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The de Broglie-Bohm causal interpretation of quantum mechanics is discussed, and applied to the hydrogen atom in several contexts. Prominent critiques of the causal program are noted and responses are given; it is argued that the de Broglie-Bohm theory is of notable interest to physics. Using the causal theory, electron trajectories are found for the conventional Schrödinger, Pauli and Dirac hydrogen eigenstates. In the Schrödinger case, an additional term is used to account for the spin; this term was not present in the original formulation of the theory but is necessary for the theory to be embedded in a relativistic formulation. In the Schrödinger, Pauli and Dirac cases, the eigenstate trajectories are shown to be circular, with electron motion revolving around the <i>z</i>-axis. Electron trajectories are also found for the 1<i>s</i>-2<i>p</i>0 transition problem under the Schrödinger equation; it is shown that the transition can be characterized by a comparison of the trajectory to the relevant eigenstate trajectories. The structures of the computed trajectories are relevant to the question of the possible evolution of a quantum distribution towards the standard quantum distribution (quantum equilibrium); this process is known as quantum relaxation. The transition problem is generalized to include all possible transitions in hydrogen stimulated by semi-classical radiation, and all of the trajectories found are examined in light of their implications for the evolution of the distribution to the standard distribution. Several promising avenues for future research are discussed.

Thesis (Ph. D.)--University of Western Sydney, 2004. / Includes bibliographical references.

Thesis (J.C.L.)--Catholic University of America, 1999. / Includes bibliographical references (leaves 72-77).

Thèse (Ph. D.)--Université Laval, 2003. / Titre de l'écran-titre (visionné le 24 mars 2004). Bibliogr.

Gallium arsenide is piezoelectric, so it is possible to generate coupled mechanical and electrical surface acoustic waves (SAWs) by applying a high-frequency voltage to a transducer on the surface of GaAs. By combining SAWs with existing low-dimensional nanostructures one can create a series of dynamic quantum dots corresponding to the minima of the travelling electric wave, and each dot carries a single electron at the SAW velocity (~ 2800 m/s). These devices may be of use in developing future quantum information processors, and also offer an ideal environment for probing the quantum mechanical behaviour of single electrons. This thesis describes a numerical and theoretical study of the dynamics ofan electron in a range of geometries. The numerical techniques for solving thetime-dependent Schrödinger equation with an arbitrary time-dependent potential will be described in Chapter 2, and then applied in Chapter 3 to calculate the transmission of an electron through an Aharonov-Bohm (AB) ring. It will be seen that an important property of the techniques used in this thesis is that they can be easily adapted to study realistic geometries, and we will see features in the AB oscillations which do not arise in simplified analytic descriptions. In Chapter 4, we will then study a device consisting of two parallel SAW channels separated by a controllable tunnelling barrier. We will use numerical simulations to investigate the effect of electric and magnetic fields upon the electron dynamics, and develop an analytic model to explain the simulation results. From the model, it will be apparent that it is possible to use this device to rotatethe state of the electron to an arbitrary superposition of the first two eigenstates. We then introduce coherent and squeezed states in Chapter 5, which are ex-cited states of the quantum harmonic oscillator. Coherent and squeezed electronicstates may be of use in quantum information processing, and could also arise dueto unwanted perturbations in a SAW device. We will discuss how these statescan be controllably generated in a SAW device, and also discuss how they couldthen be detected. In Chapter 6 we describe how to use the motion of a SAW to create a rapidly-changing potential in the frame of the electron, leading to a nonadiabatic excita-tion. The nonadiabatically-excited state oscillates from side to side within a 1Dchannel on a few-picosecond timescale, and this motion can be probed by placing a tunnelling barrier at one side of the channel. Numerical simulations will beperformed to show how this motion can be controlled, and the simulation resultswill be seen to be in good agreement with recent experimental work performed by colleagues. Finally, we will show that this device can be used to measure the initial state of an electron which is an arbitrary superposition of the first twoeigenstates.

