Neste trabalho nós investigamos o modelo de Bose-Hubbard de dois sítios atrativo sob o ponto de vista do ansatz de Bethe. Este modelo descreve o tunelamento Josephson entre dois condensados de Bose-Einstein. Nós iniciamos estabelecendo a integrabilidade do modelo através da álgebra de Yang-Baxter. Usando uma análise clássica nós obtemos o diagrama de parâmetros do sistema. Nós estudamos então as transições de fase quânticas do modelo usando os conceitos de gap de energia, emaranhamento e fidelidade. Nós encontramos que o ponto crítico obtido utilizando estes conceitos coincide com o ponto fixo de bifurcação obtido na análise clássica. Além disso, nós mostramos que este ponto crítico também pode ser identificado através de uma mudança no comportamento das soluções das equações do ansatz de Bethe do modelo para o estado fundamental. / In this work we investigate the attractive two-site Bose Hubbard model from a Bethe ansatz perspective. This model describes Josephson tunneling between two Bose-Einstein condensates. We begin by establishing the integrability of the model through the Yang- Baxter algebra. Using a classical analysis we obtain the phase space xed points of the system. Then we study the quantum phase transitions of the model using the concepts of energy gap, entanglement entropy and the delity. We nd that the critical point obtained using these concepts coincides with the bifurcation point obtained in the classical analysis. Moreover, we also show that this critical point can be also identi ed through a di erent behaviour of the ground-state solutions of the Bethe ansatz equations.

Modelos exatamente solúveis para gases de férmions e bósons ultrafrios são estudados via o método do ansatz de Bethe termodinâmico. Resultados analíticos e numéricos são obtidos para o gás de Fermi de duas componentes com população de férmions não balanceada no regime atrativo em uma dimensão. Para o modelo de três componentes, soluções numéricas das equações do ansatz de Bethe termodinâmico confirmam que as expressões analíticas para os campos críticos e os diagramas de fases são muito precisas no regime de acoplamente forte. Para o regime de acoplamento fraco, derivamos as expressões analíticas para os campos críticos e os diagramas de fases e encontramos uma concordância muito boa entre os resultados analíticos e numéricos. Também verificamos que a fase triônica ´e suprimida para o regime de acoplamento fraco. Através de um estudo numérico obtivemos os diagramas de fase em regimes intermediários, e mostramos que a transição entre os regimes forte e fraco ocorre de forma suave ao variar o parâmetro de acoplamento. Apresentamos também um estudo detalhado para o gás de bósons com três componentes, obtendo expressões analíticas para quantidades físicas como densidade de partículas, compressibilidade e magnetização. A criticalidade quântica do modelo também foi investigada. / Exactly solvable models of ultracold Fermi and Bose gases are examined via the thermodynamic Bethe Ansatz method. Analytical and numerical results are obtained for the two-component one-dimensional attractive Fermi gas with population imbalance. For the three-component model, numerical solution of the thermodynamic Bethe ansatz equations confirm that the analytical expressions for the critical fields and the resulting phase diagrams at zero temperature are highly accurate in the strong coupling regime. For the weak coupling regime we derive the analytical expressions for the critical fields and the phase diagrams. Interestingly, in the weak regime the trionic phase is supressed. By means of a numerical study we obtain the phase diagrams at intermediate coupling regimes, showing that the crossover from strong to weak regimes occurs smoothly by varying the coupling parameter. We also present a detailed study of the three component Bose gas and obtain analytical expressions for physical quantities, such as the density of particles, compressibility and magnetisation. The quantum criticality of the model is also investigated.

