Making big steps in trajectories

We consider the solution of initial value problems within the context of hybrid systems and emphasise the use of high precision approximations (in software for exact real arithmetic). We propose a novel algorithm for the computation of trajectories up to the area where discontinuous jumps appear, applicable for holomorphic flow functions. Examples with a prototypical implementation illustrate that the algorithm might provide results with higher precision than well-known ODE solvers at a similar computation time

The Hubbard Model at Infinite Dimensions: Thermodynamic and Transport Properties

We present results on thermodynamic quantities, resistivity and optical conductivity for the Hubbard model on a simple hypercubic lattice in infinite dimensions. Our results for the paramagnetic phase display the features expected from an intuitive analysis of the one-particle spectra and substantiate the similarity of the physics of the Hubbard model to those of heavy fermion systems. The calculations were performed using an approximate solution to the single-impurity Anderson model, which is the key quantity entering the solution of the Hubbard model in this limit. To establish the quality of this approximation we compare its results, together with those obtained from two other widely used methods, to essentially exact quantum Monte Carlo results.Comment: 29 pages, 16 figure

Optical fibers with interferometric path length stability by controlled heating for transmission of optical signals and as components in frequency standards

We present a simple method to stabilize the optical path length of an optical fiber to an accuracy of about 1/100 of the laser wavelength. We study the dynamic response of the path length to modulation of an electrically conductive heater layer of the fiber. The path length is measured against the laser wavelength by use of the Pound-Drever-Hall method; negative feedback is applied via the heater. We apply the method in the context of a cryogenic resonator frequency standard.Comment: Expanded introduction and outlook. 9 pages, 5 figure

Three-Dimensional Simulations of Mixing Instabilities in Supernova Explosions

We present the first three-dimensional (3D) simulations of the large-scale mixing that takes place in the shock-heated stellar layers ejected in the explosion of a 15.5 solar-mass blue supergiant star. The outgoing supernova shock is followed from its launch by neutrino heating until it breaks out from the stellar surface more than two hours after the core collapse. Violent convective overturn in the post-shock layer causes the explosion to start with significant asphericity, which triggers the growth of Rayleigh-Taylor (RT) instabilities at the composition interfaces of the exploding star. Deep inward mixing of hydrogen (H) is found as well as fast-moving, metal-rich clumps penetrating with high velocities far into the H-envelope of the star as observed, e.g., in the case of SN 1987A. Also individual clumps containing a sizeable fraction of the ejected iron-group elements (up to several 0.001 solar masses) are obtained in some models. The metal core of the progenitor is partially turned over with Ni-dominated fingers overtaking oxygen-rich bullets and both Ni and O moving well ahead of the material from the carbon layer. Comparing with corresponding 2D (axially symmetric) calculations, we determine the growth of the RT fingers to be faster, the deceleration of the dense metal-carrying clumps in the He and H layers to be reduced, the asymptotic clump velocities in the H-shell to be higher (up to ~4500 km/s for the considered progenitor and an explosion energy of 10^{51} ergs, instead of <2000 km/s in 2D), and the outward radial mixing of heavy elements and inward mixing of hydrogen to be more efficient in 3D than in 2D. We present a simple argument that explains these results as a consequence of the different action of drag forces on moving objects in the two geometries. (abridged)Comment: 15 pages, 8 figures, 30 eps files; significantly extended and more figures added after referee comments; accepted by The Astrophysical Journa

Computational Complexity of Iterated Maps on the Interval (Extended Abstract)

The exact computation of orbits of discrete dynamical systems on the interval is considered. Therefore, a multiple-precision floating point approach based on error analysis is chosen and a general algorithm is presented. The correctness of the algorithm is shown and the computational complexity is analyzed. As a main result, the computational complexity measure considered here is related to the Ljapunow exponent of the dynamical system under consideration

Inversionless gain in a three-level system driven by a strong field and collisions