The aim of this thesis was to simulate a part of a proposed experiment by Lev Vaidman by using Bohmian mechanics. To do this a numerical method for solving the Schrödinger equation and theguiding equation was created, with several ways of making the simulation more efficient.To make the simulation work more efficiently the Schrödinger equation was applied to only a small region of the whole setup. This region followed the wavefunction of significant values and could change size during the simulation. A beam splitter was constructed in the form of a thin potential barrier. The beam splitter was tested to verify that the reflected and transmitted angles agreed with expectations. A virtual detector was constructed and used for the calibration of the beam splitter to determine which potential resulted in dividing the wave packet into two wave packets of equal intensity. A fixed angle mirror was used for testing the reflection of a wave packet for the reflected angle and concluded that it agreed with the expectations for it. Testing a time dependent mirror for different frequencies and amplitudes was performed, with the result that the numerical method could be used to determine the particles’ trajectories. These results were used to construct a larger setup that was a small part of Vaidman’s proposed experiment. These setups were done in several version. All setups had one wave packet that went through one beam splitter and separated into two wave packets. These two wave packets reflected at two mirrors with different frequencies and then interfered with each other at either free space or at another beam splitter. The result of the simulation of these setups was that the particles’ trajectories could be calculated with the guiding equation. / Syftet med denna avhandling var att simulera en del av det föreslagna experimentet av Lev Vaidman med hjälp av Bohmsk mekanik. För att göra detta skapades en numerisk metod för att lösa Schrödingerekvationen och den ledande ekvationen, ”the guiding equation”, med flera sätt att effektivisera simuleringen. För att effektivisera simuleringen tillämpades Schrödingerekvationen på endast en liten region i hela uppställningen. Denna region följde vågfunktionen med betydande värden och kunde ändra storlek under simuleringen.En stråldelare konstruerades i form av en tunn potentialbarriär. Stråldelaren testades för att verifiera attde reflekterade och överförda vinklarna överensstämde med förväntningarna. En virtuell detektorkonstruerades och användes för kalibrering av stråldelaren för att bestämma vilken potential som resulterade i att vågpaketet delades in i två vågpaket med samma intensitet.En spegel med fast vinkel användes för att testa reflektionen av ett vågpaket för den reflekterade vinkeln och kom fram till att den överensstämde med förväntningarna för den. Att testa en tidsberoendespegel för olika frekvenser och amplituder utfördes med resultatet att den numeriska metoden kunde användas för att bestämma partiklarnas banor. Dessa resultat användes för att konstruera en större uppställning av ett experiment som var en liten delav Vaidmans föreslagna experiment. Dessa uppställningar gjordes i flera versioner. Alla uppställningar hade ett vågpaket som gick igenom en stråldelare och separerades i två vågpaket. Dessa två vågpaket reflekterades vid två speglar med olika frekvenser och interfererade sedan varandra antingen i en tom rymd eller vid en annan stråldelare. Resultatet av simuleringen av dessa inställningar var att partiklarnas banor kunde beräknas med ledande ekvation.

We have studied the electron quantum phase by fabricating low dimensional (d ≤ 2) mesoscopic interferometers in high-quality narrow-gap semiconductor (NGS) heterostructures. The low effective-mass electrons in NGS heterostructures enable observation of delicate quantum phases; and the strong spin-orbit interaction (SOI) in the systems gives us means by which we can manipulate the quantum-mechanical spin of these electrons through the orbital properties of the electrons. This enables the observation of spin-dependent phenomena otherwise inaccessible in non-magnetic systems. We have performed low temperature (0.4 K ≤ T ≤ 8 K), low noise (â V ~ 1μV ) transport measurements, and observed evidence of Aharonov-Bohm (AB) and Alâ tshuler-Aronov-Spivak (AAS) quantum oscillations in meso- scopic devices that we fabricated on these NGSs. Our measurements are unique in that we observe both AB and AAS in comparable magnitude in ballistic networks with strong SOI. We show that, with appropriate considerations, diffusive formalisms can be used to describe ballistic transport through rings, even in the presence of SOI. This work also contains an introduction to the physics of geometric phases in mesoscopic systems, and the experimental and analytic processes through which these phases are probed. A discussion of the results of our measurements presents the case that quantum interferometric measurements of geometric phases can be understood quite thoroughly, and that these measurements may have deeper utility in discovery than has yet been recognized. / Ph. D.

