Neste trabalho mostramos que uma grande variedade de modelos exatamente solúveis através do ansatz de Bethe coordenadas podem também ser resolvidos através de um ansatz do produto matricial. Estes modelos são descritos no caso unidimensional por cadeias quânticas, e por matrizes de transferência no caso de sistemas clássicos bi-dimensionais. Diferentemente do ansatz de Bethe, em que as auto-funções do modelo são escritas como uma combinação de ondas planas, no nosso ansatz do produto matricial elas são dadas por produtos de matrizes, onde as matrizes obedecem a uma álgebra associativa apropriada. Estas relações algébricas são obtidas impondo-se que as auto-funções escritas em termos do ansatz satisfaçam à equação de auto-valor do operador Hamiltoniano ou da matriz de transferência. A consistência das relações de comutatividade entre os elementos da álgebra implicam na exata integrabilidade do modelo. Além disso, o ansatz que propomos permite uma formulação simples e unificada para vários Hamiltonianos quânticos exatamente solúveis. Apresentamos nesta tese a formulação do nosso ansatz do produto matricial para uma grande família de redes quânticas, como os modelos anisotrópico de Heisenberg, Fateev-Zamolodchikov, Izergin-Korepin, Sutherland, t-J, Hubbard etc. Mais ainda, formulamos nosso ansatz para processos estocásticos de partículas com tamanhos e classes diferentes difundindo assimetricamente na rede. Por fim, com o objetivo de dar suporte a nossa conjectura de que todos os modelos exatamente solúveis através do ansatz de Bethe coordenadas, associados a Hamiltonianos quânticos unidimensionais ou matrizes de transferência bidimensionais, também podem ser resolvidos através de um ansatz do produto matricial, apresentamos a formulação do nosso ansatz para a matriz de transferência do modelo de seis-vértices com condição de contorno toroidal / In this work we show that a large family of exactly solved models through the coordinate Bethe ansatz can also be solved through a matrix product ansatz. The models are described in the one dimensional case by quantum Hamiltonians, and by transfer matrices in the case of two dimensional classical models. Differently from the Bethe ansatz, where the model\'s eigenfunctions are described by a plane wave combination, in our matrix product ansatz they are given by a matrix product, where the matrices obey a suitable associative algebra. Theses algebraic relations are obtained by imposing that the eigenfunctions described in terms of the ansatz satisfy the eigenvalue equation for the associated Hamiltonian or transfer matrix. The consistency of the commutativity relations among the elements of the algebra implies the exact integrability of the model. Furthermore, the matrix product ansatz we propose allows an unified and simple formulation for the solution of several exact integrable quantum Hamiltonians. We present on this thesis the formulation of our matrix product ansatz for a huge family of quantum chains such as the anisotropic Heisenberg model, Fateev-Zarnolodchikov model, Izergin-Korepin model, Sutherland model, t- J model, Hubbard model, etc. Moreover, we formulated our ansatz for stochastic process of particles with different sizes and classes diffusing asymmetrically on the lattice. Finally, in order to support our conjecture that all exactly solved models through the coordinate Bethe ansatz, associated to unidimensional quantum Hamiltonians or two-dimensional transfer matrices, can also be solved through a matrix product ansatz, we present the formulation of our ansatz, for the transfer matrix of the six-vertex model with toroidal boundary condition

Während Zulassungstests an Universitäten im Regelfall evaluiert werden, sind entsprechende Verfahren zur Evaluierung anderer Prozessschritte in Bewerbungsverfahren - wie die Einreichung von Motivationsschreiben - noch nicht etabliert. Um diese Lücke zu schließen, wird in diesem Beitrag ein Multi-Method-Ansatz zur Evaluierung von Motivationsschreiben vorgestellt, bei dem Text-Mining-Techniken mit inhaltsanalytischen Elementen kombiniert werden. Es wird dargelegt, wie unterschiedliche von Studierenden gesendete "Signale" mit Studienerfolg korrelieren, und aufgezeigt, dass soziodemografische Effekte bei der Bewertung von Motivationsschreiben berücksichtigt werden müssten.

