Random Matrices and Chaos in Nuclear Physics: Nuclear Reactions

The application of random-matrix theory (RMT) to compound-nucleus (CN) reactions is reviewed. An introduction into the basic concepts of nuclear scattering theory is followed by a survey of phenomenological approaches to CN scattering. The implementation of a random-matrix approach into scattering theory leads to a statistical theory of CN reactions. Since RMT applies generically to chaotic quantum systems, that theory is, at the same time, a generic theory of quantum chaotic scattering. It uses a minimum of input parameters (average S-matrix and mean level spacing of the CN). Predictions of the theory are derived with the help of field-theoretical methods adapted from condensed-matter physics and compared with those of phenomenological approaches. Thorough tests of the theory are reviewed, as are applications in nuclear physics, with special attention given to violation of symmetries (isospin, parity) and time-reversal invariance.Comment: 50 pages, 26 figure

Prevalence of marginally unstable periodic orbits in chaotic billiards

The dynamics of chaotic billiards is significantly influenced by coexisting regions of regular motion. Here we investigate the prevalence of a different fundamental structure, which is formed by marginally unstable periodic orbits and stands apart from the regular regions. We show that these structures both {\it exist} and {\it strongly influence} the dynamics of locally perturbed billiards, which include a large class of widely studied systems. We demonstrate the impact of these structures in the quantum regime using microwave experiments in annular billiards.Comment: 6 pages, 5 figure

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

Localized-magnon states in strongly frustrated quantum spin lattices

Recent developments concerning localized-magnon eigenstates in strongly frustrated spin lattices and their effect on the low-temperature physics of these systems in high magnetic fields are reviewed. After illustrating the construction and the properties of localized-magnon states we describe the plateau and the jump in the magnetization process caused by these states. Considering appropriate lattice deformations fitting to the localized magnons we discuss a spin-Peierls instability in high magnetic fields related to these states. Last but not least we consider the degeneracy of the localized-magnon eigenstates and the related thermodynamics in high magnetic fields. In particular, we discuss the low-temperature maximum in the isothermal entropy versus field curve and the resulting enhanced magnetocaloric effect, which allows efficient magnetic cooling from quite large temperatures down to very low ones.Comment: 21 pages, 10 figures, invited paper for a special issue of "Low Temperature Physics " dedicated to the 70-th anniversary of creation of concept "antiferromagnetism" in physics of magnetis

The spin 1/2 Heisenberg star with frustration II: The influence of the embedding medium

We investigate the spin 1/2 Heisenberg star introduced in J. Richter and A. Voigt, J. Phys. A: Math. Gen. {\bf 27}, 1139 (1994). The model is defined by $H=J_1 \sum_{i=1}^{N}{{\bf s}_0{\bf s}_i} + J_2 H_{R}\{{\bf s}_i\}$ ; $J_1,J_2 \ge 0$ , $i=1,...,N$. In extension to the Ref. we consider a more general $H_{R}\{{\bf s}_i\}$ describing the properties of the spins surrounding the central spin ${\bf s}_0$. The Heisenberg star may be considered as an essential structure element of a lattice with frustration (namely a spin embedded in a magnetic matrix $H_R$) or, alternatively, as a magnetic system $H_R$ with a perturbation by an extra spin. We present some general features of the eigenvalues, the eigenfunctions as well as the spin correlation $\langle {\bf s}_0{\bf s}_i \rangle$ of the model. For $H_R$ being a linear chain, a square lattice or a Lieb-Mattis type system we present the ground state properties of the model in dependence on the frustration parameter $\alpha=J_2/J_1$. Furthermore the thermodynamic properties are calculated for $H_R$ being a Lieb--Mattis antiferromagnet.Comment: 16 pages, uuencoded compressed postscript file, accepted to J. Phys. A: Math. Ge

Application of a trace formula to the spectra of flat three-dimensional dielectric resonators

The length spectra of flat three-dimensional dielectric resonators of circular shape were determined from a microwave experiment. They were compared to a semiclassical trace formula obtained within a two-dimensional model based on the effective index of refraction approximation and a good agreement was found. It was necessary to take into account the dispersion of the effective index of refraction for the two-dimensional approximation. Furthermore, small deviations between the experimental length spectrum and the trace formula prediction were attributed to the systematic error of the effective index of refraction approximation. In summary, the methods developed in this article enable the application of the trace formula for two-dimensional dielectric resonators also to realistic, flat three-dimensional dielectric microcavities and -lasers, allowing for the interpretation of their spectra in terms of classical periodic orbits.Comment: 13 pages, 12 figures, 1 tabl

Application of TauSpinner for studies on tau-lepton polarization and spin correlations in Z, W and H decays at LHC

The tau-lepton plays an important role in the physics program at LHC. Its spin can be used for separation of signal from background or in measuring properties of New Particles decaying to tau leptons. The TauSpinner package represents a tool to modify tau spin effects in any sample containing tau leptons. Generated events, featuring taus produced from intermediate state W, Z, H bosons can be used as an input. The information on the polarization and spin correlations is reconstructed from the kinematics of the tau lepton(s) (nutau in case of W-mediated processes) and tau decay products. By weights, attributed on the event-by-event basis, it enables numerical evaluation and/or modification of the spin effects. We review distributions to monitor spin effects in leptonic and hadronic tau decays with up to three pions, to provide benchmarks for validation of spin content of the event sample and to visualize the tau lepton spin polarization and correlation effects. The demonstration examples for use of TauSpinner libraries, are documented. New validation methods of such an approach are provided. Other topics, like TauSpinner systematic errors or sensitivity of experimental distributions to spin, are addressed in part only. This approach is of interest for implementation of spin effects in embedded tau lepton samples, where Z to mu mu events from data of muons are replaced by simulated tau leptons. Embedding is used at LHC for estimating Z to tau tau background to H to tau tau signatures.Comment: 1+41 pages, 5 figures in main text, multitude of figures in appendice

Experimental Observation of Localized Modes in a Dielectric Square Resonator

We investigated the frequency spectra and field distributions of a dielectric square resonator in a microwave experiment. Since such systems cannot be treated analytically, the experimental studies of their properties are indispensable. The momentum representation of the measured field distributions shows that all resonant modes are localized on specific classical tori of the square billiard. Based on these observations a semiclassical model was developed. It shows excellent agreement with all but a single class of measured field distributions that will be treated separately.Comment: 6 pages, 5 figures, 1 tabl

Exact eigenstates of highly frustrated spin lattices probed in high fields

Strongly frustrated antiferromagnets such as the magnetic molecule {Mo72Fe30}, the kagome, or the pyrochlore lattice exhibit a variety of fascinating properties like low-lying singlets, magnetization plateaus as well as magnetization jumps. During recent years exact many-body eigenstates could be constructed for several of these spin systems. These states become ground states in high magnetic fields, and they also lead to exotic behavior. A key concept to an understanding of these properties is provided by independent localized magnons. The energy eigenvalue of these n-magnon states scales linearly with the number n of independent magnons and thus with the total magnetic quantum number M=Ns-n. In an applied field this results in a giant magnetization jump which constitutes a new macroscopic quantum effect. It will be demonstrated that this behavior is accompanied by a massive degeneracy, an extensive (T=0)-entropy, and thus a large magnetocaloric effect at the saturation field. The connection to flat band ferromagnetism will be outlined.Comment: 4 pages, submitted to the proceedings of the Yamada Conference LX on Research in High Magnetic Fields, August 16-19, 2006 Sendai, Japa