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R. Schott

Publications and source records attributed to R. Schott.

26 records · Page 2Linked to original sources
arXiv2015

Focused ion beam induced growth of monocrystalline InAs nanowires

We investigate monocrystalline InAs nanowires (NWs) which are grown by molecular beam epitaxy (MBE) and induced by focused ion beam (FIB) implanted Au spots. With this unique combination of methods an increase of the aspect ratio, i.e. the length to width ratio, of the grown NWs up to 300 was achieved. To control the morphology and crystalline structure of the NWs, the growth parameters like temperature, flux ratios and implantation fluence are varied and optimized. Furthermore, the influence of the used molecular arsenic species, in particular the As$_2$ to As$_4$ ratio, is investigated and adjusted. In addition to the high aspect ratio, this optimization results in the growth of monocrystalline InAs NWs with a negligible number of stacking faults. Single NWsx were placed site-controlled by FIB implantation, which supplements the working field of area growth.

cond-mat.mes-hall↗
arXiv2010

Dynamic Random Walks on Motion Groups

In this note, we give an original convergence result for products of independent random elements of motion group. Then we consider dynamic random walks which are inhomogeneous Markov chains whose transition probability of each step is, in some sense, time dependent. We show, briefly, how Central Limit theorem and Local Limit theorems can be derived from the classical case and provide new results when the rotations are mutually commuting. To the best of our knowledge, this work represents the first investigation of dynamic random walks on the motion group.

math.PR↗
arXiv2008

Measurement of XUV-absorption spectra of ZnS radiatively heated foils

Time-resolved absorption of zinc sulfide (ZnS) and aluminum in the XUV-range has been measured. Thin foils in conditions close to local thermodynamic equilibrium were heated by radiation from laser-irradiated gold spherical cavities. Analysis of the aluminum foil radiative hydrodynamic expansion, based on the detailed atomic calculations of its absorption spectra, showed that the cavity emitted flux that heated the absorption foils corresponds to a radiation temperature in the range 55 60 eV. Comparison of the ZnS absorption spectra with calculations based on a superconfiguration approach identified the presence of species Zn6+ - Zn8+ and S5+ - S6+. Based on the validation of the radiative source simulations, experimental spectra were then compared to calculations performed by post-processing the radiative hydrodynamic simulations of ZnS. Satisfying agreement is found when temperature gradients are accounted for.

physics.plasm-ph↗
arXiv2006

Operator calculus approach to solving analytic systems

Solving analytic systems using inversion can be implemented in a variety of ways. One method is to use Lagrange inversion and variations. Here we present a different approach, based on dual vector fields. For a function analytic in a neighborhood of the origin in the complex plane, we associate a vector field and its dual, an operator version of Fourier transform. The construction extends naturally to functions of several variables. We illustrate with various examples and present an efficient algorithms readily implemented symbolically in Maple while suitable as well for numerical computations using languages such as C or Java.

math.CA↗
arXiv2000

Berezin quantization of the Schrodinger algebra

We examine the Schrodinger algebra in the framework of Berezin quantization. First, the Heisenberg-Weyl and sl(2) algebras are studied. Then the Berezin representation of the Schrodinger algebra is computed. In fact, the sl(2) piece of the Schrodinger algebra can be decoupled from the Heisenberg component. This is accomplished using a special realization of the sl(2) component that is built from the Heisenberg piece as the quadratic elements in the Heisenberg-Weyl enveloping algebra. The structure of the Schrodinger algebra is revealed in a lucid way by the form of the Berezin representation.

math-ph↗
arXiv2000

Representations of the Schrodinger algebra and Appell systems

We investigate the structure of the Schrodinger algebra and its representations in a Fock space realized in terms of canonical Appell systems. Generalized coherent states are used in the construction of a Hilbert space of functions on which certain commuting elements act as self-adjoint operators. This yields a probabilistic interpretation of these operators as random variables. An interesting feature is how the structure of the Lie algebra is reflected in the probability density function. A Leibniz function and orthogonal basis for the Hilbert space is found. Then Appell systems connected with certain evolution equations, analogs of the classical heat equation, on this algebra are computed.

math-ph↗
arXiv1999

Lévy Processes on $U_q(g)$ as Infinitely Divisible Representations

Lévy processes on bialgebras are families of infinitely divisible representations. We classify the generators of Lévy processes on the compact forms of the quantum algebras $U_q(g)$, where $g$ is a simple Lie algebra. Then we show how the processes themselves can be reconstructed from their generators and study several classical stochastic processes that can be associated to these processes.

math.PR↗