Made available in DSpace on 2016-06-02T20:27:37Z (GMT). No. of bitstreams: 1 2634.pdf: 730847 bytes, checksum: 78e230f57f2f8d462d8fe0f28ef3dae7 (MD5) Previous issue date: 2009-10-05 / Universidade Federal de Sao Carlos / In this work we present a study of topics related to the Aharonov-Bohm (AB) e®ect. Our framework is that of nonrelativistic quantum mechanics and we use the point of view of mathematical physics. (1) We study the solenoid of finite length and zero radius and compare their self- adjoint extensions with the known case of the solenoid of infinite length and also of zero radius in the plane. (2) By considering an infinitely long cylindrical solenoid of radius greater than zero, mainly in the plane, we present a classification of all self-adjoint SchrÄodinger operators (i.e., the possible boundary conditions on the solenoid border) that mathematically could characterize the AB operator, whose domains are contained in the natural space of twice weakly di®erentiable functions (and, of course, also square integrable). (3) We then consider the traditional Dirichlet, Neumann and Robin boundary conditions on the solenoid border and calculate and compare their scattering matrices and cross sections. Hopefully this could be used to experimentally select one of such extensions. (4) Finally, we discuss a theoretical mechanism we propose to select and so justify the usual AB hamiltonian with Dirichlet boundary conditions on the solenoid. This is obtained by way of increasing sequences of finitely long solenoids together with a natural impermeability procedure; further, it is shown that both limits commute. Such rigorous limits are in the strong resolvent sense. / Neste trabalho apresentamos um estudo de tópicos relacionados ao Efeito Aharonov- Bohm (AB). Nossa abordagem é a da mecânica quântica não-relativística e usamos o ponto de vista da física-matemática. (1) Estudamos o solenóide de comprimento ¯nito de raio zero e comparamos suas extensões auto-adjuntas com as do caso conhecido do solenóide de comprimento infinito também de raio zero no plano. (2) Considerando um solenóide cilíndrico infinito de raio maior do que zero, principalmente no plano, apresentamos uma classificação de todos os operadores de SchrÄodinger auto-adjuntos (isto é, as possíveis condições de fronteira na borda do solenóide) que matematicamente poderiam caracterizar o operador AB, cujos domínios estão contidos no espaço natural das funções duas vezes fracamente diferenciáveis (e, natural- mente, também de quadrado integrável). (3) Então consideramos as tradicionais condições de fronteira de Dirichlet, Neumann e Robin na borda do solenóide e calculamos e comparamos seus operadores de espalhamento e seções de choque. Esperamos que com tal estudo uma dessas extensões auto-adjuntas possa ser selecionada experimentalmente. (4) Final- mente, discutimos um mecanismo teórico que propomos para selecionar, e assim justificar, o usual hamiltoniano de AB com condições de Dirichlet na fronteira do solenóide. Isto é obtido por meio de uma sequência crescente de solenóides de comprimentos finitos junto com um procedimento natural de impermeabilização; além disso, mostramos que ambos os limites comutam. Tais limites rigorosos são no sentido forte do resolvente.

Made available in DSpace on 2015-05-14T12:14:02Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1192098 bytes, checksum: 690fbe77953ec5a5854ba7d642c29a4f (MD5) Previous issue date: 2000-09-08 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Os fatores de fase geométricos e topológicos têm sido objeto de grande interesse em diferentes áreas da f´sica. Nas teorias de gauge não-Abelianas, essas quantidades foram usadas no estudo de propriedades, como, por exemplo, o confinamento de quarks na cromodinâmica quântica. No contexto da mecânica quântica, a fase geométrica aparece na evolução de um sistema cuja Hamiltoniana é dependente do tempo, e é de fundamental importância no contexto da gravitação. Os fatores de fase também foram usados para se obter uma descrição da teoria independente de gauge. Nesta tese usamos o fator de fase nas teorias da gravitação de Einstein e Kaluza-Klein para investigar o efeito Aharonov-Bohm, caracterizar globalmente alguns espaços-tempos e estudar o aparecimento da fase de Berry e suas relações com os parâmetros que caracterizam os espaços-tempos considerados. Investigamos também, como o fator de fase no espaço-tempo de Kerr-Newman com defeito cônico, depende da rotação e da presença do defeito.

No description available.

