京都大学 / 0048 / 新制・課程博士 / 博士(経済学) / 甲第21530号 / 経博第598号 / 新制||経||289(附属図書館) / 京都大学大学院経済学研究科経済学専攻 / (主査)教授 江上 雅彦, 教授 西山 慶彦, 准教授 砂川 伸幸 / 学位規則第4条第1項該当 / Doctor of Economics / Kyoto University / DGAM

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With the advance in nanotechnology, we are more interested in the "smaller worlds". One of the practical applications of this is to measure a very small displacement or the mass of a nano-mechanical object. To measure such properties, one needs a very sensitive detector. A quantum point contact (QPC) is one of the most sensitive detectors. In a QPC, electrons tunnel one by one through a tunnel junction (a "hole"). The tunnel junction in a QPC consists of a narrow constriction (nm-wide) between two conductors. To measure the properties of a nano-mechanical object (which acts as a harmonic oscillator), we couple it to a QPC. This coupling effects the electrons tunneling through the QPC junction. By measuring the transport properties of the tunneling electrons, we can infer the properties of the oscillator (i.e. the nano-mechanical object). However, this coupling introduces noise, which reduces the measurement precision. Thus, it is very important to understand this source of noise and to study how it effects the measurement process. We theoretically study the transport properties of electrons through a QPC junction, weakly coupled to a vibration mode of a nano-mechanical oscillator via both the position and the momentum of the oscillator. %We study both the position and momentum based coupling. The transport properties that we study consist of the average flow of current through the junction, given by the one-time correlation of the electron tunneling event, and the current noise given by the two-time correlation of the average current, i.e, the variance. The first comprehensive experimental study of the noise spectrum of a detector coupled to a QPC was performed by the group of Stettenheim et al. Their observed spectral features had two pronounced peaks which depict the noise produced due to the coupling of the QPC with the oscillator and in turn provide evidence of the induced feedback loop (back-action). Benatov and Blencowe theoretically studied these spectral features using the Born approximation and the Markovian approximation. In this case the Born approximation refers to second order perturbation of the interaction Hamiltonian. In this approximation, the electrons tunnel independently, i.e., one by one only, and co-tunneling is disregarded. The Markovian approximation does not take into account the past behavior of the system under time evolution. These two approximations also enable one to study the system analytically, and the noise is calculated using the MacDonald formula. Our main aim for this thesis is to find a suitable theoretical model that would replicate the experimental plots from the work of Stettenheim et al. Our work does not use the Markovian approximation. However, we do use the Born approximation. This is justified as long as the coupling between the oscillator and QPC is weak. We first obtain the non-Markovian unconditional master equation for the reduced density matrix of the system. Non-Markovian dynamics enables us to study, in principle, the full memory effects of the system. From the master equation, we then derive analytical results for the current and the current noise. Due to the non-Markovian nature of our system, the electron tunneling parameters are time-dependent. Therefore, we cannot study the system analytically. We thus numerically solve the current noise expression to obtain the noise spectrum. We then compare our noise spectrum with the experimental noise spectrum. We show that our spectral noise results agree better with the experimental evidence compared to the results obtained using the Markovian approximation. We thus conclude that one needs non-Markovian dynamics to understand the experimental noise spectrum of a QPC coupled to a nano-mechanical oscillator. / Physics

