AG Mathematische Physik, Nathan Métraud (BCAM): Non-commutative evolution equation and application in many-body quantum theory.

Nathan Métraud (BCAM)

Non-commutative evolution equatin and application in many-body quantum theory

Abstract:
We study the Brocket-Wegner flow, an evolution equation on
non-commutative spaces of operators. It defines a nonlinear,
operator-valued dynamics that is particularly delicate in the presence
of unbounded operators. We discuss the main analytical difficulties
arising from non-commutativity and unboundedness, and show how they can
be overcome in two important classes of many-body quantum Hamiltonians:
quadratic fermionic Hamiltonians and generalized spin-boson models. In
these cases, despite unbounded initial data,
intrinsic structures ensure well-posedness of the flow. Using this flow
as a dynamical tool, we obtain new diagonalization results in many-body
quantum theory (joint work with Jean-Bernard Bru).