We explore the dynamics of integrable and chaotic quantum many-body systems with a focus on universal structures known as caustics, which are a type of singularity categorized by catastrophe theory. Papers I and II study light cones in quantum spin chains, which we show are caustics and therefore inherits specific functional forms. For integrable systems, the edge of the cone is a fold catastrophe, making the wavefunction locally of Airy form. We also identify the cusp catastrophe in the XY model, thus the secondary light cone is a Pearcey function. Vortex pairs appear in the dynamics, are sensitive to phase transitions, and permit the extraction of critical scaling exponents. In paper II we use a Gaussian wavefront form to distinguish integrable and chaotic models. Writing the wavefront as exp[−m(x)(x − vt)2 + b(x)t], the scaling of coefficients m(x) and b(x) is the diagnostic. The local Airy function description in free models leads to a power-law ∼ x^{−n/3} scaling, while for the chaotic case the scaling is exponential ∼ e^{−cx}. In Paper III, we study the function Fn(t) = <(A(t)B)^n>, a generalization of the four-point out-of-time ordered correlator (OTOC) F2(t), for an integrable system and show that the function Fn(t) can be recast as the return amplitude of an effective time dependent chaotic system, exhibiting signals of chaos such as a positive Lyapunov exponent, spectral statistics consistent with random matrix theory, and relaxation. In Paper IV we perform a comprehensive investigation of caustics in many-body systems in (1+1)- and (2+1)-dimensional Fock space and time. We show how a hierarchy of caustics appear in the dynamics of many-body models, using two- and three-mode Bose-Hubbard models as guiding systems. We show that, in the case of the trimer, high dimensional caustics appear and are organized by the catastrophe X9. / Thesis / Doctor of Philosophy (PhD)

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Dois tipos diferentes de hologramas (Fresnel e Fourier) foram gerados por computador. O holograma de Fresnel foi escolhido para fazer parte de um arranjo experimental que teve como objetivo estimar a rugosidade de amostras metálicas. Para isso, um novo método de aplicação de um correlator óptico foi desenvolvido. Hologramas de Fourier geralmente fazem parte do correlator óptico de VanderLugt, o qual é muito utilizado no reconhecimento de padrões. A reconstrução numérica de hologramas de Fresnel gerados por computador, "distorcidos" por superfícies metálicas (também simuladas), serviram de base para que a reconstrução óptica de um holograma de Fresnel fosse utilizada, de forma inédita, no reconhecimento de padrões para estimar a rugosidade de amostras metálicas. / Two different types of holograms (Fresnel and Fourier) have been computer-generated. The Fresnel hologram has been chosen as part of an experimental set, which meant to estimate the roughness of the metalic samples. A new method for the aplication of an optical correlator has been developed. Fourier holograms are, generally, part of the VanderLugt optical correlator, that is very used for pattern recognition. The numerical reconstruction of the computer-generated Fresnel holograms, "distorted" by metalic surfaces (simulated as well), worked as the base for the utilization, in an original way, of the optical reconstruction of a Fresnel hologram, at the pattern recognition to estimate the roughness of the metalic samples.

Dois tipos diferentes de hologramas (Fresnel e Fourier) foram gerados por computador. O holograma de Fresnel foi escolhido para fazer parte de um arranjo experimental que teve como objetivo estimar a rugosidade de amostras metálicas. Para isso, um novo método de aplicação de um correlator óptico foi desenvolvido. Hologramas de Fourier geralmente fazem parte do correlator óptico de VanderLugt, o qual é muito utilizado no reconhecimento de padrões. A reconstrução numérica de hologramas de Fresnel gerados por computador, "distorcidos" por superfícies metálicas (também simuladas), serviram de base para que a reconstrução óptica de um holograma de Fresnel fosse utilizada, de forma inédita, no reconhecimento de padrões para estimar a rugosidade de amostras metálicas. / Two different types of holograms (Fresnel and Fourier) have been computer-generated. The Fresnel hologram has been chosen as part of an experimental set, which meant to estimate the roughness of the metalic samples. A new method for the aplication of an optical correlator has been developed. Fourier holograms are, generally, part of the VanderLugt optical correlator, that is very used for pattern recognition. The numerical reconstruction of the computer-generated Fresnel holograms, "distorted" by metalic surfaces (simulated as well), worked as the base for the utilization, in an original way, of the optical reconstruction of a Fresnel hologram, at the pattern recognition to estimate the roughness of the metalic samples.

ITC/USA 2005 Conference Proceedings / The Forty-First Annual International Telemetering Conference and Technical Exhibition / October 24-27, 2005 / Riviera Hotel & Convention Center, Las Vegas, Nevada / The GPS receiver based on software radio technology is a kind of general purpose GPS signal processing platform which makes use of advanced design ideas and advanced design tools nowadays. We used FPGA device and lots of necessary peripherals such as DSP and PCI controller in our design to promote flexibility and practicability effectively. Various fast acquisition means and accurate tracking algorithms could be realized, improved and validated on this platform, besides basic GPS receiver function.

