Quantum theory is a probabilistic theory, where certain variables are hidden or non-accessible. It results in lack of representation of systems under study. However, I deduce system's representation in probabilistic manner, introducing probability of existence w, and quantize it exploiting Schrödinger's quantization rule. The formalism enriches probabilistic quantum theory, and enables system's representation in probabilistic manner.

Les effets non-perturbatifs de QCD sont à présent parmi les plus grandes sources d'incertitude dans notre connaissance de la phénoménologie du Modèle Standard. Je présenterai quelques unes des méthodes dont on dispose pour traiter ces effets en insistant particulièrement sur la QCD sur réseau. Des théories effectives peuvent être couplées à la méthode des réseaux pour étudier les secteurs chiral et de masses lourdes de quarks. Je montrerai quelques exemples tirés de la phénoménologie où ces outils peuvent être appliqués avec succès. Le couplage des mésons lourds au pion est caractérisé par une quantité non-perturbative, notée "g^", qu'il est nécessaire de connaître pour améliorer les prédictions de la théorie effective combinant à la fois les symétries chirale et des quarks lourds. Ce couplage intervient aussi dans l'étude des facteurs de forme des désintégrations semi-leptoniques lourd à léger. Ces désintégrations sont nécessaires à la détermination des éléments parmi les moins bien connus de la matrice CKM. D'autre part, les effets chiraux des mésons lourds dépendent des boucles de pions dont le vertex est effectivement le couplage g^. Ceci a généré le besoin de sa détermination théorique et expérimentale. Je présenterai les résultats des déterminations sur réseau et je les comparerai à ceux issus des autres approches. Ce sera aussi l'occasion de présenter ces différents outils et d'isoler quelques unes des limites et des améliorations envisageables, autant du point de vue des méthodes que de celui de leur application particulière au couplage g^.

Hamiltonian systems of hydrodynamic type occur in a wide range of applications including fluid dynamics, the Whitham averaging procedure and the theory of Frobenius manifolds. In 1 + 1 dimensions, the requirement of the integrability of such systems by the generalised hodograph transform implies that integrable Hamiltonians depend on a certain number of arbitrary functions of two variables. On the contrary, in 2 + 1 dimensions the requirement of the integrability by the method of hydrodynamic reductions, which is a natural analogue of the generalised hodograph transform in higher dimensions, leads to finite-dimensional moduli spaces of integrable Hamiltonians. We classify integrable two-component Hamiltonian systems of hydrodynamic type for all existing classes of differential-geometric Poisson brackets in 2D, establishing a parametrisation of integrable Hamiltonians via elliptic/hypergeometric functions. Our approach is based on the Godunov-type representation of Hamiltonian systems, and utilises a novel construction of Godunov's systems in terms of generalised hypergeometric functions. Furthermore, we develop a theory of integrable dispersive deformations of these Hamiltonian systems following a scheme similar to that proposed by Dubrovin and his collaborators in 1 + 1 dimensions. Our results show that the multi-dimensional situation is far more rigid, and generic Hamiltonians are not deformable. As an illustration we discuss a particular class of two-component Hamiltonian systems, establishing triviality of first order deformations and classifying Hamiltonians possessing nontrivial deformations of the second order.

A thesis submitted to the Faculty of Science University of the Witwatersrand Johannesburg in fulfillment of the requirements for the Master of Science Johannesburg 1997

Tratamos vários modelos que descrevem a interação entre dois subsistemas quânticos. Mostramos que dois deles são exatamente soluveis, achamos as soluções correspondentes e mostramos a relação das propriedades espectrais do banho com a decoerência. Fazemos uma análise crítica do uso de liouvillianos com forma de Lindblad e de liouvillianos obtidos através da aproximação de Born-Markov, empregando entre outras coisas os resultados dos modelos exatos. Propomos novos esquemas de aproximação que descrevem com exatidão o regime de tempos curtos e o acoplamento de dois sistemas \"pequenos\", e os testamos com os modelos exatamente solúveis antes discutidos. Fazemos aplicações aos sais orgânicos de transferência de carga, a um experimento de produção de gatos e da observação de sua decoerência subsequente e às zonas de Ramsey empregadas perifericamente nesta experiência. / Several models describing the interaction between two quantum systems are examined. The exact solution of two of them is found and the relation between the bath\'s spectral properties and decoherence is shown. Using these results and several others, we analyze the use of both Lindbland-form and Born-Markov liouvillians. New approximation schemes, appropriate for short times and small subsystems, are proposed and tested (using the above mentioned exact models). Applications are made to the treatment of organic salts, to the analysis of a recently reported experiment of production of cat states and observation of its subsequent decoherence, and to the understanding of the Ramsey zones, peripherically used in this experience.

