Semiclassical Approximations for Hamiltonians with Operator-Valued Symbols

We consider the semiclassical limit of quantum systems with a Hamiltonian given by the Weyl quantization of an operator valued symbol. Systems composed of slow and fast degrees of freedom are of this form. Typically a small dimensionless parameter ${\varepsilon \ll 1}$ controls the separation of time scales and the limit ${\varepsilon\to 0}$ corresponds to an adiabatic limit, in which the slow and fast degrees of freedom decouple. At the same time ${\varepsilon\to 0}$ is the semiclassical limit for the slow degrees of freedom. In this paper we show that the ${\varepsilon}$ -dependent classical flow for the slow degrees of freedom first discovered by Littlejohn and Flynn (Phys Rev A (3) 44(8):5239–5256, 1991), coming from an ${\varepsilon}$ -dependent classical Hamilton function and an ${\varepsilon}$ -dependent symplectic form, has a concrete mathematical and physical meaning: Based on this flow we prove a formula for equilibrium expectations, an Egorov theorem and transport of Wigner functions, thereby approximating properties of the quantum system up to errors of order ${\varepsilon^2}$ . In the context of Bloch electrons formal use of this classical system has triggered considerable progress in solid state physics (Xiao et al. in Rev Mod Phys 82(3):1959–2007, 2010). Hence we discuss in some detail the application of the general results to the Hofstadter model, which describes a two-dimensional gas of non-interacting electrons in a constant magnetic field in the tight-binding approximation.     

Palladium Release in Electrothermal Atomic Absorption Spectrometry

The absorbance signal in electrothermal atomic absorption spectrometry is a result of the processes of atom formation and dissipation and first of all depends on the initial generation of atoms from the surface. The rising part of the absorbance time profiles can be used for characterization of the release of the metals like Pd, Ag, Au etc. The method is applied to investigate the palladium release from a pyrocoated graphite support at different initial masses of the Pd. The kinetic parameters are evaluated and conclusions about the distribution of palladium on the graphite surface are made. The estimated values of apparent activation energies depend on the initial mass of analyte. The advantages and limitations of the present approach are discussed.     

Equation of state of CaMnO3: a combined experimental and computational study

Elastic properties of CaMnO₃ are of primary importance in the science and technology of CaMnO₃-based perovskites. From X-ray diffraction experiments performed at pressures up to 100 kbar using a diamond-anvil cell to hydrostatically compress our sample, a bulk modulus, K ₀, of 1734(96) kbar was obtained after fitting parameters to the third-order Birch–Murnaghan equation of state. Mean field, semiclassical simulations predict, for the first time, the third-order equation-of-state parameters and show how the bulk modulus increases with pressure (the zero pressure value being 2062.1 kbar) and decreases with the extent of nonstoichiometry caused by the formation of oxygen vacancies. These trends are amplified for the shear modulus. A more accurate model that allows for the explicit reduction of Mn ions, or localization of excess electrons, yields qualitatively similar results. The experimental and calculated axial ratios show the same trends in their variation with rising pressure.     

From holes to sponge at irradiated Ge surfaces with increasing ion energy—an effect of defect kinetics?

We show that hole patterns and sponge-like layers at irradiated Ge surfaces originate from the same driving force, namely the kinetics of ion beam induced defects in the amorphous Ge surface layer. Ge hole patterns reported earlier for irradiation with low energy (5 keV) Ga⁺ ions were reproduced for low energy Bi⁺ but also for Ge⁺ self-irradiation, which proves that the dominating driving force for morphology evolution cannot originate from the implanted impurities. At higher ion energies the well-known formation of sponge-like Ge surface layers after heavy ion irradiation was found for Bi⁺ irradiation and Ge⁺ self-irradiation, also. The transition from smooth surfaces via hole patterns to sponge-like morphologies with increasing ion energies was studied in detail. A model based on the kinetics of ion beam induced defects was developed and implemented in 3D kinetic Monte Carlo simulations, which reproduce the transition from hole patterns to sponge-like layers with increasing ion energy.     

The Formation of Pd Nanocrystals from Pd2(dba)3 Microcrystals

As‐grown platelets formed from tris‐(dibenzylideneacetone) dipalladium(0) [Pd₂(dba)₃] precursor in the presence of Pd17 RNA are investigated before and after thermal annealing. Results show that as‐grown platelets are disordered crystals of Pd₂(dba)₃ containing 1?2 nm Pd clusters and platelets grown in the absence of RNA are morphologically and structurally similar to those formed with RNA. The initially formed crystals are so sensitive to environmental variables that the degree of crystallinity can not be determined accurately by electron diffraction. X‐ray crystallography on as‐grown platelets gives a crystal structure consistent with Pd₂(dba)₃, but reveals a composition of ≈Pd_1.07(dba)₃, indicating one Pd atom in Pd₂(dba)₃ is lost from the structure. Both electron beam and thermally induced decomposition of as‐grown Pd₂(dba)₃ platelets having a hexagonal habit on the micrometer scale produces elemental Pd platelets having a hexagonal habit on the nanometer scale. These hexagonal platelets are composed of a partially sparse form of Pd₂(dba)₃ that is initially crystalline but rapidly degrades due to the loss of Pd atoms from organic ligand cages. Once released, Pd atoms aggregate to form Pd clusters, which grow and transform into well‐formed Pd nanocrystals under electron‐beam irradiation or through thermal annealing.     

Advanced Genetic Programming Based Machine Learning

A Genetic Programming based approach for solving classification problems is presented in this paper. Classification is understood as the act of placing an object into a set of categories, based on the object’s properties; classification algorithms are designed to learn a function which maps a vector of object features into one of several classes. This is done by analyzing a set of input-output examples (“training samples”) of the function. Here we present a method based on the theory of Genetic Algorithms and Genetic Programming that interprets classification problems as optimization problems: Each presented instance of the classification problem is interpreted as an instance of an optimization problem, and a solution is found by a heuristic optimization algorithm. The major new aspects presented in this paper are advanced algorithmic concepts as well as suitable genetic operators for this problem class (mainly the creation of new hypotheses by merging already existing ones and their detailed evaluation). The experimental part of the paper documents the results produced using new hybrid variants of Genetic Algorithms as well as investigated parameter settings. Graphical analysis is done using a novel multiclass classifier analysis concept based on the theory of Receiver Operating Characteristic curves. The work described in this paper was done within the Translational Research Project L282 “GP-Based Techniques for the Design of Virtual Sensors” sponsored by the Austrian Science Fund (FWF).