This work is concerned with the derivation of general analytical formulae for the matrix elements, in an M representation, of effective two-nucleon interaction. The anisotropic harmonic oscillator wave equation is solved in cylindrical coordinates and the subsequent wave functions used to find the desired matrix element expressions. Since these expressions are in a form conducive to rapid machine computation this representation is well suited for spectroscopic calculations for deformed nuclei. This is illustrated by the calculation of the relative Mng energies, by means of a limited Hartree—Fock method, of several nucleonic configurations in the 2s-ld shell. / Thesis / Master of Science (MS)

The honey bee is one of the most important crop pollinating insects in the world. Researchers have recently identified a disease that has begun to impact the honey bee population. Colony Collapse Disorder results in the death of many bee colonies every year, but the cause for this remains unknown. Investigating the cause, harmonic radars are being considered to track the foraging patterns of honey bees. This research endeavors to find an optimized waveform for use in tracking foraging bees. Harmonic oscillators were developed for a transmit frequency of 1.2 GHz and various waveforms were tested against the oscillators. Ultimately, the waveform was found to be arbitrary. The amount of power that the harmonic oscillator receives is the determining factor. Given this, a general pulsed waveform can be developed that attempts to provide the maximum possible return for a predetermined maximum range of interest.

The gauge-invariant formulation of quantum mechanics is compared to the conventional approach for the case of a one-dimensional charged harmonic oscillator in an electromagnetic field in the electric dipole approximation. The probability of finding the oscillator in the ground state or excited states as a function of time is calculated, and the two approaches give different results. On the basis of gauge invariance, the gauge-invariant formulation of quantum mechanics gives the correct probability, while the conventional approach is incorrect for this problem. Therefore, expansion coefficients or a wave function cannot always be interpreted as probability amplitudes. For a physical interpretation as probability amplitudes the expansion coefficients must be gauge invariant.

This thesis investigates both theoretical and implementation-level aspects of switching- feedback control strategies for the development of voltage-controlled oscillators. We use a modified sliding-mode compensation scheme based on various norms of the system state to achieve amplitude control for wide-tuning range oscillators. The proposed controller provides amplitude control at minimal cost in area and power consumption. Verification of our theory is achieved with the physical realization of an amplitude controlled negative-Gm LC oscillator. A wide-tuning range RF ring oscillator is developed and simulated, showing the effectiveness of our methods for high speed oscillators. The resulting ring oscillator produces an amplitude controlled sinusoidal signal operating at frequencies ranging from 170 MHz to 2.1 GHz. Total harmonic distortion is maintained below 0:8% for an oscillation amplitude of 2 Vpp over the entire tuning range. Phase noise is measured as -105.6 dBc/Hz at 1.135 GHz with a 1 MHz offset.

京都大学 / 新制・論文博士 / 博士(理学) / 乙第13434号 / 論理博第1576号 / 新制||理||1682(附属図書館) / 京都大学大学院理学研究科 / (主査)教授 谷村 吉隆, 教授 林 重彦, 教授 渡邊 一也 / 学位規則第4条第2項該当 / Doctor of Science / Kyoto University / DGAM

In this thesis we focus on two elementary unstable quantum systems, the inverted harmonic oscillator and the inverse square potential, using the methods of effective field theory (EFT) and the renormalization group (RG). We demonstrate that the phenomenon of fall to the centre associated with the inverse square potential is an example of a PT symmetry breaking transition. We also demonstrate a mapping between the inverted harmonic oscillator and the inverse square potential including a one-to-one mapping between the quantum states and boundary conditions using an EFT framework in a renormalization group invariant way. We apply these methods to the phenomenon of Schwinger pair production and study finite size effects using the RG scheme for the quantum inverted harmonic oscillator. / Thesis / Doctor of Philosophy (PhD)

We investigate the energy levels of a particle confined in the isotropic oscillator potential with a magnetic and spatially varying electric field. Here we are able to exactly solve the Schrodinger equation, using matrix methods, for the first excited states. To this end we find that the spatial gradient of the electric field acts as a magnetic field in certain circumstances. Here we present the changes in the energy levels as functions of the electric field, and other parameters.

