The Non-Trapping Degree of Scattering

We consider classical potential scattering. If no orbit is trapped at energy E, the Hamiltonian dynamics defines an integer-valued topological degree. This can be calculated explicitly and be used for symbolic dynamics of multi-obstacle scattering. If the potential is bounded, then in the non-trapping case the boundary of Hill's Region is empty or homeomorphic to a sphere. We consider classical potential scattering. If at energy E no orbit is trapped, the Hamiltonian dynamics defines an integer-valued topological degree deg(E) < 2. This is calculated explicitly for all potentials, and exactly the integers < 2 are shown to occur for suitable potentials. The non-trapping condition is restrictive in the sense that for a bounded potential it is shown to imply that the boundary of Hill's Region in configuration space is either empty or homeomorphic to a sphere. However, in many situations one can decompose a potential into a sum of non-trapping potentials with non-trivial degree and embed symbolic dynamics of multi-obstacle scattering. This comprises a large number of earlier results, obtained by different authors on multi-obstacle scattering.Comment: 25 pages, 1 figure Revised and enlarged version, containing more detailed proofs and remark

Large normally hyperbolic cylinders in a priori stable Hamiltonian systems

We prove the existence of normally hyperbolic invariant cylinders in nearly integrable hamiltonian systems

A Large Scale Double Beta and Dark Matter Experiment: GENIUS

The recent results from the HEIDELBERG-MOSCOW experiment have demonstrated the large potential of double beta decay to search for new physics beyond the Standard Model. To increase by a major step the present sensitivity for double beta decay and dark matter search much bigger source strengths and much lower backgrounds are needed than used in experiments under operation at present or under construction. We present here a study of a project proposed recently, which would operate one ton of 'naked' enriched GErmanium-detectors in liquid NItrogen as shielding in an Underground Setup (GENIUS). It improves the sensitivity to neutrino masses to 0.01 eV. A ten ton version would probe neutrino masses even down to 10^-3 eV. The first version would allow to test the atmospheric neutrino problem, the second at least part of the solar neutrino problem. Both versions would allow in addition significant contributions to testing several classes of GUT models. These are especially tests of R-parity breaking supersymmetry models, leptoquark masses and mechanism and right-handed W-boson masses comparable to LHC. The second issue of the experiment is the search for dark matter in the universe. The entire MSSM parameter space for prediction of neutralinos as dark matter particles could be covered already in a first step of the full experiment - with the same purity requirements but using only 100 kg of 76Ge or even of natural Ge - making the experiment competitive to LHC in the search for supersymmetry. The layout of the proposed experiment is discussed and the shielding and purity requirements are studied using GEANT Monte Carlo simulations. As a demonstration of the feasibility of the experiment first results of operating a 'naked' Ge detector in liquid nitrogen are presented.Comment: 22 pages, 12 figures, see also http://pluto.mpi-hd.mpg.de/~betalit/genius.htm

Latest Results from the Heidelberg-Moscow Double Beta Decay Experiment

New results for the double beta decay of 76Ge are presented. They are extracted from Data obtained with the HEIDELBERG-MOSCOW, which operates five enriched 76Ge detectors in an extreme low-level environment in the GRAN SASSO. The two neutrino accompanied double beta decay is evaluated for the first time for all five detectors with a statistical significance of 47.7 kg y resulting in a half life of (T_(1/2))^(2nu) = [1.55 +- 0.01 (stat) (+0.19) (-0.15) (syst)] x 10^(21) years. The lower limit on the half-life of the 0nu beta-beta decay obtained with pulse shape analysis is (T_(1/2))^(0_nu) > 1.9 x 10^(25) [3.1 x 10^(25)] years with 90% C.L. (68% C.L.) (with 35.5 kg y). This results in an upper limit of the effective Majorana neutrino mass of 0.35 eV (0.27 eV). No evidence for a Majoron emitting decay mode or for the neutrinoless mode is observed.Comment: 14 pages, revtex, 6 figures, Talk was presented at third International Conference ' Dark Matter in Astro and Particle Physics' - DARK2000, to be publ. in Proc. of DARK2000, Springer (2000). Please look into our HEIDELBERG Non-Accelerator Particle Physics group home page: http://www.mpi-hd.mpg.de/non_acc

Double Beta Decay, Majorana Neutrinos, and Neutrino Mass

The theoretical and experimental issues relevant to neutrinoless double-beta decay are reviewed. The impact that a direct observation of this exotic process would have on elementary particle physics, nuclear physics, astrophysics and cosmology is profound. Now that neutrinos are known to have mass and experiments are becoming more sensitive, even the non-observation of neutrinoless double-beta decay will be useful. If the process is actually observed, we will immediately learn much about the neutrino. The status and discovery potential of proposed experiments are reviewed in this context, with significant emphasis on proposals favored by recent panel reviews. The importance of and challenges in the calculation of nuclear matrix elements that govern the decay are considered in detail. The increasing sensitivity of experiments and improvements in nuclear theory make the future exciting for this field at the interface of nuclear and particle physics.Comment: invited submission to Reviews of Modern Physics, higher resolution figures available upon request from authors, Version 2 has fixed typos and some changes after referee report

Limits on different Majoron decay modes of 100^{100}Mo and 82^{82}Se for neutrinoless double beta decays in the NEMO-3 experiment

