An In nite Level Atom coupled to a Heat Bath Dissertation zur Erlangung des Grades "Doktor der Naturwissenschaften" am Fachbereich Physik, Mathematik und Informatik

Abstract

We study the mathematics of a nite particle system coupled to a heat bath. The Standard Model of Quantum Electrodynamics at temperature zero yields a Hamiltonian H describing the energy of particles interacting with photons. In the Heisenberg picture the time evolution of the physical system is the action of a one-parameter-group (τt)t∈R on a set of observables A: τt: A ↦ → τt(A), t ∈ R, A ∈ A Note, that τ is related with solutions of the Schrödinger equation for H. To consider states of A describing the physical system near its thermal equilibrium at temperature T> 0, we follow the ansatz of Jaksic and Pillet to construct a representation of A. Now, states are unit vectors in this representation and the time evolution, is described with the aid of the Standard Liouvillean L. The following results are derived or proved, respectively, in this thesis:- the construction of the representation- the self-adjointness of the Standard Liouvillean- the existence of an equilibrium state in the representation- the limit of large times for the physical system.