Wei, Bobo = 基於Bethe Ansatz解的兩個一維多體模型的研究 / 魏勃勃. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 62-68). / Abstracts in English and Chinese. / Wei, Bobo = Ji yu Bethe Ansatz jie de liang ge yi wei duo ti mo xing de yan jiu / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Cold atoms systems --- p.1 / Chapter 1.1.1 --- Optical lattice --- p.2 / Chapter 1.1.2 --- Feshbach resonance --- p.4 / Chapter 1.2 --- Outline of this work --- p.6 / Chapter 2 --- Review of Bethe ansatz method --- p.8 / Chapter 2.1 --- Introduction --- p.8 / Chapter 2.2 --- Coordinate Bethe ansatz: One-dimensional Bose gas --- p.10 / Chapter 2.2.1 --- N = 2 bosons case --- p.11 / Chapter 2.2.2 --- N = 3 bosons case --- p.13 / Chapter 2.2.3 --- Arbitrary N bosons case --- p.15 / Chapter 3 --- Persistent currents in the one-dimensional mesoscopic Hubbard ring --- p.18 / Chapter 3.1 --- Introduction --- p.18 / Chapter 3.2 --- The model and its Bethe ansatz soluiton --- p.20 / Chapter 3.3 --- The charge persistent current --- p.23 / Chapter 3.3.1 --- The charge persistent current and the on-site interaction U --- p.24 / Chapter 3.3.2 --- The charge persistent current and the system size L --- p.28 / Chapter 3.4 --- The spin persistent current --- p.30 / Chapter 3.4.1 --- The spin persistent current and the on-site interaction U --- p.30 / Chapter 3.4.2 --- The spin persistent current and the system size L --- p.32 / Chapter 3.5 --- Conclusions --- p.33 / Chapter 4 --- Exact results of two-component ultra-cold Fermi gas in a hard wall trap --- p.36 / Chapter 4.1 --- Introduction --- p.36 / Chapter 4.2 --- The model and its exact solution --- p.37 / Chapter 4.3 --- The Theoretical Background --- p.41 / Chapter 4.4 --- N = 2 --- p.44 / Chapter 4.4.1 --- Single-particle reduced density matrix and Position density distributions --- p.44 / Chapter 4.4.2 --- Momentum density distributions --- p.45 / Chapter 4.5 --- N = 3 --- p.46 / Chapter 4.5.1 --- Single-particle reduced density matrix --- p.46 / Chapter 4.5.2 --- Natural orbitals and their populations --- p.48 / Chapter 4.5.3 --- Momentum density distribution --- p.51 / Chapter 4.5.4 --- Two-particle density distributions --- p.53 / Chapter 4.6 --- Conclusions --- p.53 / Chapter 5 --- Summary and prospects --- p.54 / Chapter 5.1 --- Summary --- p.54 / Chapter 5.2 --- Prospects for further study --- p.55 / Chapter 5.2.1 --- Recent experimental advancements on realization of quantum gas --- p.55 / Chapter 5.2.2 --- Some recent work on FTG gas --- p.57 / Bibliography --- p.62 / Chapter A --- Explicit form of Bethe ansatz wave function for N = 2 fermions --- p.69 / Chapter B --- "Simplified form of Bethe ansatz wave function for N = 3, M=1 fermions" --- p.73 / Chapter C --- Explicit form of Single-particle reduced density matrix for free fermions --- p.79

De nombreux systèmes physiques peuvent être décrits par des modèles unidimensionnels (1D). C'est le cas de certains gaz d'atomes ultrafroids: dans les bonnes conditions leur dynamique a lieu suivant une seule dimension spatiale.<br />Je me suis intéressée à l'étude de quelques aspects des systèmes intégrables à 1D. D'abord je présente une étude de l'état fondamental d'un système de fermions 1D à 2 composants en interactions de contact répulsives. J'utilise l'ansatz de Bethe pour calculer le diagramme de phase du système homogène. Je prends ensuite en compte un piège harmonique et je montre que les atomes s'organisent en deux couches: une phase partiellement polarisée se trouve au centre du piège et une phase totalement polarisée aux bords.<br />Ensuite j'étudie des corrections dues aux effets de taille finie au gap du spectre d'excitations du modèle d'Hubbard 1D. J'obtiens deux termes correctifs aux résultats de la limite thermodynamique: un en loi de puissances inverses en la taille du système L, et un second exponentiel en L. Dans le régime de faible interaction ce deuxième terme peut être important.<br />Finalement j'étudie la réponse d'un système excité à la modulation temporelle de l'interaction entre atomes. Je considère le modèle de Lieb-Liniger et le modèle non-intégrable d'un gaz de fermions avec une impureté mobile. Je montre que le système non-intégrable est sensible à des excitations de fréquences de l'ordre de l'espacement moyen entre niveaux d'énergie, tandis que le système intégrable n'est excité que par des fréquences beaucoup plus grandes. Cet effet peut être utilisé comme test d'intégrabilité dans des systèmes mésoscopiques 1D et pourrait être observé expérimentalement.