We present studies of edge states induced by the Aharonov-Casher vector potential or Rashba-type spin-orbit interaction using quantum transport in InGaAs/InAlAs herterostructures. The Aharonov-Casher effect is electromagnetically dual to the Aharonov-Bohm effect and is predicted to lead to edge states in a parabolic confinement at two-dimensional sample edges. As a narrow gap material, InGaAs has a low effective mass, high mobility, and strong spin-orbit interaction, which indicate that it can be used as a good material to detect the Aharonov-Casher effect or SOI interaction. Using InGaAs, we measured the magnetoresistance in a quantum antidot in narrow short channels in a tilted magnetic field. The fine structure (mT spacing) observed in the magnetoresistance indicate a probable energy spacing between AC edge states. We also fabricated side-gate channel structures in InGaAs/InAlAs quantum wells and investigated the values of the Rashba spin-orbit coupling constant α using the weak antilocalization analysis as a function of the side-gate voltage. We take the effect of the finite width into account and find the corrected values. With the simulation of electric fields in the wide channel and narrow channel, we found that the electric field components can be changed using side-gate voltages. While our results do not indicate which electric field component is responsible, the data indicate that the deduced spin-orbit strength values in a narrow channel are tunable by the side-gate voltage. / Ph. D.

The study of quantum interference in solid-state systems yields insight in fundamental properties of mesoscopic systems. Electron quantum interference constitutes an important method to explore mesoscopic physics and quantum decoherence. This dissertation focuses on two-dimensional (2D) electron systems in $delta-$Si doped n-type In$_{0.64}$Ga$_{0.36}$As/In$_{0.45}$Al$_{0.55}$As, 2D hole systems in Si-doped p-type GaAs/Al$_{0.35}$Ga$_{0.65}$As and C-doped p-type GaAs/\Al$_{0.24}$Ga$_{0.76}$As heterostructures. The low temperature experiments study the magnetotransport of nano- and micro-scale lithographically defined devices fabricated on the heterostructures. These devices include a single ring interferometer and a ring interferometer array in 2D electron system, Hall bar geometries and narrow wires in 2D hole systems. The single ring interferometer yields pronounced Aharonov-Bohm (AB) oscillations with magnetic flux periodicity of h/e over a wide range of magnetic field. The periodicity was confirmed by Fourier transformation of the oscillations. The AB oscillation amplitude shows a quasi-periodic modulation over applied magnetic field due to local magnetic flux threading through the interferometer arms. Further study of current and temperature dependence of the amplitude of the oscillations indicates that the Thouless energy forms the measure of excitation energies giving quantum decoherence. An in-plane magnetic field was applied to the single ring interferometer to study the Berry's phase and the Aharonov-Casher effect. The ring interferometer array yields both AB oscillations and Altshuler-Aronov-Spivak (AAS) oscillations, the latter with magnetic flux periodicity of h/2e. The AAS oscillations require time-reversal symmetry and hence can be used to qualify time-reversal symmetry breaking. More importantly, the fundamental mesoscopic dephasing length associated with time-reversal symmetry breaking under applied magnetic field, an effective magnetic length, can be obtained by the analysis of the AAS oscillations over magnetic field. A theoretical model for confined ballistic system is confirmed by experimental data fitting. The AAS oscillations are barely resolved above 0.16 T and their amplitude decays with increasing magnetic field. The AB oscillations exist till above 2 T and their amplitude doesn't show the monotonic decay with increasing magnetic field. The different behavior of the AAS and AB oscillations originates in the different symmetries, respectively temporal and spatial, that they are sensitive to. The p-type 2D GaAs system has strong spin-orbit interaction (SOI). Antilocalization in a Hall bar geometry was analyzed by the 2D Hikami-Larkin-Nagaoka (HLN) theory to obtain the spin coherence time and phase coherence time. The 2D hole systems we studied have low density and high mobility, quite different from the 2D electron systems. These high-quality 2D hole systems demonstrate semi-classical ballistic phenomena in mesoscopic structures preferentially to quantum-coherence phenomena. / Ph. D.

