Geometric methods for nonlinear quantum many-body systems

Geometric methods for nonlinear quantum many-body systems

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Mathieu Lewin, Universite de Cergy-Pointoise
Jadwin Hall 343

Geometric techniques have played an important role in the seventies, for the study of the spectrum of many-body Schrödinger operators. In this talk I will present a formalism which also allows to study nonlinear systems. I will in particular define a weak topology on many-body states, which appropriately describes the physical behavior of the system in the case of lack of compactness, that is when some particles are lost at infinity. As an application I prove the existence of multi-polaron systems in the Pekar- Tomasevich approximation, in a certain regime for the coupling constant.