Made available in DSpace on 2017-07-21T19:25:51Z (GMT). No. of bitstreams: 1 Ramon F Costa.pdf: 10031939 bytes, checksum: 0a248edab54bf52531ad1b840500611c (MD5) Previous issue date: 2016-03-04 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this work we present the Aharonov-Bohm effect, as well as its implications. We also present the self-adjoint extension, an important tool in quantum mechanics. This work's main objective is to investigate the relation between the self-adjoint extension parameter and the Aharonov-Bohm system's parameters. Of particular interest is the relation between the self-adjoint extension parameter and the electron's anomalous magnetic dipole moment. This is done by comparison between two self-adjoint extension methods: Bulla-Gesztesy's and Kay-Studer's. We obtain the mathematical relation between the aforementioned quantities and conclude that the chosen methods are suitable to accomplish our goals. / Neste trabalho é apresentado o efeito e sistema de Aharonov-Bohm, além de suas implicações. Trata-se também da extensão autoadjunta de operadores em mecânica quântica. O principal objetivo é a investigação da relação entre o parâmetro da extensão autoadjunta do Hamiltoniano do sistema de Aharonov-Bohm, que tem origem matemática, e a física desse sistema. Interesse particular é dado à busca da relação entre o parâmetro da extensão e a anomalia do momento magnético do elétron. Para tal são usados dois métodos de extensão autoadjunta: o de Bulla-Gesztesy e o de Kay-Studer. A expressão matemática procurada é obtida, além de expressões para as energias dos estados ligados do sistema. Conclui-se que os métodos utilizados são adequados para atingir os objetivos propostos.

Made available in DSpace on 2016-06-02T20:16:55Z (GMT). No. of bitstreams: 1 6767.pdf: 16621562 bytes, checksum: 66df3d9efcbf65c2d47f601b4ef3f3c0 (MD5) Previous issue date: 2015-04-01 / Universidade Federal de Sao Carlos / Quantum dots grown by epitaxial techniques for optical and transport studies are usually capped by a layer of the same material on which the QDs were grown. Recently, several studies have shown how the growth parameters and materials used in this layer significantly affect the morphological, optical and electrical properties of these nanostructures. In this work Indium Arsenide quantum dots capped with a layer of Gallium Arsenide and Antimony are studied. After the growth, a rapid thermal annealing was performed, which improved significantly the size distribution of the quantum dots, increasing the optical eficiency, and inducing a change in the band structure from a Type-I to Type-II. The investigations performed by magnetophotoluminescence have shown that the effects of the topology confinement on the band structure of these quasi zero-dimensional systems are strongly modulated by an external electric field applied parallel to the magnetic field orientation. Purely quantum effects such as Aharonov-Bohm interference and the inversion of the excitonic Landfie g-factor were observed at low temperatures and for specific values of electric fields, showing that the choice of the material and growth conditions of quantum dots capping layer leads to controlled experimental results which could not be achieved using conventional growth methods of semiconductor quantum dots. / Pontos quânticos crescidos por técnicas epitaxiais para estudos ópticos e de transporte são comumente cobertos com uma camada do mesmo material sobre o qual os pontos foram crescidos. Recentemente diversos estudos têm demonstrado como os parâmetros de crescimento e materiais utilizados nesta camada afetam significativamente as propriedades morfológicas, ópticas e elétricas destas nanoestruturas. Neste trabalho são estudados pontos quânticos tradicionais de Arseneto de Índio cobertos com uma camada de Arseneto de Gálio e Antimônio. Após o crescimento foi realizado um tratamento térmico rápido que melhorou significativamente a distribuição de tamanhos dos pontos, com um aumento na eficiência óptica e uma indução na estrutura de bandas do Tipo-I para Tipo-II. As investigações por magnetofotoluminescência revelaram que os efeitos da topologia de confinamento na estrutura de bandas deste sistema quase zero-dimensional são fortemente modulados pela aplicação de um campo elétrico externo paralelo _a orientação do campo magnético. Efeitos de caráter puramente quântico como a interferência Aharonov-Bohm e a inversão do fator-g de Landé excitônico foram observados a baixas temperaturas e para valores específicos de campo elétrico, demonstrando assim que a escolha do material e condições de deposição da camada de cobertura de pontos quânticos levam a efeitos e resultados controlados experimentalmente que não poderiam ser observados utilizando métodos convencionais de crescimento de pontos quânticos semicondutores.