The preparation of states in quantum mechanics

The important problem of how to prepare a quantum mechanical system, $S$, in a specific initial state of interest - e.g., for the purposes of some experiment - is addressed. Three distinct methods of state preparation are described. One of these methods has the attractive feature that it enables one to prepare $S$ in a preassigned initial state with certainty; i.e., the probability of success in preparing $S$ in a given state is unity. This method relies on coupling $S$ to an open quantum-mechanical environment, $E$, in such a way that the dynamics of $S vee E$ pulls the state of $S$ towards an attractor, which is the desired initial state of $S$. This method is analyzed in detail.

Analyticity of the self-energy in total momentum of an atom coupled to the quantized radiation field

We study a neutral atom with a non-vanishing electric dipole moment coupled to the quantized electromagnetic field. For a sufficiently small dipole moment and small momentum, the one-particle (self-) energy of an atom is proven to be a real-analytic function of its momentum. The main ingredient of our proof is a suitable form of the Feshbach-Schur spectral renormalization group.

Dimensional Reduction without Extra Continuous Dimensions

We describe a novel approach to dimensional reduction in classical field theory. Inspired by ideas from noncommutative geometry, we introduce extended algebras of differential forms over space-time, generalized exterior derivatives and generalized connections associated with the geometry of space-times with discrete extra dimensions. We apply our formalism to theories of gauge- and gravitational fields and find natural geometrical origins for an axion- and a dilaton field, as well as a Higgs field.