Nanoscale systems have sizes intermediate between atomic and macroscopic ones. Therefore their treatment often requires a combination of methods from atomic and condensed matter physics. The conventional Landau-Zener theory, being a powerful tool in atomic physics, often fails to predict correctly nonadiabatic transition probabilities in various nanostructures because it does not include many-body effects typical for mesoscopics. In this research project the generalizations of the Landau-Zener theory that solve this problem were studied. The multistate, multiparticle and nonunitary extensions of the theory have been proposed and investigated. New classes of exactly solvable models have been derived. I discuss their applications in problems of the molecular condensate dissociation and of the driven charge transport. In application to the physics of nanomagnets new approaches in modeling the influence of the environment on the Landau-Zener evolution are proposed and simple universal formulas are derived for the extensions of the theory that include the coupling to noise and the nuclear spin bath.

Graphene – a two-dimensional honeycomb lattice of sp2-bonded carbon atoms – possesses unusual zero-gap band structure with linear band dispersions, accommodating photon-like, massless electrons that have exhibited a variety of surprising phenomena, primarily in DC transport, in the last several years. In this thesis dissertation, we investigate graphene’s AC or infrared properties in the presence of an ultrahigh magnetic field, produced by a destructive pulsed method. The linear dispersions of graphene lead to unequally spaced Landau levels in a magnetic field, which we probe through cyclotron resonance (CR) spectroscopy in the magnetic quantum limit. Specifically, using magnetic fields up to 170 T and polarized midinfrared radiation with tunable wavelengths from 9.22 to 10.67 μm, we experimentally investigated CR in large-area graphene grown by chemical vapor deposition. Circular-polarization-dependent studies revealed strong p-type doping for as-grown graphene, and the dependence of the CR fields on the radiation wavelength allowed for an accurate determination of the Fermi energy. Upon annealing the sample to remove physisorbed molecules, which shifts the Fermi energy closer to the Dirac point, we made the unusual observation that hole and electron CR emerges in the magnetic quantum limit, even though the sample is still p-type. We theoretically show that this non-intuitive phenomenon is a direct consequence of the unusual Landau level structure of graphene. Namely, if the Fermi energy lies in the n = 0 Landau level, then CR is present for both electron-active and hole-active circular polarizations. Furthermore, if the Fermi level lies in the n = 0 Landau level, the ratio of CR absorption between the electron-active and hole-active peaks allows one to accurately determine the Fermi level and carrier density. Hence, high-field CR studies allow not only for fundamental studies but also for characterization of large-area, low-mobility graphene samples.

L'3He est un liquide de Fermi modèle, isotrope, pur, de température de Fermi accessible, et dont les interactions sont aisément contrôlées en faisant varier la pression du liquide. Ce manuscrit présente des mesures précises de susceptibilité magnétique nucléaire par RMN continue de l'3He liquide en fonction de la température et de la pression. Les principaux efforts expérimentaux sont portés sur la thermométrie, la mesure de la pression de l'3He in situ pour étendre les mesures jusqu'à la pression de solidification, ainsi qu'une caractérisation soigneuse du spectromètre RMN. <br /><br />Nos mesures remettent en cause d'environ 5% les résultats de référence pour la température de Fermi effective en fonction des interactions. L'extraction du paramètre de Landau F0a dépend aussi de la masse effective déterminée par des mesures de chaleur spécifique, et par conséquent de l'échelle de température. La ré-analyse des mesures de chaleur spécifique dans l'échelle PLTS-2000 implique une augmentation de la masse effective de 4,5%. F0a est donc déterminé dans ce manuscrit pour deux échelles de température (PLTS-2000 et Greywall). Contrairement aux résultats antérieurs, la dépendance en densité de F0a ne montre pas de saturation vers les hautes pressions.

Diss.--Tübingen. / Vita. Bibliography: p. 1 xiv.

