Den här uppsatsen fokuserar på kompositören Alexandre Desplats verk i regissören Wes Andersons filmer. Uppsatsen grundar sig i filmmusikens narrativa funktioner och hur dessa står i relation till det visuella. Syftet med uppsatsen har varit att belysa filmmusikens relation till det som syns i bild, resonera kring musikaliska emotioner, semiotik och semantik. Studien har utförts genom att tolka och förstå Desplats kompositioner genom relevanta teoretiska redskap. Det visade sig till slut att Desplats verk har en vägledande och aktiv närvaro i relation till det visuella, musiken kommenterar och för berättelsen framåt. Resultaten av analyserna har varit lyckade i förhållande till syftet, att Desplat och Anderson har ett välfunnet samarbete är en självklarhet i sig men i den här nedbrytande formen framhävs just de detaljer som utgör ett gott samarbete mellan en kompositör och regissör.

Disordered photonics is the study of light in random media. In a disordered photonic medium, multiple scattering of light and coherence, together with the fundamental principle of reciprocity, produce a wide range of interesting phenomena, such as enhanced backscattering and Anderson localization of light. They are also responsible for the existence of modes in these random systems. It is known that analogous processes to Bose-Einstein condensation can occur in classical wave systems, too. Classical condensation has been studied in several contexts in photonics: pulse formation in lasers, mode-locking theory and coherent emission of disordered lasers. All these systems have the common theme of possessing a large ensemble of waves or modes, together with nonlinearity, dispersion or gain. In this work, we study light condensation and its connection with light localization in a disordered, passive dielectric medium. We develop a theory for the modes inside the disordered resonator, which combines the Feshbach projection technique with spin-glass theory and statistical physics. In particular, starting from the Maxwell’s equations, we map the system to a spherical p-spin model with p = 2. The spins are replaced by modes and the temperature is related to the fluctuations in the environment. We study the equilibrium thermodynamics of the system in a general framework and show that two distinct phases exist: a paramagnetic phase, where all the modes are randomly oscillating and a condensed phase, where the energy condensates on a single mode. The thermodynamic quantities can be explicitly interpreted and can also be computed from the disorder-averaged time domain correlation function. We launch an ab initio simulation campaign using our own code and the Shaheen supercomputer to test the theoretical predictions. We construct photonic samples of varying disorder and find computationally relevant ways to obtain the thermodynamic quantities. We observe the phase transition and also link the condensation process to the localization. Our research could be a step towards the ultimate goal: to build a ”photonic mode condenser”, which transforms a broadband spectrum to a narrow one - ideally, to a single mode - with minimal energy loss, aided solely by disorder.

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Phase transitions are critical in understanding the properties of different phases of matter, and their identification is an essential research focus in condensed matter physics. However, defining phase transitions for topological systems is more complex than for common mesoscale materials. This complexity is further compounded when disorders are present in the system. In this thesis work, we provide a comprehensive review of machine learning, topological insulators, and the conventional approach to classifying different topological phases. We focus on the Benalcazar, Bernevig, and Hughes (BBH) model, a higher-order topological insulator model, and investigate the challenges of identifying phase transitions in topological systems, particularly in the presence of disorders. To overcome these challenges, we implement the diffusion maps method, which accurately predicts the same transition points as traditional numerical calculations for both clean and disordered systems. Moreover, we demonstrate the efficacy of the diffusion maps method in predicting the transition point for the topological Anderson insulator. Our findings suggest that this approach has the potential to be generalized and applied to a broader range of disordered systems. Overall, this thesis work provides a novel method for identifying phase transition points in topological systems, which could have significant implications for the design and development of future topological materials.

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Ultrasonic wave propagation through a two-dimensional nonreciprocal phononic crystal with asymmetric aluminum rods in viscous water is studied for its application in Anderson localization and trapping of acoustic energy. A one-dimensional disorder in the otherwise 2D periodic crystal is introduced by disorienting the asymmetric rods along the rows and by keeping them equally oriented along the columns. An exponential decay of sound waves travelling along the direction of disorder is observed demonstrating Anderson localization whereas sound propagates as extended wave along the ordered direction. Localization length for the case of strong disorder with high randomness in the orientation of rods and weak disorder with weak fluctuations in the orientation of rods is evaluated. The degree of randomness in the orientation of the rods controls the localization length of the wave. Thouless's theoretical prediction for the scaling of Lyapunov exponent with disorder is experimentally observed for weak disorder at frequency in the transmission band and anomalous scaling is observed for band edge frequency. Transmission spectra of acoustic waves is also measured for opposite direction of propagation and nonreciprocity is observed for the exponentially weak transmission in the disordered direction as well as for extended states in the ordered direction. Breaking of reciprocity in the current structure is due to the broken PT symmetry. The T symmetry or the time reversal symmetry is broken by the viscous dissipation at the boundaries of scatterers and the water, and the P symmetry is broken by the asymmetric shape of the rods. Acoustic energy trapping inside a nonreciprocal phononic crystal cavity is studied by creating three configurations of cavities. These configurations are based on the orientation of the asymmetric scatterers on each side of the cavity. Only one of these configuration utilizes the nonreciprocal property of the structure. Enhancement of energy trapping in the cavity is observed for the cavity orientation utilizing nonreciprocity. The proposed enhancement of energy trapping occurs at the transmission band frequency unlike the extensively used mechanism of energy trapping at the defect modes of the band gap of the phononic crystal. All the experimental results are verified numerically using finite element based modelling in COMSOL Multiphysics. The proposed devices can be utilized for applications in one way sound transmission, noise control, isolators, circulators and energy harvesting.