Made available in DSpace on 2014-06-12T18:05:35Z (GMT). No. of bitstreams: 2 arquivo632_1.pdf: 3132391 bytes, checksum: b25862303e9c57cc119629785af995a1 (MD5) license.txt: 1748 bytes, checksum: 8a4605be74aa9ea9d79846c1fba20a33 (MD5) Previous issue date: 2010 / Faculdade de Amparo à Ciência e Tecnologia do Estado de Pernambuco / Nesta dissertação investigamos o estado fundamental e as excitações de um, dois e três mágnons do modelo de Heisenberg anisotrópico definido nas cadeias AB2 e ABC com acoplamentos ferromagnético e antiferromagnético, e na presença de campo magnético. Os resultados foram obtidos através do método analítico do ansatz de Bethe e de computação numérica: algoritmo de Lanczos para diagonalização exata e grupo de renormalização da matriz densidade (para o qual adotaremos a sigla inglesa DMRG). Em particular, medidas de correlação dos mágnons permitiram classificar a natureza das excitações de dois mágnons em estendidas ou localizadas. Realizamos também um amplo estudo do diagrama de fases (campo magnético versus anisotropia) do referido modelo. As características das fases foram evidenciadas através de medidas de magnetização em função do campo magnético, onde identificamos a existência das seguintes fases: crítica, paramagnética quântica, Lieb-ferrimagnética, Ising-antiferromagnética e -ferromagnética (com polarização total de spin). As referidas fases estão separadas por linhas de pontos críticos de condensação de mágnons, e por pontos multicríticos de Heisenberg e de Kosterlitz-Thouless

Dans cette thèse nous donnons une solution des chaînes quantiques de spin-1/2 XXZ et XYZ ouvertes avec les termes de bord intégrables les plus généraux. En utilisant la méthode de la Séparation des Variable (SoV), à la Sklyanin, on est capable, dans le cas inhomogène, de construire l’ensemble complet des états propres et des valeurs propres associés. La caractérisation de ces quantités est faite par un système maximal de N équations quadratiques, où N est la taille du système. Des méthodes différentes, comme l’ansatz de Bethe algébrique (ABA) ou autres généralisations de l’ansatz de Bethe, ont été utilisés dans le passé pour résoudre ces problèmes. Aucune méthode a pu effectivement reproduire l’ensemble complet des états propres et valeur propres dans le cas de conditions au bord les plus génériques. Une expression, sous forme d’un déterminant à la Vandermonde, pour les produits scalaires entre les états en représentation de SoV est aussi obtenue. La formule pour les produits scalaires représente la première étape pour approcher le problème relié au calcul des facteurs de forme et fonctions de corrélations. / In this thesis we give accounts on the solution of the open XXZ and XYZ quantum spin-1/2 chains with the most generic integrable boundary terms. By using the the Separation of Variables method (SoV), due to Sklyanin, we are able, in the inhomogeneous case, to build the complete set of eigenstates and the associated eigenvalues. The characterization of these quantities is made through a maximal system of N quadratic equations, where N is the size of the chain. Different methods, like the Algebraic Bethe ansatz (ABA) or other generalized Bethe ansatz techniques, have been used, in the past, in order to tackle these problems. None of them resulted effective in the reproduction of the full set of eigenstates and eigenvalues in the case of most general boundary conditions. A Vandermonde determinant formula for the scalar products of SoV states is obtained as well. The scalar product formula represents a first step towards the calculation of form factors and correlation functions.

