Global Bounds for the Lyapunov Exponent and the Integrated Density of States of Random Schr\"odinger Operators in One Dimension

In this article we prove an upper bound for the Lyapunov exponent $\gamma(E)$ and a two-sided bound for the integrated density of states $N(E)$ at an arbitrary energy $E>0$ of random Schr\"odinger operators in one dimension. These Schr\"odinger operators are given by potentials of identical shape centered at every lattice site but with non-overlapping supports and with randomly varying coupling constants. Both types of bounds only involve scattering data for the single-site potential. They show in particular that both $\gamma(E)$ and $N(E)-\sqrt{E}/\pi$ decay at infinity at least like $1/\sqrt{E}$. As an example we consider the random Kronig-Penney model.Comment: 9 page

A Higgs Mechanism for Gravity. Part II: Higher Spin Connections

We continue the work of hep-th/0503024 in which gravity is considered as the Goldstone realization of a spontaneously broken diffeomorphism group. We complete the discussion of the coset space Diff(d,R)/SO(1,d-1) formed by the d-dimensional group of analytic diffeomorphisms and the Lorentz group. We find that this coset space is parameterized by coordinates, a metric and an infinite tower of higher-spin-like or generalized connections. We then study effective actions for the corresponding symmetry breaking which gives mass to the higher spin connections. Our model predicts that gravity is modified at high energies by the exchange of massive higher spin particles.Comment: 17 pages; discussion on local Poincare invariance and matter currents added; references adde

Gamma-widths, lifetimes and fluctuations in the nuclear quasi-continuum

Statistical $\gamma$-decay from highly excited states is determined by the nuclear level density (NLD) and the $\gamma$-ray strength function ($\gamma$SF). These average quantities have been measured for several nuclei using the Oslo method. For the first time, we exploit the NLD and $\gamma$SF to evaluate the $\gamma$-width in the energy region below the neutron binding energy, often called the quasi-continuum region. The lifetimes of states in the quasi-continuum are important benchmarks for a theoretical description of nuclear structure and dynamics at high temperature. The lifetimes may also have impact on reaction rates for the rapid neutron-capture process, now demonstrated to take place in neutron star mergers.Comment: CGS16, Shanghai 2017, Proceedings, 5 pages, 3 figure

Experimental Determination of the Characteristics of a Positron Source Using Channeling

Numerical simulations and `proof of principle' experiments showed clearly the interest of using crystals as photon generators dedicated to intense positron sources for linear colliders. An experimental investigation, using a 10 GeV secondary electron beam, of the SPS-CERN, impinging on an axially oriented thick tungsten crystal, has been prepared and operated between May and August 2000. After a short recall on the main features of positron sources using channeling in oriented crystals, the experimental set-up is described. A particular emphasis is put on the positron detector made of a drift chamber, partially immersed in a magnetic field. The enhancement in photon and positron production in the aligned crystal have been observed in the energy range 5 to 40 GeV, for the incident electrons, in crystals of 4 and 8 mm as in an hybrid target. The first results concerning this experiment are presented hereafter.Comment: 3 pages, 6 figures, submitted to Linac200

A Higgs Mechanism for Gravity

In this paper we elaborate on the idea of an emergent spacetime which arises due to the dynamical breaking of diffeomorphism invariance in the early universe. In preparation for an explicit symmetry breaking scenario, we consider nonlinear realizations of the group of analytical diffeomorphisms which provide a unified description of spacetime structures. We find that gravitational fields, such as the affine connection, metric and coordinates, can all be interpreted as Goldstone fields of the diffeomorphism group. We then construct a Higgs mechanism for gravity in which an affine spacetime evolves into a Riemannian one by the condensation of a metric. The symmetry breaking potential is identical to that of hybrid inflation but with the non-inflaton scalar extended to a symmetric second rank tensor. This tensor is required for the realization of the metric as a Higgs field. We finally comment on the role of Goldstone coordinates as a dynamical fluid of reference.Comment: 15 pages, 2 figures, 3 tables, appendix C on on-shell d.o.f. added, references adde

