The many-body problems is at the heart of a great variety of macroscopic condensed matter phenomena. Our activity aims at the description of generic, classical and quantum, N-body systems, ranging from electrons in solids, cold atomic gases, and quantum magnetism to the microscopic and coarse grained description of equilibrium and non-equilibrium phase transitions.
Conceptually, the easiest description is often based on mean-field approaches. Their rigorous derivations and extensions in the context of physics of cold atomic gases is part of our activity. The main impetus is, however, to develop and apply beyond mean field methods.
These methods serve to include quantum and thermal fluctuations, to establish and quantify possible phase diagrams of Bose and Fermi gases and their mixtures from the dilute to the strongly interacting regimes. Our numerical solutions allow us direct, parameter-free comparisons with experimental results. (link to atomic gases). We further study the possibility of Cooper pair and quartett condensation in fermionic gases in analogy to phenomena in strongly interacting nuclear matter. Indeed, if there are systems with four species of fermions, two Cooper pairs can form a quartet. Competition between pairing and quartetting is then an interesting phenomenon to be investigated.
Advanced many-body approaches are also developed to describe strong correlations in quantum magnetism and spin systems.
Renormalization group theory has been particularly successful for the explanation of phase transitions. We mainly develop non-perturbative, functional renormalization group methods, extending them from equilibrium to non-equilibrium critical phenomena, such of kinetic roughening or absorbing transitions in reaction-diffusion processes (link to theme hors equilibre).
Another activity at LPMMC concerns the theoretical investigation of quantum many-body Hamiltonians. We study some of their fundamental mathematical properties with applications e.g. to the modelization of quantum crystals and polarons.
Physics of Atomic Nuclei 74, 1139—1146 (2011)
Physical Review C 81, 064310 (2010)
Journal of Physics A : Mathematical and Theoretical 44, 495001 (2011)
ESAIM : Control, Optimisation and Calculus of Variations 19, 629—656 (2013)
SIAM Journal on Mathematical Analysis 45, 1267 (2013)