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.:Inhaltsverzeichnis ABBILDUNGSVERZEICHNIS 5 1. EINLEITUNG 6 1.1 THEMENEINFÜHRUNG UND PROBLEMSTELLUNG 6 1.2 VORGEHENSWEISE UND GANG DER ARBEIT 9 2. DER ZUSAMMENHANG ZWISCHEN UNTERNEHMENSSTRATEGIE UND UNTERNEHMENSERFOLG - BEGRIFFLICHE GRUNDLAGEN 15 2.1 UNTERNEHMENSSTRATEGIE 15 2.2 KONTEXTSITUATION 20 2.3 UNTERNEHMENSERFOLG 22 2.4 ZUSAMMENFASSUNG 26 3. DIE UNTERNEHMENSLEITUNG ALS KOOPERATIVE ARBEITSORGANISATIONSFORM 27 3.1 KOOPERATIVE ARBEITSORGANISATIONSFORMEN 28 3.1.1 INTERNE GRUPPENSTRUKTUREN UND PROZESSE 31 3.1.2 GRUPPENLEISTUNG UND ERFOLGSDETERMINANTEN 41 3.1.3 TEAM VERSUS GRUPPE – DEFINITION UND KLASSIFIKATION 44 3.2 DAS TOPMANAGEMENT AUS DER TEAMPERSPEKTIVE 52 3.2.1 BEGRIFFLICHE ERKLÄRUNG UND EINORDNUNG 54 3.2.2 AUFGABENBEREICH UND ORGANISATION DES TOPMANAGEMENTS 57 3.2.3 KOOPERATIVE ZUSAMMENARBEIT AUF EBENE DES TOPMANAGEMENTS 64 3.3 ZUSAMMENFASSUNG 68 4. DER ZUSAMMENHANG ZWISCHEN TOPMANAGEMENTTEAM UND UNTERNEHMENSERFOLG AUS SICHT DER PRINZIPAL-AGENT-THEORIE 70 4.1 GRUNDLAGEN 72 4.1.1 RAHMENSTRUKTUR DES GRUNDMODELLS UND INTERESSENKONFLIKT 72 4.1.2 ASYMMETRISCHE INFORMATIONSVERTEILUNG UND UMWELTUNSICHERHEIT 75 4.1.3 RISIKOVERTEILUNG 78 4.1.4 ERWEITERUNGEN DES GRUNDMODELLS 80 4.2 TOPMANAGEMENT UND UNTERNEHMENSERFOLG AUS PRINZIPAL-AGENT-THEORETISCHER SICHT 93 4.2.1 DIE DELEGATIONSBEZIEHUNG ZWISCHEN TOPMANAGERN UND UNTERNEHMENSEIGENTÜMER 93 4.2.2 DER UNTERNEHMENSERFOLG AUS SICHT DER PRINZIPAL-AGENT-THEORIE 99 4.3 WÜRDIGUNG DER PRINZIPAL-AGENT-THEORIE 103 4.4 ZUSAMMENFASSUNG 106 5. TOPMANAGEMENTTEAM UND UNTERNEHMENSERFOLG AUS SICHT DER UPPER-ECHELONS PERSPEKTIVE 108 5.1 GRUNDLAGEN 108 5.2 DEMOGRAPHISCHE EIGENSCHAFTEN ALS STRATEGISCHE DETERMINANTEN 111 5.2.1 ALTER 111 5.2.2 BETRIEBSZUGEHÖRIGKEIT 113 5.2.3 BRANCHENSENIORITÄT 115 5.3 DIE GRUPPENZUSAMMENSETZUNG 117 5.4 KONTEXTSITUATION 125 5.5 DER EINFLUSS VERSCHIEDENER MODERATOREN 127 5.5.1 DAS KONZEPT „BEHAVIORAL INTEGRATION“ 127 5.5.2 DER „DISCRETION“-ANSATZ 130 5.5.3 DER „POWER DISTRIBUTION“-ANSATZ 134 5.5.4 DIE „EXECUTIVE JOB DEMAND“-ÜBERLEGUNG 137 5.6 WÜRDIGUNG DER UPPER-ECHELONS-THEORIE 139 5.7 ZUSAMMENFASSUNG 141 6. TOPMANAGEMENTTEAMS – EINE INTEGRATIVE PERSPEKTIVE 144 6.1 GRUNDLAGEN 144 6.1.1 KONTEXTSITUATION 145 6.1.2 VERHALTENSANNAHMEN 149 6.2 DER EINFLUSS DEMOGRAPHISCHER FAKTOREN – EINE FALLUNTERSCHEIDUNG 152 6.2.1 JUNGE TOPMANAGER 154 6.2.2 BERUFSERFAHRENE TOPMANAGER MIT UND OHNE BRANCHENBEZUG 159 6.2.3 BETRIEBSSPEZIFISCHE TOPMANAGER 164 6.2.4 ZUSAMMENFASSUNG 166 6.3 TEAMPERSPEKTIVE 168 6.3.1 TEAMZUSAMMENSETZUNG UND TEAMPROZESSE 170 6.3.2 MEHRPERIODISCHE TEAMINTERNE ZUSAMMENARBEIT 186 6.4 ZUSAMMENFASSUNG 191 7. DEUTSCHLAND – EIN SONDERWEG? 195 7.1 NATIONALE RAHMENFAKTOREN 195 7.1.1 RECHTLICHE UND WIRTSCHAFTLICHE RAHMENBEDINGUNGEN 196 7.1.2 GESELLSCHAFTLICHE WERTVORSTELLUNGEN 204 7.2 IMPLIKATIONEN DEUTSCHER KONTEXTFAKTOREN 206 7.3 FÜHRUNGSWECHSEL UND REKRUTIERUNGSVORGEHEN 213 7.4 ZUSAMMENFASSUNG 227 8. ZUSAMMENFASSUNG UND AUSBLICK 229 LITERATURVERZEICHNIS 238