Cette thèse est une étude de modèles d'image aléatoires avec des applications en synthèse de texture.Dans la première partie de la thèse, des algorithmes de synthèse de texture basés sur le modèle shot noise sont développés. Dans le cadre discret, deux processus aléatoires, à savoir le shot noise discret asymptotique et le bruit à phase aléatoire, sont étudiés. On élabore ensuite un algorithme rapide de synthèse de texture basé sur ces processus. De nombreuses expériences démontrent que cet algorithme permet de reproduire une certaine classe de textures naturelles que l'on nomme micro-textures. Dans le cadre continu, la convergence gaussienne des modèles shot noise est étudiée d'avantage et de nouvelles bornes pour la vitesse de cette convergence sont établies. Enfin, on présente un nouvel algorithme de synthèse de texture procédurale par l'exemple basé sur le récent modèle Gabor noise. Cet algorithme permet de calculer automatiquement un modèle procédural représentant des micro-textures naturelles.La deuxième partie de la thèse est consacrée à l'étude du processus feuilles mortes transparentes (FMT), un nouveau modèle germes-grains obtenu en superposant des objets semi-transparents. Le résultat principal de cette partie montre que, lorsque la transparence des objets varie, le processus FMT fournit une famille de modèles variant du modèle feuilles mortes à un champ gaussien. Dans la troisième partie de la thèse, les champs aléatoires à variation bornés sont étudiés et on établit des résultats généraux sur le calcul de la variation totale moyenne de ces champs. En particulier, ces résultats généraux permettent de calculer le périmètre moyen des ensembles aléatoires et de calculer explicitement la variation totale moyenne des modèles germes-grains classiques. / This thesis is a study of stochastic image models with applications to texture synthesis. Most of the stochastic texture models under investigation are germ-grain models. In the first part of the thesis, texture synthesis algorithms relying on the shot noise model are developed. In the discrete framework, two different random processes, namely the asymptotic discrete spot noise and the random phase noise, are theoretically and experimentally studied. A fast texture synthesis algorithm relying on these random processes is then elaborated. Numerous results demonstrate that the algorithm is able to reproduce a class of real-world textures which we call micro-textures. In the continuous framework, the Gaussian convergence of shot noise models is further studied and new bounds for the rate of this convergence are established. Finally, a new algorithm for procedural texture synthesis from example relying on the recent Gabor noise model is presented. This new algorithm permits to automatically compute procedural models for real-world micro-textures. The second part of the thesis is devoted to the introduction and study of the transparent dead leaves (TDL) process, a new germ-grain model obtained by superimposing semi-transparent objects. The main result of this part shows that, when varying the transparency of the objects, the TDL process provides a family of models varying from the dead leaves model to a Gaussian random field. In the third part of the thesis, general results on random fields with bounded variation are established with an emphasis on the computation of the mean total variation of random fields. As particular cases of interest, these general results permit the computation of the mean perimeter of random sets and of the mean total variation of classical germ-grain models.

In this work we present an introduction to the theory of point processes in space and time with focus on space--time shot--noise Cox process. Further from theoretical point of view we study its simulation, space--time separability, kernel estimate of intensity function and non--parametric estimation of some summary statistics using edge corrections. For two ambit models and one space--time separable model we do numerical calculations using the presented theory and software Wolfram Mathematica 9.0. For these three models we do simulations, we select the best bandwidth for kernel estimate of the intensity function and we also calculate some theoretical summary statistics including the pair correlation function. Powered by TCPDF (www.tcpdf.org)

This paper is concerned with estimation of space-time shot-noise Cox process parametric models. We introduce the two-step estimation method, where in the second step we use composite likelihood or Palm likelihood. For the two-step estimation method based on Palm likelihood we prove consistency and asymptotic normality theorem. Finally we compare composite likelihood with Palm likelihood in simulation studies, where we add for comparison minimum contrast method. Results for minimum contrast method are taken from the literature. 1

Cette thèse est une étude de modèles d'image aléatoires avec des applications en synthèse de texture. La plupart des modèles de champs aléatoires étudiés sont des modèles germes-grains. Dans la première partie de la thèse, des algorithmes de synthèse de texture basés sur le modèle shot noise sont développés. Dans le cadre discret, deux processus aléatoires, à savoir le shot noise discret asymptotique et le bruit à phase aléatoire, sont étudiés. On élabore ensuite un algorithme rapide de synthèse de texture basé sur ces processus. De nombreuses expériences démontrent que cet algorithme permet de reproduire une certaine classe de textures naturelles que l'on nomme micro-textures. Dans le cadre continu, la convergence gaussienne des modèles shot noise est étudiée d'avantage et de nouvelles bornes pour la vitesse de cette convergence sont établies. Enfin, on présente un nouvel algorithme de synthèse de texture procédurale par l'exemple basé sur le récent modèle Gabor noise. Cet algorithme permet de calculer automatiquement un modèle procédural représentant des micro-textures naturelles. La deuxième partie de la thèse est consacrée à l'étude du processus feuilles mortes transparentes (FMT), un nouveau modèle germes-grains obtenu en superposant des objets semi-transparents. Le résultat principal de cette partie montre que, lorsque la transparence des objets varie, le processus FMT fournit une famille de modèles variant du modèle feuilles mortes à un champ gaussien. Dans la troisième partie de la thèse, les champs aléatoires à variation bornés sont étudiés et on établit des résultats généraux sur le calcul de la variation totale moyenne de ces champs. En particulier, ces résultats généraux permettent de calculer le périmètre moyen des ensembles aléatoires et de calculer explicitement la variation totale moyenne des modèles germes-grains classiques.

