The present thesis is devoted to an analysis of the possibility of Bose condensates supporting persistent currents in the ring geometry. Our analysis is based on an approach developed by F. Bloch which focuses on the ground state energy of the condensate as a function of its angular momentum L. According to this approach, persistent currents are stable if the energy exhibits a local minimum at some nonzero angular momentum. We have used this approach for a single-species gas within a mean- eld approximation to show that persistent currents are stable at integral multiples of N*hbar, where N is the number of atoms in the system, provided a certain interaction parameter exceeds some critical value. These results are extended to a binary mixture of bosonic atoms and we show that the system is still capable of supporting persistent currents under certain conditions. Some of our conclusions contradict those appearing in the earlier literature. / Thesis (Master, Physics, Engineering Physics and Astronomy) -- Queen's University, 2012-03-27 10:05:21.831

Dans ce manuscrit, nous présentons des mesures haute résolution de chaleur spécifique Cp réalisées sur des anneaux mésoscopiques d'argent à très basses températures. Le but de cette expérience est de mettre en évidence une possible signature thermique due à la présence de courants permanents. Ce phénomène reste encore mal compris malgré de nombreuses expériences. Il existe en effet des contradictions entre les différents modèles théoriques et les résultats expérimentaux. L'approche thermique que nous exposons ici est un angle nouveau qui n'a jamais été exploré. Sous champ magnétique, une oscillation de période égale au quantum de flux Φ0=h/e (ou moitié) de Cp est attendue théoriquement. L'échantillon étudié est composé d'un grand nombre d'anneaux d'argent mésoscopiques déposés sur une membrane en silicium suspendue. Nous avons réalisé, à différentes températures, de multiples balayages en champ de la chaleur spécifique. Un traitement des signaux obtenus a ensuite été réalisé afin de repérer une éventuelle périodicité. Il a révélé la présence sur le signal de phase d'une oscillation de période h/2e n'apparaissant pas sur le module de la chaleur spécifique. Cette signature est maximale à 100mK. La fréquence et l'amplitude obtenues sont en accord avec les prédictions théoriques. La sensibilité atteinte est de ΔC~10^(-14)J/K sur le module (et de Δφ~10^(-2) degrés sur la phase) soit 10^(-21)J/K par anneau. Les résultats présentés ici apportent donc de nouveaux éléments dans l'analyse des courants permanents. / In this thesis, we report very high resolution specific heat measurements of normal metal mesoscopic silver rings at very low temperatures. The objective of this experiment is to measure the possible existence of thermal signatures due to the presence of persistent currents. This phenomenon is still misunderstood despite many measurements. Some contradictions exist between experimental results and the different theories. The thermal approach is a new point of view. Under magnetic field, the Cp variation is expected be periodic with the quantum of flux Φ0=h/e or half of the quantum of flux as it has been theoretically predicted. The studied samples is composed by a large number of silver rings with an electronic phase coherence length of few microns at low temperatures. They were deposited on the suspended membrane of a silicon sensor. We have realized, at different temperatures, a large number of identical scans of the heat capacity variation as a function of the applied field. A signal processing work on this data has then been realized to detect signal periodicities. It showed a difference between the module and the phase of the heat capacity. A peak can be observed on the FFT at a frequency corresponding to h/2e on the phase signal. The peak appears particularly at 100mK with a amplitude which is consistent with previous calculations. A sensitivity of ΔC~10^(-14)J/K on the module (Δφ~10^(-2) degrees on the phase) has been reached whether 10^(-21)J/K per ring. Thus, the presented experiences give new elements in the field of persistent currents.

