Almost holomorphic Poincare series corresponding to products of harmonic Siegel-Maass forms

We investigate Poincar\'e series, where we average products of terms of Fourier series of real-analytic Siegel modular forms. There are some (trivial) special cases for which the products of terms of Fourier series of elliptic modular forms and harmonic Maass forms are almost holomorphic, in which case the corresponding Poincar\'e series are almost holomorphic as well. In general this is not the case. The main point of this paper is the study of Siegel-Poincar\'e series of degree $2$ attached to products of terms of Fourier series of harmonic Siegel-Maass forms and holomorphic Siegel modular forms. We establish conditions on the convergence and nonvanishing of such Siegel-Poincar\'e series. We surprisingly discover that these Poincar\'e series are almost holomorphic Siegel modular forms, although the product of terms of Fourier series of harmonic Siegel-Maass forms and holomorphic Siegel modular forms (in contrast to the elliptic case) is not almost holomorphic. Our proof employs tools from representation theory. In particular, we determine some constituents of the tensor product of Harish-Chandra modules with walls

VELOX – A Demonstration Facilility for Lunar Oxygen Extraction in a Laboratory Environment

The ultimate goal of a permanent human presence on the Moon is discussed intensively within the global lunar community. Obviously, such an effort poses stringent demands not only on the technology but also on logistics, especially considering the important aspects of masses and volume for materials and replenishments of consumables. On-site propellant production (i.e. liquid oxygen) is one of the main needs and would lead to more efficient return-to-Earth or further exploration missions. Additionally, the supply of breathable air and water for the survival of the crew on the lunar surface is also a major aspect. Thus, large effort is put into the development and research of technologies for in-situ resources utilization (ISRU) to drastically reduce the required supply from Earth and to increase the level of autonomy of a lunar outpost. The major resource on the Moon for such a purpose is regolith, which covers the first meters of the lunar surface and contains about 45% of mineralogically bounded Oxygen in terms of mass. By using adequate processing methods of this material, one could be able to extract valuable minerals and volatiles for further utilization. At DLR Bremen a compact and flexible lab experimenting facility has been developed, built and tested, which shall demonstrate the feasibility of the process by extracting oxygen out of lunar regolith, respectively soil simulants and certain minerals in the laboratory case. For this purpose, important boundary conditions have been investigated such as temperatures during the process, chemical reaction characteristics and material properties for the buildup of the facility, which shall be analyzed within this paper. Since it is one of the most elaborated chemical processes regarding ISRU and has comparably low temperature and energy constraints it has been primarily concentrated on the Hydrogen-reduction process which reduces the iron oxide component of Ilmenite (FeTiO3) within the lunar regolith. Based on the obtained results, a first line-out of a planned superior test set-up and infrastructure with pre- and post-processing units such as feeding and extraction is also presented, as well as an analysis of reaction products with common methods. This paper will present the first results of DLR efforts regarding these topics. Finally, important aspects of the future development of the processes and technologies are discussed with special consideration of lunar applicability and with respect to environmental conditions as well as mass and energy constraints

Low-temperature properties of the Hubbard model on highly frustrated one-dimensional lattices

We consider the repulsive Hubbard model on three highly frustrated one-dimensional lattices -- sawtooth chain and two kagom\'{e} chains -- with completely dispersionless (flat) lowest single-electron bands. We construct the complete manifold of {\em exact many-electron} ground states at low electron fillings and calculate the degeneracy of these states. As a result, we obtain closed-form expressions for low-temperature thermodynamic quantities around a particular value of the chemical potential $\mu_0$. We discuss specific features of thermodynamic quantities of these ground-state ensembles such as residual entropy, an extra low-temperature peak in the specific heat, and the existence of ferromagnetism and paramagnetism. We confirm our analytical results by comparison with exact diagonalization data for finite systems.Comment: 20 pages, 12 figures, 2 table

Flat-Band Ferromagnetism as a Pauli-Correlated Percolation Problem

We investigate the location and nature of the para-ferro transition of interacting electrons in dispersionless bands using the example of the Hubbard model on the Tasaki lattice. This case can be analyzed as a geometric site-percolation problem where different configurations appear with nontrivial weights. We provide a complete exact solution for the 1D case and develop a numerical algorithm for the 2D case. In two dimensions the paramagnetic phase persists beyond the uncorrelated percolation point, and the grand-canonical transition is via a first-order jump to an unsaturated ferromagnetic phase.Comment: 6 pages, 5 figure