Current attempts to make precision measurements of the HI power spectrum at high redshifts have led to the construction of several low-frequency, large-N, interferometric arrays. The computational demands of digital correlators required by these arrays present a significant challenge. These demands stem from the treatment of radio telescopes as collections of two-element interferometers, which results in the need to multiply O(N²) pairs of antenna signals in an N-element array. Given the unparalleled flexibility offered by modern digital processing systems, it is apt to consider whether a different way of treating the signals from antennas in an array might be fruitful in current and future radio telescopes. Such methods potentially avoid the unfavourable N² scaling of computation rate with array size. In this thesis I examine the prospect of using direct-imaging methods to map the sky without first generating correlation matrices. These methods potentially provide great computational savings by creating images using efficient, FFT-based algorithms. This thesis details the design and deployment of such a system for the Basic Element of SKA Training II (BEST-2) array in Medicina, Italy. Here the 32-antenna BEST-2 array is used as a test bed for comparison of FX correlation and direct-imaging systems, and to provide a frontend for a real-time transient event detection pipeline. Even in the case of traditional O(N²) correlation methods, signal processing algorithms can be significantly optimized to deliver large performance gains. In this thesis I present a new mechanism for optimizing the cross-correlation operation on Field Programmable Gate Array (FPGA) hardware. This implementation is shown to achieve a 75% reduction in multiplier usage, and has a variety of benefits over existing optimization strategies. Finally, this thesis turns its focus towards The Square Kilometre Array (SKA). When constructed, the SKA will be the world's largest radio telescope and will comprise a variety of arrays targeting different observing frequencies and science goals. The low-frequency component of the SKA (SKA-low) will feature ~250,000 individual antennas, sub-divided into a number of stations. This thesis explores the impact of the station size on the computational requirements of SKA-low, investigating the optimal array configuration and signal processing realizations.

Correlatores ópticos podem realizar o reconhecimento de padrões bidimensionais a uma velocidade maior que plataformas digitais com o mesmo tamanho, peso e consumo de potência. Utilizou-se neste projeto o correlator óptico compacto com um único modulador espacial de luz, uma TV a cristal líquido comercial, posicionado no plano de Fourier. Uma câmera CCD é utilizada na saída do correlator óptico para capturar as imagens de correlação. Na entrada do correlator, a imagem da impressão digital é capturada por um prisma via eliminação da reflexão total, durante o contato da impressão digital com a superfície do prisma. Para o processo de filtragem, foi utilizado o filtro de correlação ótima. / Optical correlators can realize bidimensional pattern recognition faster than digital devices that have the same size, weight and power consumption. In this work, the compact optical correlator is implemented with only one spatial light modulator, a commercial liquid crystal television (LCTV) located at the Fourier plane. A CCD camera is used at the correlator exit to read the correlation images. The fingerprint image is read in the correlator input using a prism illuminated with a monochromatic coherent beam. The total reflection elimination in the prism surface during the fingerprint contact permits the reading of the fingerprint image. The optimal correlation filter is used in the Fourier plane to implement the filtering process.

Global Positioning System is a technology which is gaining acceptance. Originally developed for military purposes, it is being used in civilian applications such as navigation, emergency services, etc. A system-on-chip application merges different functions and applications on a single substrate. This project models a GPS receiver for a system on chip application. The GPS receiver, developed as a core, is intended to be a part of a navigation tour guide being developed. The scope of this work is the GPS C/A code on the L1 carrier. The digital signal processing back-end in a GPS receiver is modelled in this work. VHDL modeling of various communiation sub-blocks, detection and demodulation schemes is done. A coherent demodulation of the GPS signals is implemented. GPS receiver calculates the position based on the data collected from four satellites. Given four satellites, acquisition of the data from the signals is performed and data demodulated from the same. Synthetic data is generated for validation purposes. Code acuqisition and tracking of the GPS C/A signal is implemented. Cadence NC-Launch VHDL simulator is used to validated the behavioral VHDL model.

Correlatores ópticos podem realizar o reconhecimento de padrões bidimensionais a uma velocidade maior que plataformas digitais com o mesmo tamanho, peso e consumo de potência. Utilizou-se neste projeto o correlator óptico compacto com um único modulador espacial de luz, uma TV a cristal líquido comercial, posicionado no plano de Fourier. Uma câmera CCD é utilizada na saída do correlator óptico para capturar as imagens de correlação. Na entrada do correlator, a imagem da impressão digital é capturada por um prisma via eliminação da reflexão total, durante o contato da impressão digital com a superfície do prisma. Para o processo de filtragem, foi utilizado o filtro de correlação ótima. / Optical correlators can realize bidimensional pattern recognition faster than digital devices that have the same size, weight and power consumption. In this work, the compact optical correlator is implemented with only one spatial light modulator, a commercial liquid crystal television (LCTV) located at the Fourier plane. A CCD camera is used at the correlator exit to read the correlation images. The fingerprint image is read in the correlator input using a prism illuminated with a monochromatic coherent beam. The total reflection elimination in the prism surface during the fingerprint contact permits the reading of the fingerprint image. The optimal correlation filter is used in the Fourier plane to implement the filtering process.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20175号 / 理博第4260号 / 新制||理||1612(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 高柳 匡, 教授 杉本 茂樹, 教授 川合 光 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM