京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第21562号 / 理博第4469号 / 新制||理||1641(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)准教授 國友 浩, 教授 杉本 茂樹, 教授 田中 貴浩 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第19496号 / 理博第4156号 / 新制||理||1597(附属図書館) / 32532 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)准教授 笹倉 直樹, 教授 田中 貴浩, 教授 杉本 茂樹 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

In this thesis I investigate several aspects of local quantum criticality, a concept of key importance in a number of physical contexts ranging from critical heavy fermion compounds to quantum dot systems. Quantum critical points are associated with second order phase transitions at zero temperature. In contrast to their finite-temperature counterparts, the zero-point motion cannot be neglected near a quantum critical point. As a result, the incorporation of quantum dynamics leads to an effective dimension larger than the spatial dimension of the system for the order parameter fluctuations within the Ginzburg-Landau-Wilson treatment of criticality. This so-called quantum-to-classical mapping works well for the critical properties in insulating systems but apparently fails in systems containing gapless fermions. This has been experimentally most clearly been demonstrated within a particular class of intermetallic compounds called heavy fermions. A particular way in which the Ginzburg-Landau-Wilson paradigm fails is for critical Kondo destruction that seems to underlie the unconventional quantum criticality seen in the heavy fermions. I focus on studying the properties of critical Kondo destruction and the emergence of energy-over-temperature-scaling in systems without spatial degrees of freedom, i.e., so-called quantum impurity systems. In particular, I employ large-N techniques to address critical properties of this class of quantum phase transitions in and out of equilibrium. As quantum critical systems are characterized by a scale-invariant spectrum with many low-lying excitations, it may appear that any perturbation can lead to a response beyond the linear response regime. Understanding what governs the non-linear response regime near quantum criticality is an interesting area. Here, I first present a path integral version of the Schrieffer-Wolff transformation which relates the functional integral form of the partition function of the Anderson model to that of its effective low-energy model. The equivalence between the low-energy sector of the Anderson model in the Kondo regime and the spin-isotropic Kondo model is usually established via a canonical transformation performed on the Hamiltonian, followed by a projection. The resulting functional integral assumes the form of a spin path integral and includes a geometric phase factor, i.e. a Berry phase. The approach stresses the underlying symmetries of the model and allows for a straightforward generalization of the transformation to more involved models. As an example of the efficiency of the approach I apply it to a single electron transistor attached to ferromagnetic leads and derive the effective low-energy model of such a magnetic transistor. As Kondo screening is a local phenomenon, it and its criticality can be studied using the appropriate impurity model. A general impurity model to study critical Kondo destruction is the pseudogap Bose-Fermi Kondo model. Here, I concentrate on the multi-channel version of the model using the dynamical large-N study. This model allows to study the non-trivial interplay between two different mechanisms of critical Kondo destruction. The interplay of two processes that can each by itself lead to critical Kondo destruction. The zero-temperature residual entropy at various fixed points for the model is also discussed. The two channel Anderson model exhibits several continuous quantum phase transitions between weak- and strong-coupling phases. The non-crossing approximation (NCA) is believed to give reliable results for the standard two-channel Anderson model of a magnetic impurity in a metal. I revisit the reliability of the NCA for the standard two channel Anderson model (constant conduction electron density of states) and investigate its reliability for the two-channel pseudogap Anderson model. This is done by comparing finite-temperature, finite-frequency solutions of the NCA equations and asymptotically exact zero-temperature NCA solutions with numerical renormalization-group calculations. The phase diagram of this model is well established. The focus here will be on the dynamical scaling properties obtained within the NCA. Finally, I study the thermal and non-thermal steady state scaling functions and the steady-state dynamics of the pseudogap Kondo model. This model allows us to study the concept of effective temperatures near fully interacting as well as weak-coupling fixed points and compare the out-of-equilibrium scaling properties of critical Kondo destruction to those of the traditional spin-density wave (SDW) scenario. The differences I identify can be experimentally probed. This may be helpful in identifying the nature of the quantum critical points observed in certain heavy fermion compounds.