Os diodos laser são amplamente usados em física atômica em configurações de cavidade externa com uma rede de difração (Configuração Littrow ou Littrow-Metcalf), que permite sintonizar o seu comprimento de onda e filtrar do seu espectro. Mesmo com este controle, eles apresentam um excesso de ruído por volta de 40 dB acima do ruído quântico padrão, dificultando seu uso em ótica quântica. Nosso propósito neste projeto é diminuir os valores típicos de ruído do diodo laser até níveis aceitáveis que permitam trabalhar em ótica quântica. Para conseguir isto, construímos um laser em estrutura em anel com o diodo semicondutor como o meio de ganho. Caracterizamos a potência de saída do laser em função da corrente de injeção no chip. Também introduzimos um mecanismo de controle das perdas da cavidade para caracterizar a potência de saída em função das perdas. Alcançamos uma potência máxima de 25 mW para 0, 8 A, com um limiar de oscilação de 0, 45 A, e uma potência máxima de 10 mW (a 0, 8 A) com um limiar de 0, 41 A. Para caracterizar as suas propriedades de ruído, usamos a técnica da rotação de elipse para diferentes valores da corrente de injeção e de perdas controladas. Finalmente, comparamos o ruído das quadraturas do nosso novo sistema com o ruído de um laser de diodo em configuração Littrow. Enquanto o laser Littrow apresenta excesso de 40 dB no ruído da fase, encontramos valores para o ruído de amplitude do nosso novo laser entre 10 e 15 dB e do ruído de fase entre 11 e 27 dB acima do nível do ruído quântico padrão. Assim, conseguimos diminuir o ruído da quadratura fase por volta de 20 dB, porém, também incrementamos o ruído de amplitude, fazendo com que o ruído das quadraturas esteja no nível de 11 dB acimo do nível do ruído quântico padrão. Este nível é compatível com laseres de estado sólido (Nd:YAG) e pode ser facilmente reduzido com ajuda de uma cavidade de filtro. / Laser diodes are widely used in atomic physics in configurations of external cavity with a diffraction grating (Littrow or Littrow-Metcalf configuration), that allows us to tune its wavelength and filter their spectrum. Even with this control they present an excess noise about 40 dB above the standard quantum level,limiting their uses for quantum optics. Our goal in this project is to decrease the typical noise level of the diode laser, to reasonable values for future work with quantum optics. In order to do that we built a ring laser using a semiconductor chip as the gain medium. We characterize the output power of the laser as a function of the injection current. We also introduce a mechanism for controlling the losses so that, we were able to characterize the output power by changing the controlled losses. We reach a maximum power of 25 mW at 0.8 A, with the threshold current value 0.45 A, and a maximum power of 10 mW (@ 0.8 A) for 0.41 A of threshold current. In order to characterize its noise properties, we performed the ellipse rotation technique for different values of the injection current and controlled looses. Finally, we compare the quadrature noise of our new system with the noise of a diode laser in Littrow configuration. While Littrow laser present excess of of 40 dB on the phase noise, we found noise levels for the amplitude noise of our new laser between 10 to 15 dB and its phase noise between 11 to 27 dB above the standard quantum level. So, we achieved a noise reduction of the phase quadrature in 20 dB, but, we also increase the amplitude noise, obtaining a quadrature noise around 11 dB above the standard quantum limit. This level is compatible with solid state lasers (Nd:YAG) and can be easily reduced with the help of a filter cavity.