I denna avhandling, som omfattar fyra forskningsartiklar, betraktas två operatorer inom den matematiska fysiken. De båda tidigare artiklarna innehåller resultat för Schrödingeroperatorn med Aharonov-Bohm-magnetfält. I artikel I beräknas spektrum och egenfunktioner till denna operator i R2 explicit i ett antal fall då en radialsymmetrisk skalärvärd potential eller ett konstant magnetfält läggs till. I flera av de studerade fallen kan den skarpa konstanten i Lieb-Thirrings olikhet beräknas för γ = 0 och γ ≥ 1. I artikel II bevisas semiklassiska uppskattningar för moment av egenvärdena i begränsade tvådimensionella områden. Vidare presenteras ett exempel då den generaliserade diamagnetiska olikheten, framlagd som en förmodan av Erdős, Loss och Vougalter, är falsk. Numeriska studier kompletterar dessa resultat. De båda senare artiklarna innehåller ett flertal spektrumuppskattningar för Heisenberg-Laplace-operatorn. I artikel III bevisas skarpa olikheter för spektret till Dirichletproblemet i (2n + 1)-dimensionella områden med ändligt mått. Låt λk och μk beteckna egenvärdena till Dirichlet- respektive Neumannproblemet i ett område med ändligt mått. N. D. Filonov har bevisat olikheten μk+1 < λk för den euklidiska Laplaceoperatorn. I artikel IV visas detta resultat för Heisenberg-Laplaceoperatorn i tredimensionella områden som uppfyller vissa geometriska villkor. / In this thesis, which comprises four research papers, two operators in mathe- matical physics are considered. The former two papers contain results for the Schrödinger operator with an Aharonov-Bohm magnetic field. In Paper I we explicitly compute the spectrum and eigenfunctions of this operator in R2 in a number of cases where a radial scalar potential and/or a constant magnetic field are superimposed. In some of the studied cases we calculate the sharp constants in the Lieb-Thirring inequality for γ = 0 and γ ≥ 1. In Paper II we prove semi-classical estimates on moments of the eigenvalues in bounded two-dimensional domains. We moreover present an example where the generalised diamagnetic inequality, conjectured by Erdős, Loss and Vougalter, fails. Numerical studies complement these results. The latter two papers contain several spectral estimates for the Heisenberg Laplacian. In Paper III we obtain sharp inequalities for the spectrum of the Dirichlet problem in (2n + 1)-dimensional domains of finite measure. Let λk and μk denote the eigenvalues of the Dirichlet and Neumann problems, respectively, in a domain of finite measure. N. D. Filonov has proved that the inequality μk+1 < λk holds for the Euclidean Laplacian. In Paper IV we extend his result to the Heisenberg Laplacian in three-dimensional domains which fulfil certain geometric conditions. / QC 20100712

Submitted by Emanuel Varela Cardoso (emanuel.varela@ufcg.edu.br) on 2018-10-16T17:40:13Z No. of bitstreams: 1 GILSON ACIOLE RODRIGUES – DISSERTAÇÃO (PPGFísica) 2016.pdf: 1524954 bytes, checksum: 9054f2fa535b67f3184b1f692caa7c88 (MD5) / Made available in DSpace on 2018-10-16T17:40:13Z (GMT). No. of bitstreams: 1 GILSON ACIOLE RODRIGUES – DISSERTAÇÃO (PPGFísica) 2016.pdf: 1524954 bytes, checksum: 9054f2fa535b67f3184b1f692caa7c88 (MD5) Previous issue date: 2016-09-28 / Capes / A influência dos deslocamentos parafuso em sistemas quânticos tem recebido considerável atenção nos últimos anos. Alguns trabalhos são baseados na teoria geométrica de defeitos em semicondutores e desenvolvidos por Katanaev Volovich. Nesta abordagem, o semicondutor com um deslocamento parafuso é descrito por uma variedade de Riemann-Cartan onde o deslocamento parafuso está associado ao vetor Burgers. Neste limite do contínuo, um deslocamento parafuso afeta um sistema quântico como um tubo de fluxo magnético isolado, causando fenômenos de interferência tipo Aharonov-Bohm (AB). O espectro de energia de elétrons em torno deste tipo de defeito mostra uma configuração semelhante a do sistema AB. Neste trabalho, investigamos a influência de um deslocamento parafuso sobre os níveis de energia e as funções de onda de um elétron confinado em um potencial pseudo-harmônico bidimensional (2D) sob a influência de um campo magnético externo para o ponto quântico e campo Aharonov-Bohm para um pseudo-ponto quântico. As soluções exatas para autovalores de energia e funções de onda são computadas em função do campo magnético uniforme, fluxo Aharonov-Bohm, número quântico magnético e do parâmetro que caracteriza o deslocamento parafuso, o vetor Burgers. Foram investigadas as modificações devido à deslocação parafuso no coeficiente de absorção de luz e na frequência de absorção limiar. Descobrimos que conforme o vetor Burgers aumenta, as curvas de frequência são impusionadas para cima em direção ao crescimento do mesmo. Um aspecto interessante que observamos é que o fluxo Aharonov-Bohm pode ser ajustado de forma a cancelar o efeito do deslocamento parafuso. / The influence of screw dislocations in quantum systems has received considerable attention in recent years. Some works are based on the geometric theory of defects in semiconductors and developed by Katanaev Volovich. In this approach the semiconductor with a screw dislocation is described by a variety of Riemann-Cartan where the screw dislocation is associated with the Burgers vector. This limit of the continuum, a screw displacement affects a quantum system as an isolated magnetic flux tube, causing phenomena of interference type Aharonov-Bohm (AB). The electron energy spectrum around this type of defect shows a configuration similar to the AB system. In this work, we investigated the influence of a screw dislocation on the energy levels and the wavefunctions of an electron confined in a two-dimensional pseudoharmonic quantum dot under the influence of an external magnetic field inside a dot and Aharonov-Bohm field inside a pseudodot. The exact solutions for energy eigenvalues and wavefunctions are computed as functions of applied uniform magnetic field strength, Aharonov-Bohm flux, magnetic quantum number and the parameter characterizing the screw dislocation, the Burgers vector. We investigate the modifications due to the screw dislocation on the light interband absorption coefficient and absorption threshold frequency. We found that as the Burgers vector increases, the curves of frequency are pushed up towards of the growth of it. One interesting aspect which we have observed is that the Aharonov-Bohm flux can be tuned in order to cancel the screw effect of the model.