In this thesis I investigate several aspects of local quantum criticality, a concept of key importance in a number of physical contexts ranging from critical heavy fermion compounds to quantum dot systems. Quantum critical points are associated with second order phase transitions at zero temperature. In contrast to their finite-temperature counterparts, the zero-point motion cannot be neglected near a quantum critical point. As a result, the incorporation of quantum dynamics leads to an effective dimension larger than the spatial dimension of the system for the order parameter fluctuations within the Ginzburg-Landau-Wilson treatment of criticality. This so-called quantum-to-classical mapping works well for the critical properties in insulating systems but apparently fails in systems containing gapless fermions. This has been experimentally most clearly been demonstrated within a particular class of intermetallic compounds called heavy fermions. A particular way in which the Ginzburg-Landau-Wilson paradigm fails is for critical Kondo destruction that seems to underlie the unconventional quantum criticality seen in the heavy fermions. I focus on studying the properties of critical Kondo destruction and the emergence of energy-over-temperature-scaling in systems without spatial degrees of freedom, i.e., so-called quantum impurity systems. In particular, I employ large-N techniques to address critical properties of this class of quantum phase transitions in and out of equilibrium. As quantum critical systems are characterized by a scale-invariant spectrum with many low-lying excitations, it may appear that any perturbation can lead to a response beyond the linear response regime. Understanding what governs the non-linear response regime near quantum criticality is an interesting area. Here, I first present a path integral version of the Schrieffer-Wolff transformation which relates the functional integral form of the partition function of the Anderson model to that of its effective low-energy model. The equivalence between the low-energy sector of the Anderson model in the Kondo regime and the spin-isotropic Kondo model is usually established via a canonical transformation performed on the Hamiltonian, followed by a projection. The resulting functional integral assumes the form of a spin path integral and includes a geometric phase factor, i.e. a Berry phase. The approach stresses the underlying symmetries of the model and allows for a straightforward generalization of the transformation to more involved models. As an example of the efficiency of the approach I apply it to a single electron transistor attached to ferromagnetic leads and derive the effective low-energy model of such a magnetic transistor. As Kondo screening is a local phenomenon, it and its criticality can be studied using the appropriate impurity model. A general impurity model to study critical Kondo destruction is the pseudogap Bose-Fermi Kondo model. Here, I concentrate on the multi-channel version of the model using the dynamical large-N study. This model allows to study the non-trivial interplay between two different mechanisms of critical Kondo destruction. The interplay of two processes that can each by itself lead to critical Kondo destruction. The zero-temperature residual entropy at various fixed points for the model is also discussed. The two channel Anderson model exhibits several continuous quantum phase transitions between weak- and strong-coupling phases. The non-crossing approximation (NCA) is believed to give reliable results for the standard two-channel Anderson model of a magnetic impurity in a metal. I revisit the reliability of the NCA for the standard two channel Anderson model (constant conduction electron density of states) and investigate its reliability for the two-channel pseudogap Anderson model. This is done by comparing finite-temperature, finite-frequency solutions of the NCA equations and asymptotically exact zero-temperature NCA solutions with numerical renormalization-group calculations. The phase diagram of this model is well established. The focus here will be on the dynamical scaling properties obtained within the NCA. Finally, I study the thermal and non-thermal steady state scaling functions and the steady-state dynamics of the pseudogap Kondo model. This model allows us to study the concept of effective temperatures near fully interacting as well as weak-coupling fixed points and compare the out-of-equilibrium scaling properties of critical Kondo destruction to those of the traditional spin-density wave (SDW) scenario. The differences I identify can be experimentally probed. This may be helpful in identifying the nature of the quantum critical points observed in certain heavy fermion compounds.