<div>We study the Gaudin model associated to Lie algebras of classical types.</div><div><br></div><div>First, we derive explicit formulas for solutions of the Bethe ansatz equations of the Gaudin model associated to the tensor product of one arbitrary finite-dimensional irreducible module and one vector representation for all simple Lie algebras of classical type. We use this result to show that the Bethe Ansatz is complete in any tensor product where all but one factor are vector representations and the evaluation parameters are generic. We also show that except for the type D, the joint spectrum of Gaudin Hamiltonians in such tensor products is simple.</div><div><br></div><div>Second, we define a new stratification of the Grassmannian of N planes. We introduce a new subvariety of Grassmannian, called self-dual Grassmannian, using the connections between self-dual spaces and Gaudin model associated to Lie algebras of types B and C. Then we obtain a stratification of self-dual Grassmannian. </div>

Indiana University-Purdue University Indianapolis (IUPUI) / We describe a reproduction procedure which, given a solution of the gl(m|n) Gaudin Bethe ansatz equation associated to a tensor product of polynomial modules, produces a family P of other solutions called the population. To a population we associate a rational pseudodifferential operator R and a superspace W of rational functions. We show that if at least one module is typical then the population P is canonically identified with the set of minimal factorizations of R and with the space of full superflags in W. We conjecture that the singular eigenvectors (up to rescaling) of all gl(m|n) Gaudin Hamiltonians are in a bijective correspondence with certain superspaces of rational functions. We establish a duality of the non-periodic Gaudin model associated with superalgebra gl(m|n) and the non-periodic Gaudin model associated with algebra gl(k). The Hamiltonians of the Gaudin models are given by expansions of a Berezinian of an (m+n) by (m+n) matrix in the case of gl(m|n) and of a column determinant of a k by k matrix in the case of gl(k). We obtain our results by proving Capelli type identities for both cases and comparing the results. We study solutions of the Bethe ansatz equations of the non-homogeneous periodic XXX model associated to super Yangian Y(gl(m|n)). To a solution we associate a rational difference operator D and a superspace of rational functions W. We show that the set of complete factorizations of D is in canonical bijection with the variety of superflags in W and that each generic superflag defines a solution of the Bethe ansatz equation. We also give the analogous statements for the quasi-periodic supersymmetric spin chains.

<p>We derive new combinatorail formulas for vector-valued weight functions for the evolution modules over the Yangians Y (gln). We obtain them using the Nested Algebraic Bethe ansatz method.</p> <p>We also describe the asymptotic behavior of the radial solutions of the negative tt∗ equation via the Riemann-Hilbert problem and the Deift-Zhou nonlinear steepest descent method.</p>

