Abstract In this thesis, we study quantum waveguides and their spectral properties. A quantum waveguide is a system of narrow strips or tubes. That is, the waveguide has large longitudinal but small transverse sizes. The study of quantum waveguides is essential in the semi-conductor industry, and the waveguides are used to model the electron behavior in these devices. We consider two- and three-dimensional waveguides with sharp bends and question whether the quantum particle can propagate in the waveguide. It is well known that a certain type of bends and bulges cause the resonance phenomena, that is, at some energy levels the electron motion is localized in a finite area, and the propagation is disturbed. The study of waveguides leads to the interesting field of mathematics - the spectral analysis of differential operators. For a waveguide having high purity and a crystalline structure, the electron motion can be considered as a free particle motion with effective mass. This gives rise to the spectral problem, that is, the eigenvalue problem of the Laplace operator. On the boundary we set the Dirichlet conditions. This thesis consists of three parts and in each part we study waveguides which form sharp bends in the junctions where two or three outlets are joined together. To be precise, we consider waveguides which resemble the letters Y, Z, and C. We study the discrete spectrum corresponding to these waveguides and the behavior of the bound modes when the geometry is slightly changed. For this, we apply the variational, numerical, and asymptotic methods. For the Y-shaped waveguide, we let one outlet become wider than the others and found that a critical width exists, so that for smaller width values, exactly one bound state exists, but for larger values, no bound modes exist. We also let the angle between the strips to vary and found that the number of the bound modes highly depends on the opening angle of the outlets in the Y-shaped waveguide. For the Z- and C-shaped waveguides, we let the height of the waveguide change. We saw that there may appear two bound states at most. Moreover, for the C-shaped waveguide, the first is monotone increasing as a function of height and the second eigenvalue is monotone decreasing. For the Z-shaped waveguide, we show that the lowest eigenvalue as a function of the height is not monotone. / Tiivistelmä Tässä väitöskirjassa tutkitaan kvanttiaaltojohteisiin liittyvää ominaisarvo-ongelmaa. Kvanttiaaltojohteessa aallon eteneminen on rajoitettu tiettyyn suuntaan, ja johde on poikittaissuunnassa nanokokoluokkaa. Kvanttiaaltojohteiden tutkimus on tärkeä osa nykyistä puolijohdeteknologiaa. Tutkimuksessamme olemme keskittyneet kaksi- ja kolmiulotteisiin aaltojohteisiin, jotka geometrialtaan muistuttavat Y-, Z- tai C-kirjainta. Haluamme tietää millaisissa tilanteissa elektronin liike aaltojohteessa estyy. Yleisesti tiedetään, että aaltojohteessa olevat pullistumat ja mutkat johtavat niin sanottuun sidottuun tilaan, ts. tilanteeseen että tietyllä taajuudella tai energiatasolla oleva partikkeli jää lokalisoituun tilaan. Aaltojohde rakentuu puhtaasta kiderakennemateriaalista, joka on kokoluokaltaan pieni poikittaissuunnassa, niin että elektronin liikettä voidaan kuvata vapaan elektronin mallilla Schrödingerin yhtälössä, jossa elektronilla on effektiivinen massa. Tämä johtaa Laplace-operaattorin ominaisarvo-ongelmaan, reunaehtoina on aaltojohteille käytetty Dirichlet nollareuna-arvoja. Tässä väitöstutkimuksessa on tutkittu kolmea erityyppistä aaltojohdetta, joiden geometriaa voidaan kuvata kirjainten Y, C ja Z avulla. Jokaisessa tapauksessa on tutkittu spektristä erityisesti diskreettiä osaa, ja erityisesti mahdollisia muutoksia diskreetissä spektrissä geometristen parametrien muuttuessa. Diskreetin spektrin tutkimiseen on käytetty variaatiomenetelmiä, asymptoottista analyysiä sekä numeerisista menetelmistä elementtimenetelmää. Geometrialtaan kirjainta Y muistuttava aaltojohde koostuu kolmesta haarasta, joista yhden leveyden annetaan varioida. Tällöin voidaan löytää kriittinen raja, siten että jalan leveyden ollessa tätä rajaa pienempi on diskreetti spektri epätyhjä kun taas leveyden ollessa kriittistä rajaa suurempi, diskreetti spektri on tyhjä. Toisessa tapauksessa jalan leveydet pidetään samana, mutta annetaan kulman kahden haaran välillä muuttua. Voidaan nähdä, että diskreetissä spektrissä olevien ominaisarvojen lukumäärä riippuu aaltojohteen kulmasta siten että mitä pienempi kulma kahden haaran välillä, sitä enemmän ominaisarvoja on diskreetissä spektrissä. Vastaavasti Z- ja C- aaltojohteissa, aaltojohteen korkeutta säädellään. Havaitaan, että korkeuden kasvaessa, voi aaltojohteessa esiintyä korkeintaan kaksi ominaisarvoa diskreetissä spektrissä. Lisäksi C-aaltojohteen ensimmäisen ominaisarvon voidaan havaita olevan kasvava aaltojohteen korkeuden funktiona kun taas toinen ominaisarvoista on vähenevä. Toisaalta taas Z-aaltojohteen pienin ominaisarvo korkeuden funktiona ei ole monotoninen.

