Ter­min

Re­sea­rch Se­mi­nar "Com­plex Quan­tum Sys­tems": Stef­fen Pol­zer (Ge­ne­va), On the Exis­tence and Non-Exis­tence of Ground States in the Spin-Bo­son Mo­del

Ort: J2.138

The Spin-Boson model describes the interaction between a quantum-mechanical two-state system, a spin, and a Bosonic field. Its Hamiltonian is said to have a ground state if the infimum of its spectrum is an eigenvalue. Using the Feynman-Kac formula, one can express matrix elements of the semigroup generated by the Hamiltonian in terms of a self-attractive jump process. We will discuss how one can apply this representation in order to derive probabilistic criteria for the existence and non-existence of ground states. We will summarize how these criteria have been applied to show that, in the infrared-critical case, a phase transition occurs: as the coupling strength increases, the system transitions from having a ground state to having none.  Based on joint work with Volker Betz, Benjamin Hinrichs and Mino Nicola Kraft.