Orientador: José Francisco Gomes / Co-orientador: Abraham Hirsz Zimerman / Banca: Antônio Lima Santos / Banca: Clisthenis Ponce Constantinidis / Resumo: A teoria de defeitos integráveis em teoria de campos em 1+1 dimensões, foi introduzida pela escola de York [16, 17, 22], utilizando transformações de Bäcklund para descrever o defeito. Nesta dissertação estudamos o modelo de Schrödinger não linear na presença de um defeito integrável. Estudamos tanto o modelo discreto [29] como o modelo contínuo dentro dos formalismos lagrangiano [23] e da matrizr [7]. Construímos também o formalismo hamiltoniano para o modelo de Schrödinger não linear na presença de um defeito integrável. Discutimos e relacionamos os formalismos lagrangiano, hamiltoniano e da matriz r / Abstract: The theory of integrable defects in 1+1 field theory, was introduced by the school of York [16, 17, 22], employing B¨acklund transformation in order to describe the defect. In this dissertation we have studied the nonlinear Schrödinger model in the presence of an integrable defect. We study both, the discrete model [29] as the continuous model within the lagrangian [23] andr matrix [7] formalisms. Also we built the hamiltonian formalism for nonlinear Schrödinger model in the presence of an integrable defect. We discuss and relate the lagrangian, hamiltonian and r matrix formalisms / Mestre

Orientador: Edson Denis Leonel / Coorientador: Luiz Antonio Barreiro / Banca: Juliano Antônio de Oliveira / Banca: Giovani Gozzi / Resumo: O presente trabalho de pesquisa foi motivado por um modelo de bilhar unidimensional denominado de Bouncer. O modelo consiste em uma partícula movendo-se sob ação de um campo gravitacional e que colide com um plataforma móvel. Apresentaremos suas características e propriedades que motivaram a pesquisa para um bilhar bidimensional com geometria da fronteira do tipo ovóide. Os objetivos desta dissertação são de estudar as propriedades estatísticas e termodinâmicas de um bilhar ovóide com dependência temporal na fronteira em um regime dissipativo em relação as colisões entre a partícula e a fronteira. Para o bilhar bidimensional, apresentaremos as propriedades desenvolvidas inspiradas no modelo unidimensional. Desenvolvemos as expressões para determinar os expoentes críticos do sistema em relação a velocidade quadrática média, o número de colisões em função do tempo e a conexão com a termodinâmica através do teorema de equipartição de energia. Nesta dissertação apresentamos um forma alternativa de fazer a conexão com a termodinâmica através da lei de Fourier para a condução do calor, para bilhares bidimensionais e de determinar o número de colisões em função do tempo / Abstract: This work was motivated by a one-dimensional model called as bouncer. The model consists of a particle moving under the action of a gravitational field and experiences collisions with a periodic moving platform. We describe shortly its dynamical properties and move forward to a two-dimensional billiard problem of the oval-like shape. The objective of this dissertation is to study some statistical and thermodynamical properties of an oval-like shaped billiard whose boundary moves in time. Upon collision with the boundary, the particle has a fractional lose of energy produced by inelastic collisions. We then obtain equations that describe the dynamics at both sort and large time. By the use of equipartition theorem, we make a connection of the dynamical results with the thermodynamics approach. In this dissertation we present an alternative way of making the connection with thermodynamics via the Fourier's law for heat conduction / Mestre