Thesis (PhD)--Stellenbosch University, 2015. / ENGLISH ABSTRACT: Please refer to full text for abstract. / AFRIKAANSE OPSOMMING: Sien asb volteks vir opsomming.

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The gyromagnetic ratio of bound particles is an active field of experimental and theoretical research. Early measurements of corrections to the bound g-factor came from experiments involving hydrogen-like ions. As the sensitivity of such experiments has increased, it has become possible to instead use them to measure the electron-ion mass ratio -- but only if the theoretical bound g-factor is known with sufficient precision for these systems. By constructing an effective nonrelativistic Lagrangian, we derive leading order binding and recoil corrections for systems comprised of particles with arbitrary spin. Lagrangians for spin one-half and spin one-theories are developed, before moving on to the more general case of arbitrary spin. In each case, an effective nonrelativistic Lagrangian taking into account all relevant terms is constructed. The coefficients of this Lagrangian are then fixed by calculating scattering processes in both the relativistic and nonrelativistic theories. A relativistic framework for dealing with particles of arbitrary spin is considered. In this framework the relevant terms in the scattering process are heavily constrained by the symmetries required of the electromagnetic current. This allows the determination of an effective Lagrangian valid for arbitrary spin. It is found that the only coefficients which depend upon the spin of the particle in question involve derivatives of the magnetic field. This general form is consistent with the previously derived Lagrangians for spin one-half and spin one particles. With this effective nonrelativistic Lagrangian, the leading order binding and recoil corrections to the bound gyromagnetic ratio are calculated. These corrections are found to be universal, independent of the spin of the particles involved. This is understood as a consequence of the Bargmann-Michel-Telegdi equation.

京都大学 / 0048 / 新制・論文博士 / 博士(理学) / 乙第13368号 / 論理博第1572号 / 新制||理||1666(附属図書館) / 京都大学理学研究科 / (主査)教授 永江 知文, 教授 中家 剛, 准教授 成木 恵 / 学位規則第4条第2項該当 / Doctor of Science / Kyoto University / DGAM

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18787号 / 理博第4045号 / 新制||理||1582(附属図書館) / 31738 / 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 永江 知文, 教授 谷森 達, 准教授 成木 恵 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