The NEMO-3 tracking detector is located in the Fr\'ejus Underground Laboratory. It was designed to study double beta decay in a number of different isotopes. Presented here are the experimental half-life limits on the double beta decay process for the isotopes $^{100}$Mo and $^{82}$Se for different Majoron emission modes and limits on the effective neutrino-Majoron coupling constants. In particular, new limits on "ordinary" Majoron (spectral index 1) decay of $^{100}$Mo ($T_{1/2} > 2.7\cdot10^{22}$ y) and $^{82}$Se ($T_{1/2} > 1.5\cdot10^{22}$ y) have been obtained. Corresponding bounds on the Majoron-neutrino coupling constant are $< (0.4-1.9) \cdot 10^{-4}$ and $< (0.66-1.7) \cdot 10^{-4}$.Comment: 23 pages includind 4 figures, to be published in Nuclear Physics

Isomerization dynamics of a buckled nanobeam

We analyze the dynamics of a model of a nanobeam under compression. The model is a two mode truncation of the Euler-Bernoulli beam equation subject to compressive stress. We consider parameter regimes where the first mode is unstable and the second mode can be either stable or unstable, and the remaining modes (neglected) are always stable. Material parameters used correspond to silicon. The two mode model Hamiltonian is the sum of a (diagonal) kinetic energy term and a potential energy term. The form of the potential energy function suggests an analogy with isomerisation reactions in chemistry. We therefore study the dynamics of the buckled beam using the conceptual framework established for the theory of isomerisation reactions. When the second mode is stable the potential energy surface has an index one saddle and when the second mode is unstable the potential energy surface has an index two saddle and two index one saddles. Symmetry of the system allows us to construct a phase space dividing surface between the two "isomers" (buckled states). The energy range is sufficiently wide that we can treat the effects of the index one and index two saddles in a unified fashion. We have computed reactive fluxes, mean gap times and reactant phase space volumes for three stress values at several different energies. In all cases the phase space volume swept out by isomerizing trajectories is considerably less than the reactant density of states, proving that the dynamics is highly nonergodic. The associated gap time distributions consist of one or more `pulses' of trajectories. Computation of the reactive flux correlation function shows no sign of a plateau region; rather, the flux exhibits oscillatory decay, indicating that, for the 2-mode model in the physical regime considered, a rate constant for isomerization does not exist.Comment: 42 pages, 6 figure

Nonlinear analysis of spacecraft thermal models

We study the differential equations of lumped-parameter models of spacecraft thermal control. Firstly, we consider a satellite model consisting of two isothermal parts (nodes): an outer part that absorbs heat from the environment as radiation of various types and radiates heat as a black-body, and an inner part that just dissipates heat at a constant rate. The resulting system of two nonlinear ordinary differential equations for the satellite's temperatures is analyzed with various methods, which prove that the temperatures approach a steady state if the heat input is constant, whereas they approach a limit cycle if it varies periodically. Secondly, we generalize those methods to study a many-node thermal model of a spacecraft: this model also has a stable steady state under constant heat inputs that becomes a limit cycle if the inputs vary periodically. Finally, we propose new numerical analyses of spacecraft thermal models based on our results, to complement the analyses normally carried out with commercial software packages.Comment: 29 pages, 4 figure

Recent advances in neutrinoless double beta decay search

Even after the discovery of neutrino flavour oscillations, based on data from atmospheric, solar, reactor, and accelerator experiments, many characteristics of the neutrino remain unknown. Only the neutrino square-mass differences and the mixing angle values have been estimated, while the value of each mass eigenstate still hasn't. Its nature (massive Majorana or Dirac particle) is still escaping. Neutrinoless double beta decay ($0\nu$-DBD) experimental discovery could be the ultimate answer to some delicate questions of elementary particle and nuclear physics. The Majorana description of neutrinos allows the $0\nu$-DBD process, and consequently either a mass value could be measured or the existence of physics beyond the standard should be confirmed without any doubt. As expected, the $0\nu$-DBD measurement is a very difficult field of application for experimentalists. In this paper, after a short summary of the latest results in neutrino physics, the experimental status, the R&D projects, and perspectives in $0\nu$-DBD sector are reviewed.Comment: 36 pages, 7 figures, To be publish in Czech Journal of Physic

A topological classification of convex bodies

The shape of homogeneous, generic, smooth convex bodies as described by the Euclidean distance with nondegenerate critical points, measured from the center of mass represents a rather restricted class M_C of Morse-Smale functions on S^2. Here we show that even M_C exhibits the complexity known for general Morse-Smale functions on S^2 by exhausting all combinatorial possibilities: every 2-colored quadrangulation of the sphere is isomorphic to a suitably represented Morse-Smale complex associated with a function in M_C (and vice versa). We prove our claim by an inductive algorithm, starting from the path graph P_2 and generating convex bodies corresponding to quadrangulations with increasing number of vertices by performing each combinatorially possible vertex splitting by a convexity-preserving local manipulation of the surface. Since convex bodies carrying Morse-Smale complexes isomorphic to P_2 exist, this algorithm not only proves our claim but also generalizes the known classification scheme in [36]. Our expansion algorithm is essentially the dual procedure to the algorithm presented by Edelsbrunner et al. in [21], producing a hierarchy of increasingly coarse Morse-Smale complexes. We point out applications to pebble shapes.Comment: 25 pages, 10 figure