Lieb-Mattis ferrimagnetism in diluted magnetic semiconductors

We show the possibility of long-range ferrimagnetic ordering with a saturation magnetisation of the order of 1 Bohr magneton per spin for arbitrarily low concentration of magnetic impurities in semiconductors, provided that the impurities form a superstructure satisfying the conditions of the Lieb-Mattis theorem. Explicit examples of such superstructures are given for the wurtzite lattice, and the temperature of ferrimagnetic transition is estimated from a high-temperature expansion. Exact diagonalization studies show that small fragments of the structure exhibit enhanced magnetic response and isotropic superparamagnetism at low temperatures. A quantum transition in a high magnetic field is considered and similar superstructures in cubic semiconductors are discussed as well.Comment: 6 pages,4 figure

Mg I emission lines at 12 and 18 micrometer in K giants

The solar Mg I emission lines at 12 micrometer have already been observed and analyzed well. Previous modeling attempts for other stars have, however, been made only for Procyon and two cool evolved stars, with unsatisfactory results for the latter. We present high-resolution observational spectra for the K giants Pollux, Arcturus, and Aldebaran, which show strong Mg I emission lines at 12 micrometer as compared to the Sun. We also present the first observed stellar emission lines from Mg I at 18 micrometer and from Al I, Si I, and presumably Ca I at 12 micrometer. To produce synthetic line spectra, we employ standard non-LTE modeling for trace elements in cool stellar photospheres. We compute model atmospheres with the MARCS code, apply a comprehensive magnesium model atom, and use the radiative transfer code MULTI to solve for the magnesium occupation numbers in statistical equilibrium. We successfully reproduce the observed Mg I emission lines simultaneously in the giants and in the Sun, but show how the computed line profiles depend critically on atomic input data and how the inclusion of energy levels with n > 9 and collisions with neutral hydrogen are necessary to obtain reasonable fits.Comment: 9 pages, 6 figures, accepted for publication in Astronomy & Astrophysic

The sawtooth chain: From Heisenberg spins to Hubbard electrons

We report on recent studies of the spin-half Heisenberg and the Hubbard model on the sawtooth chain. For both models we construct a class of exact eigenstates which are localized due to the frustrating geometry of the lattice for a certain relation of the exchange (hopping) integrals. Although these eigenstates differ in details for the two models because of the different statistics, they share some characteristic features. The localized eigenstates are highly degenerate and become ground states in high magnetic fields (Heisenberg model) or at certain electron fillings (Hubbard model), respectively. They may dominate the low-temperature thermodynamics and lead to an extra low-temperature maximum in the specific heat. The ground-state degeneracy can be calculated exactly by a mapping of the manifold of localized ground states onto a classical hard-dimer problem, and explicit expressions for thermodynamic quantities can be derived which are valid at low temperatures near the saturation field for the Heisenberg model or around a certain value of the chemical potential for the Hubbard model, respectively.Comment: 16 pages, 6 figure, the paper is based on an invited talk on the XXXI International Workshop on Condensed Matter Theories, Bangkok, Dec 2007; notation of x-axis in Fig.6 corrected, references update

Microscopic magnetic modeling for the SS=1/2 alternating chain compounds Na3_3Cu2_2SbO6_6 and Na2_2Cu2_2TeO6_6

The spin-1/2 alternating Heisenberg chain system Na$_3$Cu$_2$SbO$_6$ features two relevant exchange couplings: $J_{1a}$ within the structural Cu$_2$O$_6$ dimers and $J_{1b}$ between the dimers. Motivated by the controversially discussed nature of $J_{1a}$, we perform extensive density-functional-theory (DFT) calculations, including DFT+$U$ and hybrid functionals. Fits to the experimental magnetic susceptibility using high-temperature series expansions and quantum Monte Carlo simulations yield the optimal parameters $J_{1a}$ = $-$217 K and $J_{1b}$ = 174 K with the alternation ratio $\alpha = J_{1a}/J_{1b} \simeq$ $-$1.25. For the closely related system Na$_2$Cu$_2$TeO$_6$, DFT yields substantially enhanced $J_{1b}$, but weaker $J_{1a}$. The comparative analysis renders the buckling of the chains as the key parameter altering the magnetic coupling regime. Numerical simulation of the dispersion relations of the alternating chain model clarify why both antiferromagnetic and ferrromagnetic $J_{1a}$ can reproduce the experimental magnetic susceptibility data.Comment: published version: 11 pages, 8 figures, 5 tables + Supplemental materia