The conformal bootstrap method is a non-perturbative method that uses the symmetry in a conformal field theory to constrain and solve for the observables in the theory. We consider a conformal field theory with the symmetry group SU(N) and four general scalar fields as the only low dimensional operators. The four-point correlation function of a quartic interaction of four general scalar fields in a conformal field theory can be written as a sum over primary operators. In order to study the four-point correlator a large-N expansion is made, where N comes from the symmetry group SU(N). Using the conformal bootstrap method the anomalous dimension of the primary operators in the four-point correlator is calculated. Using the AdS/CFT correspondence the anomalous dimension of the primary operators is also calculated using Witten diagrams. / Konform fältteori är en kvantfältteori med konform symmetri. Konform symmetri är en symmetri som bevarar vinklar och lokalt ser ut som en kombination av en rotation och en förändring i skala. En metod för att beräkna de observerbara kvantiteterna i en konform fältteori är metoden "conformal boostrap". Denna metod går ut på att använda symmetrin i en konform fältteori för att begränsa och beräkna värdet på de observerbara kvantiteterna i teorin.En av de observerbar kvantiteterna i en fältteori är en korrelationsfunktion. Korrelationsfunktioner beskriver interaktionerna mellan partiklarna i en fältteori.  I detta arbete studerar vi en interaktion mellan fyra skalärfält genom att studera fyra-punkts korrelationsfunktionen för denna interaktion. Metoden vi använder är "conformal bootstrap" men vi testar också om AdS/CFT dualiteten håller för våra beräkningar. AdS/CFT dualiteten är en ekvivalens av två olika teorier, en strängteori i ett (d+1)-dimensionellt anti-de Sitter (AdS) rum och en konform fältteori (CFT) i den d-dimensionella gränsen av anti-de Sitter rummet. Enligt denna dualitet kan en observerbar kvantitet beräknas från båda dessa två teorier och ge samma resultat. Teorin vi studerar har symmetrigrupp SU(N) och vi arbetar i dimension två. Vi arbetar också med att N, matrisrangen i teorin, är stort då detta är den gräns där AdS/CFT dualiteten gäller. Enligt konform fältteori så kan en fyra-punkts korrelationsfunktion av fyra skalärer beskrivas som en summa över vad som kallas primära fält. Genom att använda "conformal bootstrap" metoden beräknas den anormala dimensionen, vilket är en korrektion av första icke-triviala ordning till dimensionen, av dessa primära fält. Samma kvantitet beräknas också från strängteorisidan av AdS/CFT dualiteten genom användandet av så kallade Witten diagram. Resultatet från båda sidor av dualiteten visas stämma överens.

In dieser Arbeit praesentieren wir Resultate der topologischen Suszeptibilitaet “chi” und untersuchen die Faktorisierung der reinen SU(N) Yang-Mills Eichtheorie im 't Hooft'schen Grenzwert grosser N. Ein entscheidender Teil der Berechnung von chi in der Gittereichtheorie ist die Abschaetzung des topologischen Ladungsdichtekorrelators, die durch ein schlechtes Signal-Rausch- Verhaeltnis beeintraechtigt ist. Um dieses Problem abzuschwaechen, fuehren wir einen neuen, auf einem mehrstufigen Vorgehen beruhenden Algorithmus ein, um die Korrelationsfunktion von Observablen zu berechnen, die mit dem Yang-Mills Gradientenfluss geglaettet wurden. Angewandt auf unsere Observablen, erhalten wir Ergebnisse, deren Fehlerskalierung besser ist, als die von herkoemmlichen Monte-Carlo Simulationen. Wir bestimmen die topologische Suszeptibilitaet in der reinen Yang-Mills Eichtheorie fuer Eichgruppen mit N = 4,5,6 und drei verschiedenen Gitterabstaenden. Um das Einfrieren der Topologie zu umgehen, wenden wir offene Randbedingungen an. Zusaetzlich wenden wir die korrekte Definition der topologischen Ladungsdichte durch den Gradientenfluss an. Unser Endresultat im des Grenzfalls von grossen N repraesentiert eine neue Qualitaet in der Verifikation der Witten-Veneziano Formel. Schliesslich benutzen wir die Gitterformulierung, um die Erwartungswertfaktorisierung des Produkts eichinvarianter Operatoren im Grenzwert grosser N zu verifizieren. Wir arbeiten mit durch den Yang-Mills Grandientenfluss geglaetteten Wilsonschleifen und Simulationen bis zur Eichgruppe SU(8). Die Extrapolationen zu grossen N sind in Ueberstimmung mit der Faktorisierung sowohl fuer endlichen Gitterabstand als auch in Kontinnumslimes. Unsere Daten erlauben uns nicht nur die Verifizierung der Faktorisierung, sondern auch einen hochpraezisen Test des 1/N Skalierungsverhaltens. Hier konnten wir das quadratische Skalierungsverhalten in 1/N finden, welches von 't Hooft vorhergesagt wurde. / In this thesis we present results for the topological susceptibility “chi”, and investigate the property of factorization in the 't Hooft large N limit of SU(N) pure Yang-Mills gauge theory. A key component in the lattice gauge theory computation of chi is the estimation of the topological charge density correlator, which is affected by a severe signal to noise problem. To alleviate this problem, we introduce a novel algorithm that uses a multilevel type approach to compute the correlation function of observables smoothed with the Yang-Mills gradient flow. When applied to our observables, the results show an scaling of the error which is better than the one of standard Monte-Carlo simulations. We compute the topological susceptibility in the pure Yang-Mills gauge theory for the gauge groups with N = 4, 5, 6 and three different lattice spacings. In order to deal with the freezing of topology, we use open boundary conditions. In addition, we employ the theoretically sound definition of the topological charge density through the gradient flow. Our final result in the limit N to infinity, represents a new quality in the verification of the Witten-Veneziano formula. Lastly, we use the lattice formulation to verify the factorization of the expectation value of the product of gauge invariant operators in the large N limit. We work with Wilson loops smoothed with the Yang-Mills gradient flow and simulations up to the gauge group SU(8). The large N extrapolations at finite lattice spacing and in the continuum are compatible with factorization. Our data allow us not only to verify factorization, but also to test the 1/N scaling up to very high precision, where we find it to agree very well with a quadratic series in 1/N as predicted originally by 't Hooft for the case of the pure Yang-Mills gauge theory.