A helium film coated quasi‐parabolic mirror to focus a beam of ultra‐cold spin polarized atomic hydrogen

A 350 mK helium‐4‐coated mirror was used to increase the intensity of an ultra‐cold electron‐spin‐polarized atomic hydrogen beam. The mirror uses the observed specular reflection of atomic hydrogen from a superfluid‐helium‐covered surface. A quasi‐parabolic polished copper mirror was installed with its focus at the 5 mm diameter exit aperture of an atomic hydrogen stabilization cell in the gradient of an 8 T solenoid field. The four‐coned mirror shape, which was designed specifically for operation in the gradient, increased the beam intensity focused by a sextupole magnet into a compression tube detector by a factor of about 7.5.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87512/2/40_1.pd

Worldsheet correlators in AdS(3)/CFT(2)

The AdS_3/CFT_2 correspondence is checked beyond the supergravity approximation by comparing correlation functions. To this end we calculate 2- and 3-point functions on the sphere of certain chiral primary operators for strings on AdS_3 x S^3 x T^4. These results are then compared with the corresponding amplitudes in the dual 2-dimensional conformal field theory. In the limit of small string coupling, where the sphere diagrams dominate the string perturbation series, beautiful agreement is found.Comment: 23 page

A Bayesian Approach to Inverse Quantum Statistics

A nonparametric Bayesian approach is developed to determine quantum potentials from empirical data for quantum systems at finite temperature. The approach combines the likelihood model of quantum mechanics with a priori information over potentials implemented in form of stochastic processes. Its specific advantages are the possibilities to deal with heterogeneous data and to express a priori information explicitly, i.e., directly in terms of the potential of interest. A numerical solution in maximum a posteriori approximation was feasible for one--dimensional problems. Using correct a priori information turned out to be essential.Comment: 4 pages, 6 figures, revte

The First INTEGRAL AGN Catalog

We present the first INTEGRAL AGN catalog, based on observations performed from launch of the mission in October 2002 until January 2004. The catalog includes 42 AGN, of which 10 are Seyfert 1, 17 are Seyfert 2, and 9 are intermediate Seyfert 1.5. The fraction of blazars is rather small with 5 detected objects, and only one galaxy cluster and no star-burst galaxies have been detected so far. A complete subset consists of 32 AGN with a significance limit of 7 sigma in the INTEGRAL/ISGRI 20-40 keV data. Although the sample is not flux limited, the distribution of sources shows a ratio of obscured to unobscured AGN of 1.5 - 2.0, consistent with luminosity dependent unified models for AGN. Only four Compton-thick AGN are found in the sample. Based on the INTEGRAL data presented here, the Seyfert 2 spectra are slightly harder (Gamma = 1.95 +- 0.01) than Seyfert 1.5 (Gamma = 2.10 +- 0.02) and Seyfert 1 (Gamma = 2.11 +- 0.05).Comment: 17 pages, 12 figures, accepted for publication in Ap

Scattering Theory Approach to Random Schroedinger Operators in One Dimension

Methods from scattering theory are introduced to analyze random Schroedinger operators in one dimension by applying a volume cutoff to the potential. The key ingredient is the Lifshitz-Krein spectral shift function, which is related to the scattering phase by the theorem of Birman and Krein. The spectral shift density is defined as the "thermodynamic limit" of the spectral shift function per unit length of the interaction region. This density is shown to be equal to the difference of the densities of states for the free and the interacting Hamiltonians. Based on this construction, we give a new proof of the Thouless formula. We provide a prescription how to obtain the Lyapunov exponent from the scattering matrix, which suggest a way how to extend this notion to the higher dimensional case. This prescription also allows a characterization of those energies which have vanishing Lyapunov exponent.Comment: 1 figur