Modelos matemáticos de motoneurônios têm sido desenvolvidos para auxiliar na compreensão dos fenômenos que envolvem o sistema neuromuscular. Entretanto, a maioria dos modelos já desenvolvidos baseou-se na premissa de que a árvore dendrítica tem um comportamento passivo, o que ocorre em animais anestesiados, mas pode não ocorrer durante o comportamento motor normal de um animal intacto. Experimentos com animais descerebrados, em que as vias monoaminérgicas encontravam-se ativas, mostraram que os motoneurônios podem apresentar comportamentos mais complexos decorrentes da presença de condutâncias iônicas voltagem-dependentes que se situam nos dendritos e são responsáveis pela gênese de uma corrente de entrada persistente. Nesse sentido, um primeiro objetivo deste trabalho foi o de desenvolver novos modelos matemáticos de motoneurônios de diferentes tipos (i.e. dos tipos S, FR e FF), computacionalmente eficientes e contendo em seus compartimentos dendríticos uma condutância de cálcio do tipo L, de forma que os fenômenos de biestabilidade, potencial platô e amplificação da corrente sináptica efetiva possam ser gerados. Um segundo objetivo foi o de verificar como a presença da condutância iônica ativa no dendrito influencia o comportamento motoneuronal quando o mesmo está sujeito a entradas sinápticas de diferentes tipos. Os novos modelos foram parametrizados baseando-se em dados da literatura experimental para motoneurônios de gatos descerebrados e validados segundo os protocolos experimentais básicos que permitem caracterizar cada tipo de modelo como sendo totalmente ou parcialmente biestável. As entradas sinápticas foram simuladas por processos pontuais de Poisson e os trens de potenciais de ação dos motoneurônios foram analisados. Uma modulação senoidal da intensidade do processo pontual foi usada para estimar as respostas em frequência de cada modelo. Observou-se que, funcionalmente, a presença da condutância iônica dendrítica pode favorecer a ação do motoneurônio durante tarefas posturais, pois, uma vez ativada, a corrente de entrada persistente eleva a excitabilidade motoneuronal tornando os disparos mais regulares, além de prover uma alta sensibilidade dos modelos a entradas sinápticas de baixa frequência, correspondentes às oscilações observadas durante a manutenção da postura ereta quieta. / Mathematical models of motoneurons have been developed as an aid to the understanding of phenomena involving the neuromuscular system, but most of these models have been based on the hypothesis of a passive dendritic tree. This holds for anesthetized animals but not necessarily during normal motor behavior of the intact animal. Experiments with decerebrate animals in which the monoaminergic tracts were maintained intact have shown that more complex behaviors may emerge in motoneurons due to dendritic voltage-gated ionic conductances, which are responsible for a persistent inward current. Therefore, the first aim of this work was to develop computationally-efficient new motoneuron models of different types (i.e. type S, FR and FF) that include a dendritic L-type calcium conductance so that bistability, plateau potential and enhancement of effective synaptic current may be generated. The second aim of this research was to evaluate the effects of the active dendritic ionic conductance on the input-output mapping of presynaptic to postsynaptic spike trains. The new models were parameterized based on data reported in experimental literature on the decerebrate cat preparation, and they were validated using appropriate protocols for either fully or partially bistable dynamics. The synaptic inputs were simulated by Poisson point processes and the output spike trains were analyzed. Sinusoidal modulation of the point process intensity was used for the estimation of each models frequency response. The results suggested that an active dendritic ionic conductance in motoneurons has a functional role during postural tasks, because, when activated, the persistent inward current enhances the motoneuronal excitability, reducing the variability of interspike intervals, and focusing the sensitivity of the models to low frequency inputs that correspond to the low-frequency oscillations that typically occur during quiet standing posture.