Nanoscale systems have sizes intermediate between atomic and macroscopic ones. Therefore their treatment often requires a combination of methods from atomic and condensed matter physics. The conventional Landau-Zener theory, being a powerful tool in atomic physics, often fails to predict correctly nonadiabatic transition probabilities in various nanostructures because it does not include many-body effects typical for mesoscopics. In this research project the generalizations of the Landau-Zener theory that solve this problem were studied. The multistate, multiparticle and nonunitary extensions of the theory have been proposed and investigated. New classes of exactly solvable models have been derived. I discuss their applications in problems of the molecular condensate dissociation and of the driven charge transport. In application to the physics of nanomagnets new approaches in modeling the influence of the environment on the Landau-Zener evolution are proposed and simple universal formulas are derived for the extensions of the theory that include the coupling to noise and the nuclear spin bath.

There are two main tools for determining the stability of nonlinear partial differential equations (PDEs): Lyapunov Theory and linearization. The former has the advantage of providing stability results for nonlinear equations directly, while the latter considers the stability of linear equations and then further justification is needed to show the linear stability implies local stability of the nonlinear equation. Linearization has the advantage of investigating stability on a simpler equation; however, the justification can be difficult to prove. Both Lyapunov Theory and linearization are applied to the Landau--Lifshitz equation, a nonlinear PDE that describes the behaviour of magnetization inside a magnetic object. It is known that the Landau-Lifshitz equation has an infinite number of stable equilibrium points. We present a control that forces the system from one equilibrium to another. This is proved using Lyapunov Theory. The linear Landau--Lifshitz equation is also investigated because it provides insight to the nonlinear equation. The linear model is shown to be well--posed and its eigenvalue problem is solved. The resulting eigenvalues suggest an appropriate control for the nonlinear Landau--Lifshitz equation. Mathematically, the control causes the initial equilibrium to no longer be an equilibrium and the second point to be an asymptotically stable equilibrium point. This implies the magnetization has moved to the second equilibrium and hence the control objective is successfully achieved. The existence of multiple stable equilibria is closely related to hysteresis. This is a phenomenon that is often characterized by a looping behaviour; however, the existence of a loop is not sufficient to identify hysteretic systems. A more precise definition is required, which is presented, and applied to the Landau--Lifshitz equation (both linear and nonlinear) to establish the presence of hysteresis.

Vlasov's equation describes the time evolution of the distribution function for a collisionless physical system of identical particles, such as plasma or galaxies. Together with Poisson's equation, which yields the potential, it forms the Vlasov-Poisson system. In Euclidean space this system has been extensively studied in the past century. It has been recently shown that the Valsov-Poisson system exhibits an interesting, counter-intuitive phenomenon called Landau damping. Our universe, however, may not be at on a large scale, so it is important to introduce and study a natural extension of the Vlasov-Poisson systems to spaces of constant curvature. Our starting point is the unit sphere S2, but we further restrict our study to one of its great circles. We show that, even for this reduced model, the potential function has more singularities than in the classical case. Our main result is to derive a Penrose stability criterion for the linear Landau damping phenomenon. / Graduate / 0405 / shengyis@uvic.ca

Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references and index.

Universiẗat, Diss., 2000--Konstanz.

