Masters thesis of Liam Farrell, under the supervision of Dr. Duncan O'Dell. Successfully defended on August 26, 2021. / Caustics are regions created by the natural focusing of waves. Some examples include rainbows, spherical aberration, and sonic booms. The intensity of a caustic is singular in the classical ray theory, but can be smoothed out by taking into account the interference of waves. Caustics are generic in nature and are universally described by the mathematical theory known as catastrophe theory, which has successfully been applied to physically describe a wide variety of phenomena. Interestingly, caustics can exist in quantum mechanical systems in the form of phase singularities. Since phase is such a central concept in wave theory, this heralds the breakdown of the wave description of quantum mechanics and is in fact an example of a quantum catastrophe. Similarly to classical catastrophes, quantum catastrophes require some previously ignored property or degree of freedom to be taken into account in order to smooth the phase divergence. Different forms of spontaneous pair-production appear to suffer logarithmic phase singularities, specifically Hawking radiation from gravitational black holes. This is known as the trans-Planckian problem. We will investigate Hawking radiation formed in an analogue black hole consisting of a flowing ultra-cold Bose-Einstein condensate. By moving from an approximate hydrodynamical continuum description to a quantum mechanical discrete theory, the phase singularity is cured. We describe this process, and make connections to a new theory of logarithmic catastrophes. We show that our analogue Hawking radiation is mathematically described by a logarithmic Airy catastrophe, which further establishes the plausibility of pair-production being a quantum catastrophe / Thesis / Master of Science (MSc)

Ce travail a pour objet une étude théorique des formes de société politique et des contraintes de production de leur unité collective. Le questionnement qui l’anime interroge les modalités de base génératrices d’une dimension collective, par laquelle faire tenir les agents sociaux ensemble, dans un espace commun. Ces formes sont considérées à partir de l’enseignement apporté par l’œuvre de Marcel Gauchet. Les travaux de ce dernier ont approfondi les modes différenciés de structuration de l’existence collective, selon le déploiement d’un fonctionnement autonome des collectivités humaines-sociales, par extraction hors de l’hétéronomie. Autour de l’instauration et de la modification possible des configurations d’un espace humain-social, il s’agit de s’interroger spécifiquement sur les contraintes de mise en forme, inhérentes aux possibilités de déploiement de cet espace. Cette formation interne sera appréhendée par un angle dynamique, issu des travaux fournis par l’œuvre morphologique de René Thom. Au travers de la théorie des catastrophes (TC), il a dressé une liste de formes stables et de processus de changement, instables dans le temps, mais robustes dans les dimensions qui en permettent le déploiement. Depuis l’analyse d’un système dynamique nécessaire à l’intelligence de ce déploiement, une articulation problématique se découvre : l’organisation de la dimension collective dans l’immanence, et la gestion politique de la dimension historique, incitent à questionner l’historicité interne des collectivités, à partir de la notion de processus morphologique et selon les déformations que ce processus peut connaître. Les éclairages que cette notion de processus apporte, indiquent l’effectivité d’un travail de la forme, dans l’étude du tenir ensemble des collectivités politiques. / This work aims to understand the way societies are shaped and to identify the constraints within they move themselves. It tries to answer the question of how social agents turn out to act collectively in shared social space, in other words to make society. This work take forms into account following Marcel Gauchet’s work. Indeed Marcel Gauchet has managed to grasp the differentiated patterns structuring collective life, characterising them as resulting from the deployment of an autonomous functioning of human-social communities, by extraction from heteronomy. The present work goes on step further and, considering the establishment and possible change of the configurations of a human-social space, it wonders about the constraining framework of the formation of this space. This internal shaping is looked into from René Thom’s morphological approach. Indeed, through his Catastrophe Theory (CT), René Thom compiled a list of stable forms and processes of change, unstable over time, but steady as far as the conditions of their formation are concerned. It accentuates the core issue: the organization of the collective dimension through immanence, and the political management of the historical dimension drive us to examine the inner historicity of communities from the concept of morphological process and according to the distortions it may undergo. This concept proves useful to understand the morphological dynamic which enable communities to hold together.

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