Exactly soluble models of decoherence

Superselection rules induced by the interaction with the environment are a basis to understand the emergence of classical observables within quantum theory. The aim of this article is to investigate the decoherence effects, which lead to superselection sectors, with the help of exactly soluble Hamiltonian models. Starting from the examples of Araki and of Zurek more general models with scattering are presented for which the projection operators onto the induced superselection sectors do no longer commute with the Hamiltonian. The example of an environment given by a free quantum field indicates that infrared divergence plays an essential role for the emergence of induced superselection sectors. For all models the induced superselection sectors are uniquely determined by the Hamiltonian, whereas the time scale of the decoherence depends crucially on the initial state of the total system.Comment: 12 pages, Late

Learning action oriented perceptual features for robot navigation

Machine learning can offer an increase in the flexibility and applicability of robotics at several levels of control. In this paper, we characterize two symbolic learning tasks in the field of robotics. We outline an approach for learning features from sensory data and for using these features to learn more complex ones. We illustrate our approach with first experiments in the field of navigation. The paper is written in English

Modelling phase transitions via Young measures

We consider the elastic theory of single crystals at constant temperature where the free energy density depends on the local concentration of one or more species of particles in such a way that for a given local concentration vector certain lattice geometries (phases) are preferred. Furthermore we consider possible large deformations of the crystal lattice. After deriving the physical model, we indicate by means of a suitable implicite time discretization an existence result for measure-valued solutions that relies on a new existence theorem for Young measures in infinite settings. This article is an overview of [2]

Inequalities for Markov operators, majorization and the direction of time

In this paper, we connect the following partial orders: majorization of vectors in linear algebra, majorization of functions in integration theory and the order of states of a physical system due to their temporal-causal connection. Each of these partial orders is based on two general inequalities for Markov operators and their adjoints. The first inequality compares pairs composed of a continuous function (observables) and a probability measure (statistical states), the second inequality compares pairs of probability measure. We propose two new definitions of majorization, related to these two inequalities. We derive several identities and inequalities illustrating these new definitions. They can be useful for the comparison of two measures if the Radon-Nikodym Theorem is not applicable. The problem is considered in a general setting, where probability measures are defined as convex combinations of the images of the points of a topological space (the physical state space) under the canonical embedding into its bidual. This approach allows to limit the necessary assumptions to functions and measures. In two appendices, the finite dimensional non-uniform distributed case is described, in detail. Here, majorization is connected with the comparison of general piecewise affine convex functions. Moreover, the existence of a Markov matrix, connecting two given majorizing pairs, is shown

Inequalities for Markov operators, majorization and the direction of time

In this paper, we connect the following partial orders: majorization of vectors in linear algebra, majorization of functions in integration theory and the order of states of a physical system due to their temporal-causal connection. Each of these partial orders is based on two general inequalities for Markov operators and their adjoints. The first inequality compares pairs composed of a continuous function (observables) and a probability measure (statistical states), the second inequality compares pairs of probability measure. We propose two new definitions of majorization, related to these two inequalities. We derive several identities and inequalities illustrating these new definitions. They can be useful for the comparison of two measures if the Radon-Nikodym Theorem is not applicable. The problem is considered in a general setting, where probability measures are defined as convex combinations of the images of the points of a topological space (the physical state space) under the canonical embedding into its bidual. This approach allows to limit the necessary assumptions to functions and measures. In two appendices, the finite dimensional non-uniform distributed case is described, in detail. Here, majorization is connected with the comparison of general piecewise affine convex functions. Moreover, the existence of a Markov matrix, connecting two given majorizing pairs, is shown

Capacitance measurements of bulk salinity and brine movement in first-year sea ice

Thesis (M.S.) University of Alaska Fairbanks, 2007Sea ice is an important component of the global climate system, as it changes the properties of the ocean-atmosphere interface. Understanding sea ice requires detailed knowledge of its temperature and bulk salinity. To measure these attributes using non-destructive in-situ techniques, instruments were frozen into first-year sea ice, and analysed jointly with ice-core, mass balance and climate data. The bulk salinity of the ice is calculated from measurements of temperature and complex dielectric permittivity at 50 MHz in landfast ice in McMurdo Sound, Antarctica, the Chukchi Sea, Alaska, and in an outdoor tank experiment in Fairbanks, Alaska. A simple relation for estimating brine volume fraction and bulk salinity in columnar, bubble-free ice from the real part of the complex dielectric permittivity was derived. For relative brine volumes below 50-70 % the error in the derived bulk salinity was below 15%. The observed brine movement events are analyzed. The data clearly indicate the extent and impact of brine movement on ice temperature and salinity. The analysis of a drainage event recorded by both the temperature and dielectric permittivity probe provided insight into gravity drainage of brine driven by a large brine reservoir in the freeboard layer.1. Capacitance probe measurements of brine volume and bulk salinity in first-year sea ice -- 1.1. Abstract -- 1.2. Introduction -- 1.3. Methodology -- 1.3.1. Complex dialectric permittivity of sea ice -- 1.3.2. Instrumentation -- 1.3.3. Laboratory and field experiments -- 1.3.3.1. Measurements in Landfast sea ice in McMurdo Sound, Antarctica, July 10 -- November 11, 2002 -- 1.3.3.2. Measurements in landfast sea ice off Barrow, Alaska, February 2 -- June 4, 2003 -- 1.3.3.3. Outdoor ice tank experiment, Fairbanks, Alaska, February 8-April 20, 2003 -- 1.4. Results and analysis -- 1.4.1. Field data -- 1.4.1.1. McMurdo Sound -- 1.4.1.2. Barrow -- 1.4.1.3. Ice tank experiment -- 1.4.2. Deriving the bulk salinity of the ice from complex dielectric permittivity measurements -- 1.4.2.1. Apparent aspect ratio of brine inclusions in sea ice -- 1.4.2.2. Establishing the relation between the real part of the complex dielectric permittivity and bulk salinity of sea ice -- 1.4.2.3. Salinity change in the landfast sea ice at Barrow, Alaska, 2003 -- 1.4.2.4. Sources of error -- 1.5. Conclusions -- 1.6. Figures -- 1.7. Tables -- 1.8. References -- 2. Analysis of brine movement in first-year sea ice based on a case study of temperature and dielectric permittivity data -- 2.1. Abstract -- 2.2. Introduction -- 2.2.1. Aims -- 2.2.2. Theory -- 2.3. Study area and instrumentation -- 2.4. Results and analysis -- 2.4.1. Analysis of individual events -- 2.4.2. Analysis of heat flow -- 2.5. Discussion and conclusion -- 2.6. Figures -- 2.7. Tables -- 2.8. References -- General conclusions -- References

Arbeitsgemeinschaft: Topological Robotics

The purpose of the Arbeitsgemeinschaft was to enable PhD students and researchers to study Topological Robotics, a new field investigating topological problems motivated by robotics and engineering as well as problems of practical robotics requiring topological tools. The topics broadly fell into the areas of Topology of configuration spaces, Topological complexity of robot motion planning algorithms and Stochastic topology