Modelos matemáticos de motoneurônios têm sido desenvolvidos para auxiliar na compreensão dos fenômenos que envolvem o sistema neuromuscular. Entretanto, a maioria dos modelos já desenvolvidos baseou-se na premissa de que a árvore dendrítica tem um comportamento passivo, o que ocorre em animais anestesiados, mas pode não ocorrer durante o comportamento motor normal de um animal intacto. Experimentos com animais descerebrados, em que as vias monoaminérgicas encontravam-se ativas, mostraram que os motoneurônios podem apresentar comportamentos mais complexos decorrentes da presença de condutâncias iônicas voltagem-dependentes que se situam nos dendritos e são responsáveis pela gênese de uma corrente de entrada persistente. Nesse sentido, um primeiro objetivo deste trabalho foi o de desenvolver novos modelos matemáticos de motoneurônios de diferentes tipos (i.e. dos tipos S, FR e FF), computacionalmente eficientes e contendo em seus compartimentos dendríticos uma condutância de cálcio do tipo L, de forma que os fenômenos de biestabilidade, potencial platô e amplificação da corrente sináptica efetiva possam ser gerados. Um segundo objetivo foi o de verificar como a presença da condutância iônica ativa no dendrito influencia o comportamento motoneuronal quando o mesmo está sujeito a entradas sinápticas de diferentes tipos. Os novos modelos foram parametrizados baseando-se em dados da literatura experimental para motoneurônios de gatos descerebrados e validados segundo os protocolos experimentais básicos que permitem caracterizar cada tipo de modelo como sendo totalmente ou parcialmente biestável. As entradas sinápticas foram simuladas por processos pontuais de Poisson e os trens de potenciais de ação dos motoneurônios foram analisados. Uma modulação senoidal da intensidade do processo pontual foi usada para estimar as respostas em frequência de cada modelo. Observou-se que, funcionalmente, a presença da condutância iônica dendrítica pode favorecer a ação do motoneurônio durante tarefas posturais, pois, uma vez ativada, a corrente de entrada persistente eleva a excitabilidade motoneuronal tornando os disparos mais regulares, além de prover uma alta sensibilidade dos modelos a entradas sinápticas de baixa frequência, correspondentes às oscilações observadas durante a manutenção da postura ereta quieta. / Mathematical models of motoneurons have been developed as an aid to the understanding of phenomena involving the neuromuscular system, but most of these models have been based on the hypothesis of a passive dendritic tree. This holds for anesthetized animals but not necessarily during normal motor behavior of the intact animal. Experiments with decerebrate animals in which the monoaminergic tracts were maintained intact have shown that more complex behaviors may emerge in motoneurons due to dendritic voltage-gated ionic conductances, which are responsible for a persistent inward current. Therefore, the first aim of this work was to develop computationally-efficient new motoneuron models of different types (i.e. type S, FR and FF) that include a dendritic L-type calcium conductance so that bistability, plateau potential and enhancement of effective synaptic current may be generated. The second aim of this research was to evaluate the effects of the active dendritic ionic conductance on the input-output mapping of presynaptic to postsynaptic spike trains. The new models were parameterized based on data reported in experimental literature on the decerebrate cat preparation, and they were validated using appropriate protocols for either fully or partially bistable dynamics. The synaptic inputs were simulated by Poisson point processes and the output spike trains were analyzed. Sinusoidal modulation of the point process intensity was used for the estimation of each models frequency response. The results suggested that an active dendritic ionic conductance in motoneurons has a functional role during postural tasks, because, when activated, the persistent inward current enhances the motoneuronal excitability, reducing the variability of interspike intervals, and focusing the sensitivity of the models to low frequency inputs that correspond to the low-frequency oscillations that typically occur during quiet standing posture.

Ces dernières années d'importantes avancées techniques dans la manipulation des gaz atomiques ultrafroids ont ouvert la voie à la réalisation de fluides quantiques mésoscopiques de basse dimension. L'objet de cette thèse est l'étude théorique de certains systèmes mésoscopiques réalisables avec un gaz de Bose unidimensionel. Ces systèmes présentent des phénomènes quantiques intéressants, et sont potentiellement utiles en vue d'applications technologiques. Nous étudions le phénomène des courants permanents induits dans un gaz confiné sur un anneau par la rotation d'une barrière de potentiel, nous examinons la faisabilité d'un qubit fondé sur la superposition d'états de courant dans un réseau en forme d'anneau traversé par un champ de jauge et contenant un 'weak-link', ainsi que l'excitation dipolaire du gaz dans un 'split-trap' induit par le déplacement hors équilibre du potentiel externe. Dans tous ces cas, nous combinons diverses approches analytiques et numériques, qui permettent de couvrir l'ensemble des régimes d'interactions. Nous mettons en lumière un régime jusque-là inconnu, d'écrantage maximal des barrières de potentiel par le fluide, dû à une competition entre les effets des interactions et des fluctuations quantiques. Ces résultats ont des conséquences significatives sur le comportement de tels systèmes et, de ce fait, sont importants pour les réalisations en cours et à venir de dispositifs à gaz d'atomes ultrafroids. / Thanks to the experimental breakthrough of the last years in the manipulation of ultra cold atomic gases, it has become possible to realize low-dimensional and mesoscopic quantum fluids. The object of this thesis is the theoretical investigation of a few mesoscopic systems that can be realized with a one-dimensional Bose gas. These systems exhibit interesting quantum phenomena, and are potentially relevant for technological applications. We study the phenomenon of persistent currents induced by stirring the gas confined on a ring with a potential barrier, we examine the feasibility of a qubit based on the superposition of current states in a ring lattice threaded by a gauge field in the presence of a weak-link, and we investigate the dipole excitation of the gas in a split trap induced by an out-of-equilibrium displacement of the external potential. In all these cases, we apply a combination of analytical and numerical approaches that allow to cover all the interaction regimes. As a recurring theme, we disclose a so-far unknown regime of maximal screening of the barrier potential by the fluid, arising from the interplay of effects due to interactions and quantum fluctuations. These results have significant consequences for the behaviour of such systems and are important for the ongoing and future realization of ultracold atomic gases devices.

