<p dir="ltr">Long-range exciton transport, when coupled with reduced exciton-exciton annihilation (EEA), is pivotal for the enhanced performance of organic photovoltaics and the efficiency of natural light-harvesting systems. This thesis explores strategies to optimize exciton transport and EEA rates in molecular materials by manipulating the quantum nature of excitons, particularly exciton delocalization. In addition, we also aim to understand factors limiting the transport of delocalized excitons within molecular materials. To this end, self-assembled perylene diimide (PDI) molecular aggregates are ideal candidates for this study due to their conducive properties for engineering exciton delocalization. <b>Chapter 1 </b>establishes a fundamental understanding of exciton delocalization, outlining strategies to tune this phenomenon within PDI aggregates and presenting the open questions this thesis addresses. <b>Chapter 2 </b>details the synthesis of PDI aggregates and delineates the spectroscopic techniques used for characterization, including steady-state absorption and emission, transient photoluminescence (PL), and transient absorption spectroscopy. It also describes the microscopy methods implemented to visualize exciton transport, such as transient PL microscopy and transient absorption microscopy (TAM). <b>Chapter 3 </b>introduces the thesis's primary theme: the suppression of exciton-exciton annihilation (EEA) in molecular aggregates through quantum interference. This chapter demonstrates that the spatial phase relationship of delocalized excitons is crucial in EEA, with band bottom excitons in H aggregates exhibiting an oscillating spatial phase relationship displaying a coherent suppression of EEA. <b>Chapter 4 </b>discusses how coupling to static and dynamic disorder affects coherent exciton propagation. High spatial and temporal resolution TAM experiments, along with temperature-dependent studies, help disentangle the contributions of static and dynamic disorder to exciton transport. <b>Chapter 5 </b>delves into the concept of band shape engineering, whereby the microscopic electronic couplings within PDI aggregates are fine-tuned by altering the packing motifs to regulate exciton transport. Through low-temperature TAM experiments, this chapter illustrates how the interplay between long-range Coulombic and short-range charge transfer electronic couplings can determine exciton bandwidth and influence the coherent propagation of excitons. <b>Chapter 6 </b>provides a summary of the work and discusses future directions, paving the way for continued exploration in the field of exciton transport and interaction in molecular aggregates.</p>

La théorie des matrices aléatoires a des applications dans des domaines variés : mathématiques, physique, finance, ... En physique, le concept de matrices aléatoires a été utilisé pour l'étude du transport électronique dans des structures mésoscopiques, de systèmes désordonnés, de l'intrication quantique, de modèles d'interfaces 1D fluctuantes en physique statistique, des atomes froids, ... Dans cette thèse, on s'intéresse au transport AC cohérent dans un point quantique, à des propriétés d'interfaces fluctuantes 1D sur un substrat et aux propriétés topologiques de fils quantiques multicanaux. La première partie commence par une introduction générale a la théorie des matrices aléatoires ainsi qu'a la principale méthode utilisée dans cette thèse : le gaz de Coulomb. Cette technique permet entre autres d'étudier la distribution d'observables qui prennent la forme de statistiques linéaires des valeurs propres, qui représentent beaucoup de quantités physiques pertinentes. Cette méthode est ensuite appliquée à des exemples concrets pour étudier le transport cohérent et les problèmes d'interfaces fluctuantes en physique statistique. La seconde partie se concentre sur un modèle de fil désordonné : l'équation de Dirac multicanale avec masse aléatoire. Nous étendons le puissant formalisme utilisé pour l'étude de systèmes unidimensionnels au cas quasi-1D, et établissons une connexion avec un modèle de matrices aléatoires. Nous utilisons ce résultat pour obtenir la densité d'états et les propriétés de localisation. Nous montrons également que ce système présente une série de transitions de phases topologiques (changement d'un nombre quantique de nature topologique, sans changement de symétrie), contrôlées par le désordre. / Random matrix theory has applications in various fields: mathematics, physics, finance, ... In physics, the concept of random matrices has been used to study the electronic transport in mesoscopic structures, disordered systems, quantum entanglement, interface models in statistical physics, cold atoms, ... In this thesis, we study coherent AC transport in a quantum dot, properties of fluctuating 1D interfaces on a substrate and topological properties of multichannel quantum wires. The first part gives a general introduction to random matrices and to the main method used in this thesis: the Coulomb gas. This technique allows to study the distribution of observables which take the form of linear statistics of the eigenvalues. These linear statistics represent many relevant physical observables, in different contexts. This method is then applied to study concrete examples in coherent transport and fluctuating interfaces in statistical physics. The second part focuses on a model of disordered wires: the multichannel Dirac equation with a random mass. We present an extension of the powerful methods used for one dimensional system to this quasi-1D situation, and establish a link with a random matrix model. From this result, we extract the density of states and the localization properties of the system. Finally, we show that this system exhibits a series of topological phase transitions (change of a quantum number of topological nature, without changing the symmetries), driven by the disorder.