The goal of the original research presented in this thesis is to study the strong coupling regime of Quantum Field Theories (QFTs) with different methods, making concrete predictions about the phase structure and the dynamics of these theories, and on their observables. The focus is on (gauge) field theories in three spacetime dimensions, which are an interesting laboratory to understand the properties of strong coupling in setups that are usually simpler than in the more familiar case of gauge theories in four dimensions. Importantly, topological effects play a relevant role in three dimensions, thanks to the presence of the so-called Chern-Simons term.The thesis contains a short introduction to QFTs in 3d, principles and applications of infrared dualities, large N techniques, and holography. Indeed, the web of infrared dualities, the large N expansion, and the holographic correspondence between QFT and gravity are the main tools which we use to investigate the strongly coupled regimes of 3d QFTs.Then, the original material is presented. In a first line of research, we focus on the study of the phase diagram of a 3d gauge theory making use of conjectured infrared dualities, extending such dualities to the case where more than one mass parameter can be dialed. In a second line of research, we study a class of 3d gauge theories by engineering their gravity dual in a string theory setup. We prove the existence of multiple phase transitions between phases characterized by both massless particles and topological sectors. In a third line of research, we use holography as a tool to explore the interplay between the physics of 4d QCD and 3d gauge theories. In particular, we analyze the properties of 3d domain walls, which appear as soliton-like solutions of 4d QCD in specific parametric regimes. Finally, we propose a boundary construction of 3d large N vector models, which appear as critical points of theories obtained by coupling degrees of freedom localized on a 3d boundary to a 4d bulk theory. This construction allows to prove new dualities and uncovers a new computational tool for 3d vector models. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

This dissertation aims to apply the configurational perspective to organizational surveys. The studies included in this dissertation demonstrate that an increasingly popular configurational method can be applied to large dataset sizes similar to organizational surveys. This method is called fuzzy set qualitative comparative analysis (fsQCA). Additionally, the incremental insights of fsQCA are illustrated by taking traditional methods into comparison. At the same time, the presented research addresses current methodological challenges to fsQCA in order to shed light on its application in the context of organizational surveys and to reduce reasons inhibiting researchers to use this method. The first study conceptualized and empirically investigated differently complex interplays of core manageable factors predicting and influencing high levels of affective commitment. Specifically, the results indicate that job design, organizational treatment, leadership, and recognition were consistently found to be essential in terms of incremental, relative, and configurational importance for the management of affective commitment. The second study aims to deepen the understanding of the formation of change-supportive intentions by adopting a configurational perspective. Investigating the theory of planned behavior in a longitudinal setting, the results suggest the combination of high change-related attitude and high change-related perceived behavioral control as the most consistent and reliable solution for fostering high change-supportive intentions. Both the first and second study addressed methodological challenges by adopting robustness tests for large-N fsQCA to increase trustworthiness and reduce sensitivity of the results. Additionally, as required for fsQCA data preparation, recommendations for thresholds were made and different calibration techniques investigated. The third study connects these two studies by performing a simulation on artificial small-N and large-N datasets comparing regression analysis, fsQCA, and its different calibration techniques. In particular, new insights on the joint use of both methods and methodological recommendations on the calibration of fsQCA could be given. In sum, the presented research highlights the applicability of fsQCA to organizational surveys and that a configurational approach can further enrich the understanding of organizations and organizational life.

