. Knöpfle, O. Kochetov, V. N. Kornoukhov, K. Kröninger, V. Kusminov, M. Laubenstein, A. Lazzaro, V. I. Lebedev, B. Lehnert, D. Lenz, H. Liao, M. Lindner, I. Lippi, J. Liu, X. Liu, A. Lubashevskiy, B. Lubsandorzhiev, A. A. Machado, B. Majorovits, W. Maneschg, G. Marissens, S. Mayer, G. Meierhofer, I. Nemchenok, L. Niedermeier, S. Nisi, J. Oehm, C. O'Shaughnessy, L. Pandola, P. Peiffer, K. Pelczar, A. Pullia, S. Riboldi, F. Ritter, C. Rossi Alvarez, C. Sada, M. Salathe, C. Schmitt, S. Schönert, J. Schreiner, J. Schubert, O. Schulz, U. Schwan, B. Schwingenheuer, H. Seitz, E. Shevchik, M. Shirchenko, H. Simgen, A. Smolnikov, L. Stanco, F. Stelzer, H. Strecker, M. Tarka, U. Trunk, C. A. Ur, A. A. Vasenko, S. Vogt, O. Volynets, K. von Sturm, V. Wagner, M. Walter, A. Wegmann, M. Wojcik, E. Yanovich, P. Zavarise, I. Zhitnikov, S. V. Zhukov, D. Zinatulina, K. Zuber, G. Zuzel

The GERDA collaboration is performing a search for neutrinoless double beta decay of ^{76}Ge with the eponymous detector. The experiment has been installed and commissioned at the Laboratori Nazionali del Gran Sasso and has started operation in November 2011. The design, construction and first operational results are described, along with detailed information from the R&D phase. Read More

We perform extensive monomer-resolved computer simulations of suitably-designed amphiphilic dendritic macromolecules over a broad range of densities, proving the existence and stability of cluster crystals formed in these systems, as predicted previously on the basis of effective pair potentials [B. M. Mladek et al. Read More


In this article we describe the background challenges for the CUORE experiment posed by surface contamination of inert detector materials such as copper, and present three techniques explored to mitigate these backgrounds. Using data from a dedicated test apparatus constructed to validate and compare these techniques we demonstrate that copper surface contamination levels better than 10E-07 - 10E-08 Bq/cm2 are achieved for 238U and 232Th. If these levels are reproduced in the final CUORE apparatus the projected 90% C. Read More


We report the results of a search for axions from the 14.4 keV M1 transition from Fe-57 in the core of the sun using the axio-electric effect in TeO2 bolometers. The detectors are 5x5x5 cm3 crystals operated at about 10 mK in a facility used to test bolometers for the CUORE experiment at the Laboratori Nazionali del Gran Sasso in Italy. Read More


We collected 19.4 days of data from four 750 g TeO2 bolometers, and in three of them we were able to set the energy threshold around 3 keV using a new analysis technique. We found a background rate ranging from 25 cpd/keV/kg at 3 keV to 2 cpd/keV/kg at 25 keV, and a peak at 4. Read More

We consider metric graphs with a uniform lower bound on the edge lengths but no further restrictions. We discuss how to describe every local self-adjoint Laplace operator on such graphs by boundary conditions in the vertices given by projections and self-adjoint operators. We then characterize the lower bounded self-adjoint Laplacians and determine their associated quadratic form in terms of the operator families encoding the boundary conditions. Read More

We consider Delone sets with finite local complexity. We characterize validity of a subadditive ergodic theorem by uniform positivity of certain weights. The latter can be considered to be an averaged version of linear repetitivity. Read More

The GERDA and Majorana experiments will search for neutrinoless double-beta decay of germanium-76 using isotopically enriched high-purity germanium detectors. Although the experiments differ in conceptual design, they share many aspects in common, and in particular will employ similar data analysis techniques. The collaborations are jointly developing a C++ software library, MGDO, which contains a set of data objects and interfaces to encapsulate, store and manage physical quantities of interest, such as waveforms and high-purity germanium detector geometries. Read More

We consider the construction and classification of some new mathematical objects, called ergodic spatial stationary processes, on locally compact Abelian groups, which provide a natural and very general setting for studying diffraction and the famous inverse problems associated with it. In particular we can construct complete families of solutions to the inverse problem from any given pure point measure that is chosen to be the diffraction. In this case these processes can be classified by the dual of the group of relators based on the set of Bragg peaks, and this gives a solution to the homometry problem for pure point diffraction. Read More