Ce travail de thèse présente une étude numérique et théorique de l’influence des effets coopératifs sur la localisation de la lumière dans des vapeurs atomiques, suivie d’une étude expérimentale de ces effets coopératifs dans le régime de diffusion multiple dans des nuages d’atomes froids dilués. Le premier chapitre décrit le modèle que nous utilisons, basé sur l’Hamiltonien effectif d’interaction matière rayonnement, afin d’étudier numériquement la localisation de la lumière et les effets coopératifs. Nous discutons également des différences fondamentales existant entre la situation réelle où la lumière est assimilée à une onde vectorielle et l’approximation scalaire plus facile à traiter analytiquement. Le deuxième chapitre se concentre sur la présentation des résultats numériques complétée d’une comparaison systématique entre les cas scalaire et vectoriel. Nous remarquons dans cette partie que l’approximation scalaire, valable dans la limite des milieux spatialement dilués, présente des différences drastiques avec le cas vectoriel lorsque nous considérons des milieux spatialement denses. Nous n’observons pas également d’indications suffisantes nous permettant de discriminer le fait que les effets coopératifs ne soient pas à la base des mécanismes de localisation de la lumière. Dans la dernière partie nous nous intéressons expérimentalement aux signatures des effets coopératifs dans le régime de diffusion multiple en confrontant à nos résultats expérimentaux plusieurs approches théoriques tenant compte ou pas des effets d’interférences. / In this thesis we present a numerical and theoretical study of the interplay between cooperative effects and light localization in atomic vapour, completed by an experimental study of these cooperative effects for dilute cold atom clouds in the multiple scattering regime. The first chapter describes the model we use, based on the light matter effective Hamiltonian, in order to investigate numerically light localization and cooperative effects. We also discuss the fundamental differences existing between the real situation where light is considered as a vector wave and its scalar approximation easier to treat analytically. The second chapter focuses on the numerical results where we compare systematically the scalar and the vector cases. We show that the scalar approximation, valid for spatially dilute systems, leads to drastic differences compared to the vector case when we consider spatially dense clouds. We also do not observe sufficient proofs to establish that cooperative effects are not at the origin of light localization mechanisms. In the last chapter we investigate experimentally the signatures of cooperative effects in the multiple scattering regime, comparing our results to several theoretical approaches taking or not into account interference effects related to the wave nature of light.

[pt] Nesta dissertação propomos um formalismo de operadores de projeção para obter a energia do estado fundamental do Hamiltoniano da Impureza de Anderson com repulsão Coulombiana U infinita. Este formalismo consiste em projetar o espaço de Hilbert em um subespaço de uma unica função correspondente ao estado fundamental do mar de Fermi, onde uma versão renormalizada do Hamiltoniano opera. A energia do estado fundamental pode ser obtida através de um processo autoconsistente. conhecendo a energia e possível calcular as propriedades fundamentais do sistema como a magnetização em função do campo magnético externo, a susceptibilidade magnética, a dependência da ocupação eletrônica como função da energia local da impureza e a temperatura Kondo, a qual caracteriza o comportamento universal do problema Kondo. / [en] In this dissertation we propose a projector operator formalism to obtain the ground state energy of the Impurity Anderson Hamiltonian with innite Coulomb repulsion U. This formalism consists in projecting the Hilbert space into a sub-space of one function corresponding to the ground state of the free Fermi sea where a renormalized version of the Hamiltonian operates. The ground state energy can be obtained through a self-consistent process. From the knowledge of the energy, it is possible to calculate the fundamental properties of the system as it is the magnetization as a function of an external magnetic field, the magnetic susceptibility, the dependence of the electronic occupation as a function of the local energy of the impurity and the Kondo temperature, which characterizes the universal behavior of a Kondo problem.