MOURA, V. N. Teoria de Ginzburg-Landau com parâmetro de ordem escondido aplicada ao estudo da supercondutividade de interface. 2017. 91 f. Dissertação (Mestrado em Física) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2017. / Submitted by Giordana Silva (giordana.nascimento@gmail.com) on 2017-04-17T18:51:33Z No. of bitstreams: 1 2017_tese_vnmoura.pdf: 11920515 bytes, checksum: 49171d0bcfd692c4e5ba8badf2e28c04 (MD5) / Approved for entry into archive by Giordana Silva (giordana.nascimento@gmail.com) on 2017-04-17T18:52:06Z (GMT) No. of bitstreams: 1 2017_tese_vnmoura.pdf: 11920515 bytes, checksum: 49171d0bcfd692c4e5ba8badf2e28c04 (MD5) / Made available in DSpace on 2017-04-17T18:52:06Z (GMT). No. of bitstreams: 1 2017_tese_vnmoura.pdf: 11920515 bytes, checksum: 49171d0bcfd692c4e5ba8badf2e28c04 (MD5) Previous issue date: 2017 / In recent years, several experiments have been reported in which interface superconductivity was observed in heterostructures of different materials, inclunding non-superconductors. The origin of this superconductivity has not yet been elucidated and there is no well-established theory to explain this phenomenon. In 2015 a model based on the Ginzburg-Landau theory was proposed that would explain the interface superconductivity phenomenon assuming a system with two order parameters. It has been proposed that the order parameter characterizing the bulk material with a defective or doped layer permits the formation of a second parameter which competes with the former and prevails over it in the vicinity of the interface. The superconductivity at the interface is then explained by the growth of this second order parameter only in this region, remaining still ``hidden" inside the bulk. The model was applied to a one-dimensional system with an interface, which presented a surprising result: the ``hidden" superconductivity appers in quantized critical temperatures, this allowing the existence of several eigenstates of the system, with different critical temperatures. In this dissertation, we use this model and investigate the unfolding of hidden superconductivity and its quantized temperatures. We observe that the interfaces resemble one-dimensional quantum wells, with the critical temperature playing the role of the energy in the quantum case. Following this idea we use numerical methods to solve the Ginzburg-Landau equations for a system with an arbitrary number of parallel interfaces. Our results show that in this case, the critical temperatures are quantized and degenerate when the interfaces are very separated, but it has its degeneracy broken when we approach the interfaces, as it happens in a lattice of square wells. We then proposed a tight-binding model to estimate critical temperatures on parallel interfaces and verified the validity of this approximation through the numerical solution of the complete problem. We also analyze the vortex states for a square two-dimensional defect, verifying the possibility of creating or destroying vortices in the region of `` hidden" superconductivity through an external magnetic field. / Nos últimos anos foram reportados diversos experimentos em que a supercondutividade de interface foi observada em heteroestruturas de diferentes materiais, inclusive em não-supercondutores extit{a priori}. A origem dessa supercondutividade ainda não foi elucidada e não existe uma teoria bem estabelecida para explicar esse fenômeno. Em 2015 foi proposto um modelo com base na teoria de Ginzburg-Landau que explicaria o fenômeno de supercondutividade de interface assumindo um sistema com dois parâmetros de ordem. Foi proposto que o parâmetro de ordem que caracteriza o material extit{bulk} com uma camada defeituosa, ou dopada, permite a formação de um segundo parâmetro que compete com o primeiro e prevalece sobre ele nas proximidades da interface. A supercondutividade na interface é então explicada pelo crescimento deste segundo parâmetro de ordem apenas nesta região, permancecendo ainda ``escondido" dentro do extit{bulk}. O modelo foi aplicado para um sistema unidimensional com uma interface, apresentando um resultado surpreendente: a supercondutividade escondida aparece em temperaturas críticas quantizadas, podendo então existir vários autoestados do sistema, com diferentes temperaturas críticas. Nessa dissertação utilizamos esse modelo e investigamos os desdobramentos da supercondutividade escondida e suas temperaturas quantizadas. Percebemos que as interfaces assemelham-se com poços quânticos unidimensionais, com a temperatura crítica fazendo o análogo ao da energia no caso quântico. Seguindo essa ideia utilizamos métodos numéricos para resolver as equações de Ginzburg-Landau para um sistema com um número arbitrário de interface paralelas. Nossos resultados mostram que neste caso, as temperaturas críticas, além de quantizadas, são degeneradas quando as interfaces estão muito separadas, mas tem essa degenerescência quebrada quando aproximamos as interfaces, como ocorre em uma rede de poços quadrados. Propusemos então um modelo tipo extit{tight-binding para estimar temperaturas críticas em interfaces paralelas e verificamos a validade dessa aproximação através da solução numérica do problema completo. Analisamos também os estados de vórtices para um defeito bidimensional quadrado, verificando a possibilidade de se criar ou destruir vórtices na região de supercondutividade escondida através de um campo magnético externo.