Inversionless gain in a three-level system driven by a strong external field and by collisions with a buffer gas is investigated. The mechanism of populating of the upper laser level contributed by the collision transfer as well as by relaxation caused by a buffer gas is discussed in detail. Explicit formulae for analysis of optimal conditions are derived. The mechanism developed here for the incoherent pump could be generalized to other systems.Comment: RevTeX, 9 pages, 4 eps figure

Optimized Herschel/PACS photometer observing and data reduction strategies for moving solar system targets

The "TNOs are Cool!: A survey of the trans-Neptunian region" is a Herschel Open Time Key Program that aims to characterize planetary bodies at the outskirts of the Solar System using PACS and SPIRE data, mostly taken as scan-maps. In this paper we summarize our PACS data reduction scheme that uses a modified version of the standard pipeline for basic data reduction, optimized for faint, moving targets. Due to the low flux density of our targets the observations are confusion noise limited or at least often affected by bright nearby background sources at 100 and 160\,$\mu$m. To overcome these problems we developed techniques to characterize and eliminate the background at the positions of our targets and a background matching technique to compensate for pointing errors. We derive a variety of maps as science data products that are used depending on the source flux and background levels and the scientific purpose. Our techniques are also applicable to a wealth of other Herschel solar system photometric observations, e.g. comets and near-Earth asteroids. The principles of our observing strategies and reduction techniques for moving targets will also be applicable for similar surveys of future infrared space projects.Comment: Accepted for publication in Experimental Astronom

From ferromagnetism to spin-density wave: Magnetism in the two channel periodic Anderson model

The magnetic properties of the two-channel periodic Anderson model for uranium ions, comprised of a quadrupolar and a magnetic doublet are investigated through the crossover from the mixed-valent to the stable moment regime using dynamical mean field theory. In the mixed-valent regime ferromagnetism is found for low carrier concentration on a hyper-cubic lattice. The Kondo regime is governed by band magnetism with small effective moments and an ordering vector \q close to the perfect nesting vector. In the stable moment regime nearest neighbour anti-ferromagnetism dominates for less than half band filling and a spin density wave transition for larger than half filling. $T_m$ is governed by the renormalized RKKY energy scale \mu_{eff}^2 ^2 J^2\rho_0(\mu).Comment: 4 pages, RevTeX, 3 eps figure

Dynamical Cluster Approximation Employing FLEX as a Cluster Solver

We employ the Dynamical Cluster Approximation (DCA) in conjunction with the Fluctuation Exchange Approximation (FLEX) to study the Hubbard model. The DCA is a technique to systematically restore the momentum conservation at the internal vertices of Feynman diagrams relinquished in the Dynamical Mean Field Approximation (DMFA). FLEX is a perturbative diagrammatic approach in which classes of Feynman diagrams are summed over analytically using geometric series. The FLEX is used as a tool to investigate the complementarity of the DCA and the finite size lattice technique with periodic boundary conditions by comparing their results for the Hubbard model. We also study the microscopic theory underlying the DCA in terms of compact (skeletal) and non-compact diagrammatic contributions to the thermodynamic potential independent of a specific model. The significant advantages of the DCA implementation in momentum space suggests the development of the same formalism for the frequency space. However, we show that such a formalism for the Matsubara frequencies at finite temperatures leads to acausal results and is not viable. However, a real frequency approach is shown to be feasible.Comment: 15 pages, 24 figures. Submitted to Physical Review B as a Regular Articl

Magnetic Properties of the t-J Model in the Dynamical Mean-Field Theory

We present a theory for the spin correlation function of the t-J model in the framework of the dynamical mean-field theory. Using this mapping between the lattice and a local model we are able to obtain an intuitive expression for the non-local spin susceptibility, with the corresponding local correlation function as input. The latter is calculated by means of local Goldstone diagrams following closely the procedures developed and successfully applied for the (single impurity) Anderson model.We present a systematic study of the magnetic susceptibility and compare our results with those of a Hubbard model at large U. Similarities and differences are pointed out and the magnetic phase diagram of the t-J model is discussed.Comment: 28 pages LaTeX, postscript figures as compressed and uuencoded file included fil