Interstellar plasma — interstellar clouds in particular — play an important role in determining the structure and evolution of galaxies. Understanding the time evolution of such plasmas requires knowledge of the chemical processes that drive their dynamics. Two processes are studied in this dissertation: radiative electron attachment (REA) via dipole-bound states (DBSs) and dissociative recombination (DR). Of the several hundred molecules detected in the interstellar medium, only eight anions have been detected: CN-, C3N-, C5N-, C7N-, C4H-, C6H-, C8H-, and C10H-. Their production mechanism is not well known; REA was suggested as a possible formation pathway, but previous theoretical studies have found that REA rate coefficients were too low to explain the formation of CN-, C3N-, and C5N-. It was later suggested that including DBSs — an electron weakly bound at a large distance to the large dipole moment of a neutral molecule — could appreciably enhance the REA rate coefficients. The first portion of this study is dedicated to investigating the role of the large dipole moment of rotating C3N using an accurate \it ab initio approach with electronic and rotational resolution. DBS wavefunctions of C3N- are calculated and used to obtain REA cross sections that produce even smaller rate coefficients, suggesting that C3N- is efficiently formed by a different process. The second part of this study investigates DR in the difficult case of molecules with low-lying eletronic resonances, although these are not necessary for the approach. An approach to treat both direct and indirect mechanisms of DR in a diatomic ion with electronic, vibrational, and rotational resolution using R-matrix scattering calculations, frame transformation theory, and multichannel quantum defect theory is presented and applied to the CH+ and CF+ molecular ions at low collision energies. The calculated CH+ cross sections agree well with recent rotationally state-resolved experimental results and overall better than previous theoretical results. The calculated CF+ cross sections agree well with experimental results, although these do not have rotational resolution, and overall better than previous theoretical results at low energies. Additionally, the method can study rovibronic (de-)excitation — a process in competition with DR. These are calculated and compared to previous theoretical calculations for CH+, which which our results agree well with the exception of dipole-driven rotational excitation cross sections. This discrepancy is tentatively attibuted to negelcting the contribution of higher partial waves in the description of the incident electron, which will be incorporated in future studies.

Made available in DSpace on 2015-05-15T11:46:04Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 695566 bytes, checksum: 26f7afc275ad83fa634352b9d522415e (MD5) Previous issue date: 2012-04-26 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this dissertation, we study the existence of two types of non-negative weak solutions for a class of problems of Schrodinger-Poisson type. This kind of problem models, for example, several physical phenomena in quantum mechanics. Initially, by minimization arguments, Splitting Lemma and the Variational Principle of Ekeland we find a weak solution that minimizes the minimum energy level associated to the variety of Nehari N. This is the so-called ground state solution. Afterwards we will find, by using the Linking Theorem, a strictly positive weak solution which is not a ground state solution: the so-called bound state solution. / Nesta dissertação, estudaremos a existência de dois tipos de soluções fracas não negativas para uma classe de problemas do tipo Schrödinger-Poisson, os quais modelam fenômenos físicos, por exemplo, em Mecânica Quântica. Inicialmente, encontraremos através de argumentos de minimização, do Lema Splitting e do Princípio Variacional de Ekeland, uma solução fraca que minimiza o nível de energia mínima associado a variedade de Nehari N. Tal solução é denominada do tipo ground state. Em seguida, encontraremos através do Teorema de Linking, uma solução fraca estritamente positiva que não é do tipo ground state. Tal solução é denominada do tipo bound state.

The double hypernuclear systems are studied within the context of the hyperspherical approach. Possible bound states of these systems are sought as zeros of the corresponding three-body Jost function in the complex energy plane. Hypercentral potentials for the system are constructed from known potentials in order to determine bound states of the system. Calculated binding energies for double- hypernuclei having A = 4 − 20, are presented. / Physics / M.Sc. (Physics)

The double hypernuclear systems are studied within the context of the hyperspherical approach. Possible bound states of these systems are sought as zeros of the corresponding three-body Jost function in the complex energy plane. Hypercentral potentials for the system are constructed from known potentials in order to determine bound states of the system. Calculated binding energies for double- hypernuclei having A = 4 − 20, are presented. / Physics / M.Sc. (Physics)