We apply the Segal process of group simplification to the linear harmonic oscillator. The result is a finite quantum theory with three quantum constants instead of the usual one. We compare the classical (CLHO), quantum (QLHO), and finite (FLHO) linear harmonic oscillators and their canonical or unitary groups. The FLHO is isomorphic to a dipole rotator with N=l(l+1) states where l is very large for physically interesting case. The position and momentum variables are quantized with uniform finite spectra. For fixed quantum constants and large N there are three broad classes of FLHO: soft, medium, and hard corresponding respectively to cases where ratio of the of potential energy to kinetic energy in the Hamiltonian is very small, almost equal to one, or very large The field oscillators responsible for infra-red and ultraviolet divergences are soft and hard respectively. Medium oscillators approximate the QLHO. Their low-lying states have nearly the same zero-point energy and level spacing as the QLHO, and nearly obeying the Heisenberg uncertainty principle and the equipartition principle. The corresponding rotators are nearly polarized along the z-axis. The soft and hard FLHO's have infinitesimal 0-point energy and grossly violate equipartition and the Heisenberg uncertainty principle. They do not resemble the QLHO at all. Their low-lying energy states correspond to rotators polaroizd along x-axis or y-axis respectively. Soft oscillators have frozen momentum, because their maximum potential energy is too small to produce one quantum of momentum. Hard oscillators have frozen position, because their maximum kinetic energy is too small to produce one quantum of momentum. Hard oscillators have frozen position, because their maximum kinetic energy is too small to excite one quantum of position.

In this thesis the path integral formalism is applied to the calculation of the dynamics of dissipative quantum systems. The time evolution of a system of bilinearly coupled bosonic modes is treated using the real-time path integral technique in coherent-state representation. This method is applied to a damped harmonic oscillator within the Caldeira-Leggett model. In order to get the stationary trajectories the corresponding Lagrangian function is diagonalized and then the path integrals are evaluated by means of the stationary-phase method. The time evolution of the reduced density matrix in the basis of coherent states is given in simple analytic form for weak system-bath coupling, i.e. the so-called rotating-wave terms can be evaluated exactly but the non-rotating-wave terms only in a perturbative manner. The validity range of the rotating-wave approximation is discussed from the viewpoint of spectral equations. In addition, it is shown that systems without initial system-bath correlations can exhibit initial jumps in the population dynamics even for rather weak dissipation. Only with initial correlations the classical trajectories for the system coordinate can be recovered. The path integral formalism in a combined phase-space and coherent-state representation is applied to the problem of curve-crossing dynamics. The system of interest is described by two coupled one-dimensional harmonic potential energy surfaces interacting with a heat bath. The mapping approach is used to rewrite the Lagrangian function of the electronic part of the system. Using the Feynman-Vernon influence-functional method the bath is eliminated whereas the non-Gaussian part of the path integral is treated using the perturbation theory in the small coordinate shift between potential energy surfaces. The vibrational and the population dynamics is considered in a lowest order of the perturbation. The dynamics of a Gaussian wave packet is analyzed along a one-dimensional reaction coordinate. Also the damping rate of coherence in the electronic part of the relevant system is evaluated within the ordinary and variational perturbation theory. The analytic expressions for the rate functions are obtained in the low and high temperature regimes.

LIMA JÚNIOR, Vanderley Aguiar de. Entropia e informação de sistemas quânticos amortecidos. 2014. 65 f. Dissertação (Mestrado em Física) - Programa de Pós-Graduação em Física, Departamento de Física, Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2014. / Submitted by Edvander Pires (edvanderpires@gmail.com) on 2015-04-09T19:28:55Z No. of bitstreams: 1 2014_dis_valimajunior.pdf: 987183 bytes, checksum: 660164955bb5a5c19b5d2d3bb2013a82 (MD5) / Approved for entry into archive by Edvander Pires(edvanderpires@gmail.com) on 2015-04-10T20:50:41Z (GMT) No. of bitstreams: 1 2014_dis_valimajunior.pdf: 987183 bytes, checksum: 660164955bb5a5c19b5d2d3bb2013a82 (MD5) / Made available in DSpace on 2015-04-10T20:50:41Z (GMT). No. of bitstreams: 1 2014_dis_valimajunior.pdf: 987183 bytes, checksum: 660164955bb5a5c19b5d2d3bb2013a82 (MD5) Previous issue date: 2014