Phase Transition in the Infrared-Divergent Spin-Boson Model
Steffan Polzer
The spin-boson model describes the interaction between a quantum mechanical two level system and a bosonic field. Its Hamiltonian, a self-adjoint and lower-bounded operator, is said to have a ground state if the infimum of its spectrum is an eigenvalue. I present recent work in which we show that, in the infrared-divergent model, a phase transition occurs: as the coupling strength increases, the system transitions from having a ground state to having none. Along the way we will get to know both the Feynman-Kac formula and how it allows us to translate the functional analytic problem into the language of probability theory, as well as some important models and tools of mathematical statistical mechanics. Based on joint work with Volker Betz, Benjamin Hinrichs and Mino Nicola Kraft.