Submitted by Vasti Diniz (vastijpa@hotmail.com) on 2017-09-12T12:27:38Z No. of bitstreams: 1 arquivototal.pdf: 987629 bytes, checksum: 073f4a58e014f0b46588edf144d4a42b (MD5) / Made available in DSpace on 2017-09-12T12:27:38Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 987629 bytes, checksum: 073f4a58e014f0b46588edf144d4a42b (MD5) Previous issue date: 2016-02-19 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this dissertation we work with the Horava-Lifshitz-like Gross-Neveu model in (2+1) dimensions in the Large N expansion. Firstly we make an article revision [6] where it is shown that the Gross-Neveu Model in the 1/N expansion presents a dynamic mass generation by means of the introduction of an auxiliary field, which results in the dynamical parity broken. We calculate the gap equation where we will see the generated mass dependence with the coupling constant. After that, we will put a gauge field to the model and study the polarization tensor which will generate an induced Chern-Simons term in the Effective Lagrangian. As a novelty, we work with the Gross-Neveu Model in the context of Horava-Lifshitz, where anisotropic scaling is done, thus breaking the Lorentz invariance. We introduce an auxiliary field and we study the cases which the value of the critical dynamic exponent Z is even and when it is odd. In the case where z is even, there is no dynamic mass generation so the parity symmetry is conserved and we will not have the term induced of Chern-Simons either. In the case where z is odd, we will have the dynamic mass generation and the dynamic parity symmetry will occur. Finally we couple a gauge field in the model and find the Chern-Simons term, which clearly shows the anisotropy of space and time for values of z> 1 / Nesta dissertacao trabalhamos corn o modelo de Gross-Neveu ern (2+1) dimensoes na expansao 1/N no contexto de Horava-Lifshitz. Primeiro, faremos uma revisao do artigo [6], onde se mostra que o Modelo de Gross-Neveu na expansao 1/N apresenta uma geracao dinamica de massa mediante a introducao de urn campo auxiliar, o que traz como consequencia a quebra dinamica da simetria de paridade. Calculamos a equacao de gap, onde veremos a dependencia da massa gerada corn a constante de acoplamento. ApOs isso, acoplaremos urn campo de gauge ao modelo, estudamos o tensor de polarizacao, o qual vai gerar urn termo induzido de tipo Chern-Simons na lagrangiana efetiva. Como novidade, trabalhamos corn o Modelo de Gross-Neveu no contexto de Horava-Lifshitz, onde se faz urn escalonamento anisotrOpico, quebrando, assim, a invariancia de Lorentz. Introduzimos urn campo auxiliar e estudamos os casos ern que o valor do exponente dinamico critico z é par quando é Impar. No caso ern que z é par, nao ha geracao dinamica de massa pelo que a simetria de paridade é conservada e tambern nao teremos o termo induzido de Chern-Simons. No caso ern que z é impar, vamos ter a geracao dinamica de massa vai ocorrer a quebra dinamica de simetria de paridade. Finalmente, acoplamos urn campo de gauge no modelo e encontramos o termo tipo Chern-Simons, o qual mostra claramente a anisotropia do espaco tempo para valores de z > 1.

There is an ample body of literature which seek to investigate the role of religion in armed conflict. Yet, the role of religion in unarmed civil resistance has not received an equal amount of scholarly attention. Apart from some single and comparative case studies showcasing the pertinent role of religion on nonviolent campaign success, little has been done to investigate its effect across broader cases. By conducting a large-N analysis of 143 nonviolent campaigns from 1975 to 2013 globally, this study aims to fill in the research gap and answer the following question: How does religious support affect the success of nonviolent campaigns? Furthermore, this study seeks to investigate whether unique forms of religious support, i.e. traditional support and religiopolitical support, have a different effect on nonviolent campaign success. The results indicate that religious support does not have a statistically significant effect on the success of nonviolent campaigns. The study also reveals that religious support type does not have a statistically different effect on the chance of nonviolent campaign success. Thus, this study challenges the generalizability of case studies demonstrating the effectiveness of religiously-supported nonviolent campaigns. Avenues for future research include conducting a large-N study on the effect of religious support on the level of mass mobilisation and the resilience capacity of nonviolent campaigns.