Cette thèse est consacrée à l'étude de la théorie mathématique qui sous-tend la construction et la résolution d'une classe particulière de systèmes quantiques exactement solubles: son objectif est d'utiliser les superalgèbres de Lie comme un outil pour construire et résoudre des chaînes de spins intégrables.<br />Nous développons une approche générale et systématique permettant de construire et traiter simultanément une large classe de systèmes intégrables partageant la même super--symétrie, allant du cas bien connu où tous les sites portent la représentation fondamentale (comme par exemple dans le cas du modèle t-J) à des situations plus complexes d'intérêt physique comprennent chaînes de spins alternée, avec impuretés, etc...<br /><br />Les deux premiers chapitres sont consacrés à un examen des résultats connus concernant le Yangien de la superalgèbre de Lie gl(m|n), nécessaire pour introduire la version graduée de la méthode de diffusion inverse quantique. Nous appliquons notre approche dans le chapitre 3 aux chaînes fermées et dans le chapitre 4 aux chaînes ouvertes. Dans ce chapitre sont étudiés les homologues super--symétriques de l'algèbre de réflexion et du Yangien twisté, qui sont les structures algébriques permettant d'imposer des conditions aux bords qui préservent l'intégrabilité. Dans le dernier chapitre, la méthode dite de fusion est traitée en détail pour des chaînes de spins avec supersymétrie sl(1|2).<br /><br />La méthode de résolution que nous utilisons, tant dans le cas fermé que dans le cas ouvert, est la généralisation au cas supersymétrique de l'Ansatz de Bethe analytique, pour lequel les équations de Bethe paramétrant les nombres quantiques du système sont obtenus comme conditions d'analyticité pour les valeurs propres des Hamiltoniens.

Die Forschung zum Zusammenhang zwischen Topmanagementteams und Unternehmenserfolg stellt ein zum Teil fragmentarisches und wenig konzeptionelles Bild dar. Vor diesem Hintergrund geht es in vorliegender Arbeit um die Frage, inwiefern die Beziehung zwischen Topmanagementteams und Eigentümern optimiert werden kann, wenn bei der Zusammensetzung des Vorstandsteams neben vertraglichen Komponenten auch demografische Eigenschaften berücksichtigt werden.

Spin-1/2 chains demonstrate some of the striking effects of interactions and quantum fluctuations in one-dimensional systems. The XXZ model has been used to study the unusual properties of anisotropic spin chains in an external magnetic field. The zero temperature phase diagram for this model exhibits a critical or quasi-long-range-ordered phase which is a realization of a Luttinger liquid. While many static properties of spin-1/2 chains have been explained by combinations of analytical techniques such as bosonization and Bethe ansatz, the standard approach fails in the calculation of some time-dependent correlation functions. I present a study of the longitudinal dynamical structure factor for the XXZ model in the critical regime. I show that an approximation for the line shape of the dynamical structure factor in the limit of small momentum transfer can be obtained by going beyond the Luttinger model and treating irrelevant operators associated with band curvature effects. This approach is able to describe the width of the on-shell peak and the high-frequency tail at finite magnetic field. Integrability is shown to affect the low-energy effective model at zero field, with consequences for the line shape. The power-law singularities at the thresholds of the particle-hole continuum are investigated using an analogy with the X-ray edge problem. Using methods of Bethe ansatz and conformal field theory, I compute the exact exponents for the edge singularities of the dynamical structure factor. The same methods are used to study the long-time asymptotic behavior of the spin self-correlation function, which is shown to be dominated by a high-energy excitation.

Spin-1/2 chains demonstrate some of the striking effects of interactions and quantum fluctuations in one-dimensional systems. The XXZ model has been used to study the unusual properties of anisotropic spin chains in an external magnetic field. The zero temperature phase diagram for this model exhibits a critical or quasi-long-range-ordered phase which is a realization of a Luttinger liquid. While many static properties of spin-1/2 chains have been explained by combinations of analytical techniques such as bosonization and Bethe ansatz, the standard approach fails in the calculation of some time-dependent correlation functions. I present a study of the longitudinal dynamical structure factor for the XXZ model in the critical regime. I show that an approximation for the line shape of the dynamical structure factor in the limit of small momentum transfer can be obtained by going beyond the Luttinger model and treating irrelevant operators associated with band curvature effects. This approach is able to describe the width of the on-shell peak and the high-frequency tail at finite magnetic field. Integrability is shown to affect the low-energy effective model at zero field, with consequences for the line shape. The power-law singularities at the thresholds of the particle-hole continuum are investigated using an analogy with the X-ray edge problem. Using methods of Bethe ansatz and conformal field theory, I compute the exact exponents for the edge singularities of the dynamical structure factor. The same methods are used to study the long-time asymptotic behavior of the spin self-correlation function, which is shown to be dominated by a high-energy excitation.

The main work of this thesis involves the calculation, using the Bethe ansatz, of two of the signature quantities of the one-dimensional delta-function Bose gas. These are the density matrix and concomitantly its Fourier transform the occupation numbers, and the correlation function and concomitantly its Fourier transform the structure factor. The coefficient of the delta-function is called the coupling constant; these quantities are calculated in the finite-coupling regime, both expansions around zero coupling and infinite coupling are considered. Further to this, the density matrix in the infinite coupling limit, and its first order correction, is recast into Toeplitz determinant form. From this the occupation numbers are calculated up to 36 particles for the ground state and up to 26 particles for the first and second excited states. This data is used to fit the coefficients of an ansatz for the occupation numbers. The correlation function in the infinite coupling limit, and its first order correction, is recast into a form which is easy to calculate for any N, and is determined explicitly in the thermodynamic limit.

Univ., Diss.--Paderborn, 2007.