Made available in DSpace on 2016-12-23T14:34:49Z (GMT). No. of bitstreams: 1 Diego Henrique Carvalho dos Santos.pdf: 664413 bytes, checksum: 9b89955577d748bc73682dc9f48c6e83 (MD5) Previous issue date: 2012-12-07 / O objetivo deste trabalho é apresentar como se dá a correspondência entre teoria de calibre e conexões em espaços …brados. Mais precisamente estabelecemos um dicionário entre a teoria de calibre da mecânica quântica de uma partícula carregada sujeita a um campo eletromagnético e o estudo das conexões em …brados por círculos e por retas complexas. Em seguida, analisamos dois objetos de estudo em física utilizando o conhecimento adquirido no estudo da geometria de espaços …brados. As classes de Chern e a holonomia de uma conexão nos fornecerão uma visualização geométrica de, respectivamente, monopolos magnéticos e o efeito Aharonov-Bohm / The aim of this work is to present how works the correspondence between the gauge theory and connections in ber bundles. More precisely establishing a dictionary between gauge theory of the quantum mechanics of a charged particle under the in‡uence of an electromagnetic eld and the studies of connections in circle bundles and line bundles. Then, we analyzed two objects of studies in physics using the knowledge acquired in the study of the geometry of ber bundles. The Chern classes and the holonomy of a connection will provide a geometrical visualization of, respectively, magnetic monopoles and the Aharonov-Bohm e¤ect

Cette thèse est consacrée à l’étude expérimentale des propriétés magnéto-optiques intrinsèques des nanotubes de carbone mono-paroi par spectroscopie de photoluminescence résolue en temps.Un dispositif de microscopie optique confocale de grande ouverture numérique (NA = 0.95),incluant un cryostat magnétique, permet l’étude de nanotubes suspendus à l’échelle individuelle,à température cryogénique (jusqu’à 2 Kelvin) et sous champ magnétique (jusqu’à 7 Tesla). L’évolution des spectres et des déclins de photoluminescence avec le champ magnétique montre l’influence de l’effet Aharonov-Bohm sur les deux excitons singulets de plus basse énergie, c’est à-dire l’exciton fondamental qui est optiquement inactif (exciton noir) et un exciton d’énergie supérieure séparé de quelques milliélectronvolts qui est optiquement actif (exciton brillant). L’interprétation de ces résultats à partir d’un modèle d’équations de taux qui intègre le couplage Aharonov-Bohm entre ces deux excitons permet de déterminer séparément les durées de vie excitoniques et de fournir des informations quantitatives sur la relaxation de l’énergie depuis les niveaux supérieurs photo-excités. La relaxation de l’énergie suite à la photo-excitation de la transition S22 conduit à une efficacité de peuplement de l’état brillant quatre fois plus faible que celle de l’état noir, mais qui augmente significativement lorsque la relaxation se produit depuis les niveaux excitoniques KK’. D’autre part, le bon rapport signal à bruit obtenu dans les spectres de photoluminescence permet de révéler l’existence d’un couplage intrinsèque en champ nul entre l’exciton noir et l’exciton brillant ainsi que le maintien de la mobilité excitonique dans les nanotubes suspendus à la température de l’hélium liquide. / This thesis is dedicated to the experimental study of the intrinsic magneto-optical properties of single-walled carbon nanotubes through time-resolved photoluminescence spectroscopy. Measurements are performed on suspended nanotubes samples at the single-object level using a home-built confocal optical microscope with a large numerical aperture (NA = 0.95) operating at cryogenic temperature (down to 2K) and high magnetic field (up to 7T). The evolution of the photoluminescence spectra and decay signals with increasing magnetic fields shows the influence of the Aharonov-Bohm effect on the two lowest-energy singlet excitons, namely the ground exciton which is optically inactive (dark exciton) and an exciton lying a few millielectron volts higher in energy which is optically active (bright exciton). A model of these results based on rate equations and including the Aharonov-Bohm coupling between these two excitons enables to determine separately the excitons lifetimes and to derive quantitative information on the energy relaxation from the photo-excited higher levels. The energy relaxation following the photo-excitation of the S22 transition leads to a bright state population efficiency four times lower than that of the dark state, but it significantly increases when energy relaxation occurs from the KK’ excitonic levels. Thanks to a good signal to noise ratio, the photoluminescence spectra also reveal the presence of an intrinsic zero-field coupling between the dark and the brightexcitons, as well as an excitonic mobility preserved at liquid helium temperature in suspended nanotubes.

