Quantum-Mechanical Matter Interacting with the Quantized Radiation Field

University Of Alabama At Birmingham, Birmingham AL

Investigators

Abstract

Within the standard model of non-relativistic quantum mechanical matter interacting with the quantized radiation field methods are developed to show that an isolated atom or molecule prepared in a, possibly highly exited, bound state is unstable and eventually relaxes to its ground state by emitting photons. Similarly, the exited states of a free charged particle are not stable. It is shown that photons which are not bound to the electron escape ballisticly while the particle relaxes to a state of minimal energy followed by a cloud of soft photons (dressed one-electron state) in which it propagates according to a reduced dynamics. The key problem in the case of an atom is to show that no infrared problem occurs. For a free charged particle an infrared problem does occure and one has to deal with nonequivalent representations of the CCR. - The proofs require as an ingredient good control over the spectral properties of the Hamilton operator and, in addition, asymptotic completeness of Rayleigh scattering and Compton scattering of the respective system. These prerequisites are established by methods and techniques inspired by similar methods and techniques in the spectral and scattering theory of $N$-particle Schr\"odinger operators, such as Mourre theory, propagationestimates, the construction of suitable propagation observables and others. In addition ideas and methods from constructive quantum field theory (soft photon bounds, Rosen estimates, renormalization group analysis) are employed. This research leads to a mathematically rigorous understanding of physical phenomena such as the radiative decay of atoms, the photo effect, and Compton scattering. These are phenomena which are at the heart of many technical devices and which determine our visual impression of the world. Furthermore the phenomenon of radiative decay (or the relaxation to the ground state) and the similar phenomenon of return to equilibrium at positive temperature play key roles in attempts to understand dissipative, irreversible behavior in the quantum theory of open systems. The mathematical methods which are developed apply equally to other physical systems such a particle in a crystal interacting with quantized lattice vibrations (phonons), and find currently application in the study of return to equilibrium of matter interacting with radiation at positive temperature.