La génération à la demande d'excitations quantiques dans un état contrôlé permet la construction de systèmes quantiques de plus en plus complexe. Cependant, la réponse collective de la mer de Fermi à une perturbation comprend généralement à la fois des électrons et des trous, ce qui rend la manipulation d'un nombre limité de degrés de liberté difficile. Une méthode permettant de générer une excitation élémentaire résolue en temps dans un conducteur cohérent unidimensionnel a été proposée : l'application de pulses de tension de forme lorentzienne. Un pulse Vp(t) de forme quelconque injecte un nombre fini de paires électron-trou. La seule possibilité de supprimer les trous et de laisser la mer de Fermi intacte est d'appliquer des pulses lorentziens dont le flux est quantifié. Les paquets d'onde transférés sont des quasi-particules et appelés Levitons. Ils ont des propriétés statistiques remarquables : ils minimisent le bruit de grenaille. Dans cette thèse, on étudie la génération de ces objets et on démontre que des pulses lorentziens constituent une source d'électrons à la demande. Des pulses GHz sont appliqués sur un contact ponctuel quantique (QPC) semi-réfléchissant et refroidi au-dessous de 50mK. Le bruit de grenaille photo-assisté (PASN) généré est proportionnel au nombre total d'électrons et de trous, ce qui permet de tester la source. Le PASN permet également de déterminer la distribution en énergie et le profil temporel des paquets d'onde. / The on-demand generation of well-controlled quantum excitations leads to the operation of increasingly complex quantum systems. However, the collective response of the Fermi sea to a perturbation typically includes holes and electrons and the control of a few degrees of liberty is difficult to achieve. A means of generating a time-resolved elementary excitation through short-time voltage pulses Vp(t) applied on the contacts of a one-dimensional coherent conductor has been predicted. For most voltage pulses, a finite number of neutral electron-hole pairs are injected. The only possibility to suppress hole-generation, which means that the Fermi sea appears unmodified, is through lorentzian-shaped voltage pulses with quantized flux. The transferred quantum states, termed levitons, have strikingly simple statistical properties: they minimize the shot noise when impinging a static potential barrier. In this thesis, we study the generation of this states and show that lorentzian pulses implement an on-demand electron source. GHz pulses are applied on a partially-transmitting quantum point contact (QPC) below 50mK and realized from a two-dimensional electron gas in a GaAs/AlGaAs heterostructure. The resulting Photo-Assisted Shot Noise (PASN) is proportional to the number of electrons and holes, thus testing the source properties. Additional characterizations performed with the PASN include the energy distribution of the excitations and their time-domain extension.

Cette thèse est une étude de modèles d'image aléatoires avec des applications en synthèse de texture.Dans la première partie de la thèse, des algorithmes de synthèse de texture basés sur le modèle shot noise sont développés. Dans le cadre discret, deux processus aléatoires, à savoir le shot noise discret asymptotique et le bruit à phase aléatoire, sont étudiés. On élabore ensuite un algorithme rapide de synthèse de texture basé sur ces processus. De nombreuses expériences démontrent que cet algorithme permet de reproduire une certaine classe de textures naturelles que l'on nomme micro-textures. Dans le cadre continu, la convergence gaussienne des modèles shot noise est étudiée d'avantage et de nouvelles bornes pour la vitesse de cette convergence sont établies. Enfin, on présente un nouvel algorithme de synthèse de texture procédurale par l'exemple basé sur le récent modèle Gabor noise. Cet algorithme permet de calculer automatiquement un modèle procédural représentant des micro-textures naturelles.La deuxième partie de la thèse est consacrée à l'étude du processus feuilles mortes transparentes (FMT), un nouveau modèle germes-grains obtenu en superposant des objets semi-transparents. Le résultat principal de cette partie montre que, lorsque la transparence des objets varie, le processus FMT fournit une famille de modèles variant du modèle feuilles mortes à un champ gaussien. Dans la troisième partie de la thèse, les champs aléatoires à variation bornés sont étudiés et on établit des résultats généraux sur le calcul de la variation totale moyenne de ces champs. En particulier, ces résultats généraux permettent de calculer le périmètre moyen des ensembles aléatoires et de calculer explicitement la variation totale moyenne des modèles germes-grains classiques.