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Transport and Localization in Classical and Quantum Billiards
Črt Lozej, 2020, doktorska disertacija

Opis: In this thesis the classical and quantum dynamics in billiard systems are considered. Extensive numerical studies of the classical transport properties in several examples of billiard families including the ergodic Bunimovich stadium and cut-circle billiards and the mixed-type Robnik and lemon billiards are performed. The analysis of the transport is based on the random model of diffusion which assumes that due the strongly chaotic dynamics the motion of the orbit on the discretized phase space is temporally uncorrelated. The cause of the deviations from the random model dynamics is traced to dynamical trapping due to stickiness. A novel approach to locally quantifying stickiness based on the statistics of the recurrence times is presented and applied to distinguish between exponential decays of recurrence times and other types of decays. This enables the identification of sticky areas in the chaotic components. Detailed maps of their structure for a wide range of parameter values, mapping the evolution of the mixed-phase spaces and revealing some particularly interesting special examples are presented. The recurrence time distributions in sticky areas are found to be well described by a mixture of exponential decays. The transport of particle ensembles in the momentum space of classical billiards is described by using an inhomogeneous diffusion model and the classical transport times are determined. The classical transport times are vital for the analysis of the localization of chaotic eigenstates in quantum billiards. The control parameter that describes the the degree of localization of the chaotic quantum eigenstates is the ratio between the Heisenberg time (Planck's constant divided by the mean level spacing) and the classical transport time. Extensive numerical calculations of the high-lying spectra and eigenstates of the stadium, Robnik and lemon quantum billiards are performed. The spectral statistics are analysed in terms of the standard methods of quantum chaos. The level repulsion exponent of localized eigenstates is found to be a rational function of the control parameter. The degree of localization is determined with respect to localization measures based on the Poincaré-Husimi representation of the eigenstates. The mean localization measure is found to be a rational function of the control parameter and linearly related to the level repulsion exponent. The distributions of the localization measures are analysed and found to be of a universal shape well described by a two parameter empirical distribution in billiards with no apparent stickiness. The nonuniversal system specific features of localization measure distributions are related to the presence of sticky areas in the phase spaces of classical billiards with specific examples shown.
Ključne besede: Transport, localization, chaos, quantum chaos, Hamiltonian systems, level spacing distribution, mixed phase space, billiard, quantum billiard, Husimi functions, stickiness, cantorus, chaotic eigenstates, level repulsion.
Objavljeno: 13.01.2021; Ogledov: 191; Prenosov: 39
.pdf Celotno besedilo (24,93 MB)

Design of an Embedded Position Sensor with Sub-mm Accuracy
Matej Nogić, 2019, magistrsko delo

Opis: This master’s thesis presents the development of a machine-vision based localization unit developed at Robert Bosch GmbH, Corporate Sector Research and Advance Engineering in Renningen, Germany. The localization unit was developed primarily for position detection purposes with three degrees of freedom in highly versatile manufacturing systems but has an immense potential to be used anywhere where a precise, low-cost localization method on a two-dimensional surface is required. The complete product development cycle was carried out, from the components selection, schematic and optical system design, to the development of machine vision algorithms, four-layer Printed Circuit Board design and evaluation using an industrial robot. Thanks to the use of a patented two-dimensional code pattern, the localization unit can cover a surface area of 49 km2. The size and speed optimized, self-developed machine-vision algorithms running on a Cortex-M7 microcontroller allow achieving an accuracy of 100 µm and 60 Hz refresh rate.
Ključne besede: localization, machine-vision, code pattern, image sensor, embedded system
Objavljeno: 14.01.2020; Ogledov: 302; Prenosov: 0

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