Made available in DSpace on 2016-06-02T20:15:22Z (GMT). No. of bitstreams: 1 3511.pdf: 19319243 bytes, checksum: e177f4d29b58e26b9530851f33a85734 (MD5) Previous issue date: 2011-03-14 / Universidade Federal de Sao Carlos / In classical Physics, the motion of an electrically charged particle is affected only by the presence of a magnetic field if the particle enters a region of space in which the field is present. Meanwhile, in quantum Physics, a charged carrier can be affected by the electromagnetic vector potential ~A, even in regions where the magnetic field ~B is not present. This surprising contrast between classical and quantum Physics has been experimentally proven in several beautiful experiments in semiconducting, metallic and superconducting material systems, and has been called Aharonov-Bohm effect. More recently, however, several theoretical works have discussed the plausible existence of this effect even for neutral particles! In this PhD Thesis project it is shown the first clear experimental observation of the Aharonov-Bohm effect in neutral excitons in InAs quantum rings. Signatures of this effect appear as oscillations in the intensity of the photoluminescence emission bands with increasing magnetic fields and also depending on the dimensions of the quantum rings. These oscillations are affected by the uniaxial strain field due to the piezoelectricity of the asymmetric InAs rings, as revealed by the atomic force microscopy, transmission electron microscopy images and X-Ray Diffraction measurements using synchrotron light. A theoretical model that describes the behavior of the excitonic interference pattern and its modulation with temperature and uniaxial electric fields has been used for the interpretation of the experimental data. The detection of AB oscillations mediated by electron-hole pair correlation is a fundamental quantum mechanical effect that will trigger further studies in this area of fundamental physics as well as technological applications. / Em Física clássica, o movimento de uma partícula carregada só é afetado pela presença de um campo magnético se a partícula entrar em uma região do espaço na qual o campo está presente. Ao mesmo tempo, em Física quântica, a partícula contendo carga elétrica pode ser afetada por um potencial eletromagnético ~ A, mesmo em regiões onde o campo magnético ~B é zero. Esse contraste surpreendente entre Física clássica e Física quântica tem sido provado em interessantes experimentos em materiais semicondutores, metais e supercondutores, e tendo sido denominado efeito Aharonov-Bohm. Mais recentemente, entretanto, muitos trabalhos teóricos têm discutido a plausibilidade da existência desse efeito mesmo para partículas neutras! Nessa tese de Doutorado será demonstrado pela primeira vez a observação experimental do efeito Aharonov-Bohm em éxcitons neutros contidos em anéis quânticos de InAs. Assinaturas desse efeito aparecem como oscilações na intensidade integrada das bandas de emissão em experimentos de fotoluminescência com o aumento do campo magnético e dependem também das dimensões dos anéis. Essas oscilações são afetadas pelos campos de compressão/expansão uniaxial devido a piezoeletricidade provinda da assimetria dos anéis, como revelado pelas imagens de microscopia de força atômica, microscopia eletrônica de transmissão e difração de raios-X utilizando luz síncrotron. Um modelo teórico que descreve o comportamento no padrão de interferência excitônico e sua modulação com a temperatura e campos elétricos uniaxiais foi usado para a interpretação dos resultados experimentais. A detecção das oscilações Aharonov-Bohm mediada pela correlação do par elétron-buraco é um efeito fundamental de mecânica quântica e os estudos mostrados aqui poderão não só instigar outras investigações em Física fundamental assim como em aplicações tecnológicas.