Submitted by Vasti Diniz (vastijpa@hotmail.com) on 2017-09-19T14:26:49Z No. of bitstreams: 1 arquivototal.pdf: 24337857 bytes, checksum: 4dcf09dcc5c804cc2b7b0de0feb30331 (MD5) / Made available in DSpace on 2017-09-19T14:26:49Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 24337857 bytes, checksum: 4dcf09dcc5c804cc2b7b0de0feb30331 (MD5) Previous issue date: 2013-03-25 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The Graphene is a two-dimensional(2-D) semiconductor crystal with null gap, where charge carriers behave as massless particles. In this speci c dynamics in the limit of low energies, the energy dispersion relation is linear, and this material can be described by massless Dirac equation contrasts with the semiconductors, for which the charge carriers are massive. In this framework, there is the problem of the electronic con nement in graphene because of tunneling. For overcome this di culty, is proposed a new model of quantum ring, based on Dirac oscillator and models of rings Tan-Inkson and Bakke- Furtado. From this new coupling, are obtainable the energy spectrum, persistent currents and positive spinors to a graphene sheet with / without topological defect type disclination by massless Dirac equation (2+1). / O grafeno e um cristal bidimensional(2-D) semicondutor com gap nulo, onde os portadores de cargas se comportam como part culas sem massa. Nesta din^amica espec ca, no limite de baixas energias, a rela c~ao de dispers~ao de energia e linear, sendo que este material pode ser descrito pela equa c~ao de Dirac sem massa contrastando com os semicondutores, cujos portadores de cargas t^em massa. Neste quadro, h a o problema do con namento eletr^onico no grafeno devido ao tunelamento. Para contornar esta di culdade, e proposto um novo modelo de anel qu^antico, baseado no oscilador de Dirac e nos modelos de an eis de Tan-Inkson e Bakke-Furtado. A partir desse novo acoplamento, s~ao obtidos o espectro de energia, as correntes persistentes e os espinores positivos para uma folha de grafeno com/sem defeito topol ogico do tipo desclina c~ao, via equa c~ao de Dirac (2+1) sem massa

Made available in DSpace on 2015-05-14T12:13:59Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 798447 bytes, checksum: d94f874d062caea280c4ce462ab3837a (MD5) Previous issue date: 2011-12-22 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work, we explore the link between geometry and physical properties in 2D quantum rings. With focus on the non-orientable mesoscopic structures, we solve the quantum Möbius strip problem, a quantum ring whose lockdown surface is a Möbius strip, and investigate how the physical properties of those structures answer to the geometric variation of this particular configuration. More precisely, we investigate how the adoption of boundary conditions associated to this specific geometric configuration, in particular, can change the general properties of the 2D quantum rings. In addition, we still study the generalized version of the problem, where the Möbius strip has a finite number n of torsions. / Neste trabalho, exploramos o elo entre geometria e propriedades físicas no caso de anéis quânticos bidimensionais. Com o foco nas estruturas mesoscópicas não-orientáveis, resolvemos o problema da faixa de Möbius quântica, um anel quântico cuja superfície de confinamento é uma faixa de Möbius, e investigamos de que maneira as propriedades físicas de tais estruturas respondem à variação geométrica característica dessa particular configuração de confinamento. Mais precisamente, investigamos o modo pelo qual a adoção de condições de contorno associadas a essa configuração geométrica específica, em particular, pode interferir nas propriedades gerais dos anéis quânticos bidimensionais. Além disso, ainda estudamos a versão generalizada do problema, em que a faixa de Möbius apresenta um número finito n de torções.

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