Die Arbeit beinhalted verschiedene Studien, die die Grundwasser (GW)-Oberflächenwasser (OW)-Interaktion im Norddeutschen Tiefland untersuchen. Dabei werden zwei Ansätze verfolgt: der hydrogeologische und der limnologische Ansatz. Ersterer betrachtet die Interaktionen aus dem Blickpunkt der unterirdischen Wasserbewegung. Diese ist hauptsächlich gesteuert durch die Verteilung der hydraulische Leitfähigkeit (Sediment) und des hydraulischen Gradienten. Es ist immer noch eine Herausforderung beide Steuerungsgrößen richtig abzuschätzen. Mit neuen Ansätzen, welche auf der Wechselwirkung zwischen verschiedenen Landschafskomponenten basieren (Wasserstände, Topographie, Vegetation, Nährstoffe), wurde klein- bis mesoskalige Sedimentverteilungen in einer Aue untersucht und beschrieben. Des Weiteren konnte mit einem einfachen Grundwassermodell gezeigt werden, das verschiedene Grundwasserstonckwerke (regionale Skala) die Interaktion zwischen GW und einem See beeinflussen können. Der limnologische Ansatz basiert auf der Annahme, dass Bereiche in einem See identifiziert werden können an denen Grundwasser zutritt. In der vorliegenden Arbeit, wurden eine Methode getestet, die auf der unterschiedlichen Temperatur von beiden Wasserkörpern basiert: Im Frühjahr ist das GW wärmer als das Seewasser und sollte sich an der Seeoberfläche einschichten. Mittels thermalen Luftbildaufnahmen sollten somit Grundwasserzutritte identifizierbar sein. Die Studien aber zeigten, dass dies nur unter bestimmten Voraussetzungen möglich ist und seeinterne Prozesse bei der Interpretation der Temperaturverteilung an der Seeoberfläche berücksichtigt werden müssen. Somit besteht noch ein erhöhter Forschungsbedarf bezüglich des limnologischen Ansatzes. Dennoch birgt dieser ein großes Potential, denn er eröffnet die Möglichkeit kurzfristig auf grundwasserbürtige Einträge in OW direkt an der Sediment-Wasser-Grenze zu reagieren und verschafft somit Zeit für aufwändigere hydrogeologische Untersuchungen. / The thesis constists of different studies, which are investigating groundwater-surface water interaction in North-German-Lowlands. Therefore, two different approaches were used: the hydrogeological and the limnological one. The former is based on the classical hydrogeological point of view: the subsurface water movement is mainly driven by hydraulic conductivity (sediment) and the hydraulic gradient. However, the characterisation of both is still a challange. Different methods were used to characterize small- and meso-scale sediment distributions within a lowland floodplain. These are based on the interactions of different landscape components (water level fluctuations, topography, vegetation, nutrient distributions). Furthermore, a simple groundwater model was set up to illustrate how regional groundwater flow impacts local groundwater-lake interactions. The limnological approach is based on the assumption that areas of groundwater exfiltration into a lake are detectable directly at the sediment-water interface. For this purpuse, it was assuemed that temperature differences between both water bodies could be used as follows: in spring the groundwater temperature is higher than that of lakes. Hence, the warmer groundwater float on the lake surface. That should be detectable by thermal infrared imaging. However, the studies could illustrate, that this is only true for specific conditions. Furthermore, lake internal processes need to be considered for interpreting temperature distributions at the lake surface. As a consequence, the limnological approach requires more research activities, since it gives the opportunity to initate short-term measures on groundwater inputs in surface waters. This would also guarantee larger time spans for time-consuming hydrogeological studies.

[pt] A primeira parte da dissertação é dedicada ao estudo do modelo em meios porosos em contato com reservatórios e à obtenção, heurística, da equação hidrodinâmica para esse modelo, com o intuito de iniciar o estudo do limite hidrodinâmico que garante que a evolução da densidade de partículas desse modelo é descrita pela solução fraca da equação hidrodinâmica, nomeadamente, a equação em meios porosos com condições de Dirichlet. A segunda parte da dissertação é dedicada ao estudo do método da representação matricial, a chamada matriz ansatz, que será utilizado para caracterizar as medidas estacionárias de sistemas de partículas fora do equilíbrio. Usaremos o processo de exclusão simples simétrico como motivação para apresentar as técnicas utilizadas nesse método. Munido dessas técnicas conseguimos obter pela primeira vez a função de correlação de segunda ordem para o processo de exclusão simples simétrico em contato com reservatórios lentos, e além disso, conseguimos obter informação do estado estacionário do modelo em meios porosos em contato com reservatórios. / [en] The first part of the dissertation is dedicated to the study of the porous medium model in contact with reservoirs and to, heuristically, obtain the hydrodynamic equation for this model, with the pursuit of starting the study of the hydrodynamic limit which guarantees that the evolution of the density of particles of this model is described by the weak solution of the hydrodynamic equation, namely, the porous medium equation with Dirichlet boundary conditions. The second part of the dissertation is dedicated to the study of the matrix representation method, the so-called matrix ansatz, which will be used to characterize the stationary measures of particle systems out of equilibrium. For warming up, we will use the symmetric simple exclusion process as a toy model to present the techniques used in this method. With those techniques, for the first time we obtained the second order correlation function for the symmetric simple exclusion process in contact with slow reservoirs, and in addition, we were able to obtain information about the steady state of the porous medium model in contact with reservoirs.