Description du projet
Approches améliorées de l’approximation du comportement des systèmes quantiques à plusieurs corps
Les propriétés physiques des systèmes quantiques à plusieurs corps sont généralement décrites à l’aide des équations de Schrödinger. Cependant, il est en général impossible de résoudre ces équations avec les techniques numériques actuelles. Les physiciens utilisent donc souvent des théories d’approximation dans la pratique, qui se focalisent sur quelques comportements collectifs des systèmes décrits. À l’aide d’analyses mathématiques, ils confirment si les modèles choisis décrivent effectivement le comportement des systèmes. L’objectif global du projet RAMBAS, financé par l’UE, est de valider certaines approximations effectives clés utilisées en physique quantique à plusieurs corps. En s’appuyant sur de nouvelles techniques tirées de l’analyse fonctionnelle, de la théorie spectrale, du calcul des variations et des équations différentielles partielles, RAMBAS espère élever les approximations standard des systèmes quantiques à un niveau supérieur, fournissant ainsi aux physiciens de nouveaux outils mathématiques.
Objectif
From first principles of quantum mechanics, physical properties of many-body quantum systems are usually encoded into Schroedinger equations. However, since the complexity of the Schroedinger equations grows so fast with the number of particles, it is generally impossible to solve them by current numerical techniques.
Therefore, in practice approximate theories are often applied, which focus only on some collective behaviors of the systems in question.
The corroboration of such effective models largely depends on mathematical methods. The overall goal of RAMBAS is to justify key effective approximations used in many-body quantum physics, including the mean-field, quasi-free, and random-phase approximations, as well as to derive subtle corrections in critical regimes.
Building on my unique expertise in mathematical physics, I will 1) develop general techniques to understand corrections to the mean-field and Bogoliubov approximations for dilute Bose gases, 2) introduce rigorous bosonization methods and combine them with existing techniques from the theory of Bose gases to understand Fermi gases, and 3) employ the bosonization structure of Fermi gases to study the many-body quantum dynamics in long time scales, thus deriving quantum kinetic equations.
By applying and suitably inventing mathematical techniques from functional analysis, spectral theory, calculus of variations and partial differential equations, RAMBAS will take standard approximations of quantum systems to the next level, with special focus on those particularly challenging situations where the particle correlation plays a central role but is yet not adequately addressed. RAMBAS will thereby provide the physics community with crucial mathematical tools, which are at the same time rigorous and applicable.
Champ scientifique
- natural sciencesphysical sciencesquantum physics
- natural sciencesmathematicsapplied mathematicsmathematical physics
- natural sciencesmathematicspure mathematicsmathematical analysisfunctional analysis
- natural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equations
Mots‑clés
Programme(s)
- HORIZON.1.1 - European Research Council (ERC) Main Programme
Régime de financement
HORIZON-ERC - HORIZON ERC GrantsInstitution d’accueil
80539 MUNCHEN
Allemagne