Description des corrélations à N-corps dans la dynamique des systèmes de fermions en interaction

par Thomas Czuba

Projet de thèse en Structure et réactions nucléaires

Sous la direction de Denis Lacroix.

Thèses en préparation à université Paris-Saclay , dans le cadre de École doctorale Particules, Hadrons, Énergie et Noyau : Instrumentation, Imagerie, Cosmos et Simulat , en partenariat avec Laboratoire de Physique des deux Infinis Irène Joliot-Curie (laboratoire) et de Faculté des sciences d'Orsay (référent) depuis le 30-09-2019 .

  • Résumé

    Le but de ce sujet de stage et thèse est de fournir de nouveaux outils théorique permettant de simuler les phénomènes physiques dans les systèmes de fermions fortement corrélés. Plusieurs stratégies sont envisagées, des méthodes utilisant des sauts quantiques entre états de Slater, des méthodes traitant les corrélations comme un ensemble de fluctuations initiales (méthodes d'espace des phases) et des méthodes traitant explicitement des interférences entre les différentes trajectoires de champ moyen (similaire aux intégrales de chemin). Ce sujet est par nature interdisciplinaire et trouvera des applications dans divers domaines de physiques allant de la théorie des systèmes quantiques ouverts, des systèmes atomiques sur réseaux, des petit supraconducteurs ou encore des systèmes auto-liés tels que les noyaux atomiques. Une description plus détaillée est donnée dans la version anglaise du sujet.

  • Titre traduit

    Treatment of many-body correlations in the dynamics of small Fermi systems

  • Résumé

    Mean-field theories, including density functional theories, are among the most used methods to treat static and dynamical properties of complex many-body systems. Replacing the initial problem of interacting particles by a set of independent particles moving in a self-consistent mean field (see picture), these approaches are designed to describe one-body properties. The mean-field theory has reached a certain degree of maturity and is nowadays extensively used in many areas of physics. In this approach, one-body degrees of freedom (DoF) are treated as classical or quasi-classical objects. For these reasons, mean-field theories recurrently fail to reproduce important effects associated to the quantum fluctuations induced by strong correlations between the constituent of the system. As a consequence, this framework generally reproduces mean properties like collective but misses important aspects like quantum fluctuations around the mean value: (i) dissipative effects leading to the disappearance of ordered collective vibrations into disorder and (ii) quantum tunneling in many-body systems (iii) quantum fluctuations beyond the independent particle picture. To overcome these difficulties, one should go beyond mean-field and treat the coherent superposition of independent particle systems. During the internship eventually followed by a thesis, several theories will be formally developed and then applied to describe non-equilibrium dynamics in strongly interacting systems: 1. Phase-space method: this approach starts from the simple question “Can we replace the initial problem by an ensemble of independent mean-field trajectories and still grasp the important correlation effect?” The answer is yes and this could be achieved by adding a noise to the evolution. In the envisaged approach, important correlations are expected to be included through a statistical treatment of the initial conditions. This approach has already demonstrated its applicability but still resists the application in the context of density functional theory. 2. Quantum Jump approach: dissipation is always accompanied by fluctuations. The challenge in this case is to introduce these fluctuations through the development of stochastic Schrödinger equation (SSE) able to describe quantum and dissipative effects. Few attempts in that direction have been made in the past but a versatile and fully well-founded approach still remains to be proposed. 3. Coherent mixing of many-body states: while the two above mentioned strategy replaces the initial problem by a set of independent many-body evolutions, a third strategy is to follow simultaneously a set of trajectories treating explicitly the interferences between them. Formal and numerical aspects related to this strategy are at the forefront of today's development in theoretical and numerical physics developments. The goal of the internship and latter of the thesis will be (i) to acquire a complete knowledge of theories able to treat correlations in many-body fermionic (and eventually bosonic) systems (ii) propose and test new theoretical approaches using one or several of the above-mentioned strategies. It is anticipated that several new methods will be proposed and applied to different fields of physics ranging from condensed matter, atomic physics to nuclear physics systems. Before addressing these issues, during the internship, simpler situations of quantum systems interacting with complex surrounding environment will be considered. This will be a crucial step for the student to grasp the theoretical concepts as well as to acquire the numerical skills.