Stable and metastable phases of Fe and Al and structural anomalies of Zn and Cd have been studied by epitaxial Bain path (EBP) and minimum path (MNP) first-principles procedures, based on finding equilibrium structures from minimizing the Gibbs free energy G with respect to structure at a given hydrostatic pressure p and temperature T . The main accomplishments are as follows. (1) This dissertation illustrates the effectiveness of the MNP procedure for finding stable and metastable phases of an element by studying four Bravais phases of Fe including body-centered tetragonal (bct), body-centered cubic (bcc), face-centered cubic (fcc) and rhombohedral (rh) phases. The determination of absolute stability using MNP is new; MNP finds all the elastic constants cjj of a given state and the eigenvalues of the elastic constants matrix, which determine the absolute stability of the state. / (2) We have extended our search for stable and metastable phases from zero temperature to finite temperature, which requires the calculations of the Debye temperature Od from cjj in the case of no symmetry. The Debye theory is modified by introducing a parameter B2 that gives the fraction of the full Debye zero-point energy possessed by the actual dispersive mode frequencies. The value of the lattice parameter of fcc Al at low temperatures,a(T) , is shown to be accurately determined by the modified Debye theory of lattice vibrations and first-principles total energy band calculations with the MNP procedure. (3) The existence of structural anomalies in hcp Zn and Cd has been shown from first-principles total-energy calculations using WIEN2k with the EBP procedure. / Evaluation of the pressure dependence of various elastic quantities which are much more sensitive to the anomaly shows that the anomalies in hcp Zn and hcp Cd exist over a considerable range of pressure; several abrupt changes in the electron distribution are thereby indicated in that pressure range. (4) Calculations on the zone-center transverse optical phonon frequencies Vto(p) of hcp Zn, which found oscillatory behavior of Vto(p) in the pressure range of the anomalies, support the conclusions made in (3) on the structural anomalies. Based on this dissertation research four papers have been published in refereed journals. / by Florin Apostol. / Thesis (Ph.D.)--Florida Atlantic University, 2008. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2008. Mode of access: World Wide Web.

In a projective plane (PG(2, K) defined over an algebraically closed field K of characteristic p = 0, we give a complete classification of 3-nets realizing a finite group. The known infinite family, due to Yuzvinsky, arised from plane cubics and comprises 3-nets realizing cyclic and direct products of two cyclic groups. Another known infinite family, due to Pereira and Yuzvinsky, comprises 3-nets realizing dihedral groups. We prove that there is no further infinite family and list all possible sporadic examples. If p is larger than the order of the group, the same classification holds true apart from three possible exceptions: Alt4, Sym4 and Alt5. / by Nicola Pace. / Thesis (Ph.D.)--Florida Atlantic University, 2012. / Includes bibliography. / System requirements: Adobe Reader. / Mode of access: World Wide Web.

In this work, a two-dimensional model representing the vortices that animals produce, when they are flying/swimming, was constructed. A D{shaped cylinder and an oscillating airfoil were used to mimic these body{shed and wing{generated vortices, respectively. The parameters chosen are based on the Reynolds numbers similar to that which is observed in nature (104). In order to imitate the motion of ying/swimming, the entire system was suspended into a water channel from frictionless air{bearings. The position of the apparatus in the channel was regulated with a linear, closed loop PI controller. Thrust/drag forces were measured with strain gauges and particle image velocimetry (PIV) was used to examine the wake structure that develops. The Strouhal number of the oscillating airfoil was compared to the values observed in nature as the system transitions between the accelerated and steady states... As suggested by previous work, this self-regulation is a result of a limit cycle process that stems from nonlinear periodic oscillations. The limit cycles were used to examine the synchronous conditions due to the coupling of the foil and wake vortices. Noise is a factor that can mask details of the synchronization. In order to control its effect, we study the locking conditions using an analytic technique that only considers the phases.. The results suggest that Strouhal number selection in steady forward natural swimming and flying is the result of a limit cycle process and not actively controlled by an organism. An implication of this is that only relatively simple sensory and control hardware may be necessary to control the steady forward motion of man-made biomimetically propelled vehicles. / by Cyndee L. Finkel. / Thesis (Ph.D.)--Florida Atlantic University, 2013. / Includes bibliography. / Mode of access: World Wide Web. / System requirements: Adobe Reader.