arXiv subjects

Marcel Griesemer

Publications and source records attributed to Marcel Griesemer.

23 records · Page 2Linked to original sources

arXiv2008

Analytic Perturbation Theory and Renormalization Analysis of Matter Coupled to Quantized Radiation

For a large class of quantum mechanical models of matter and radiation we develop an analytic perturbation theory for non-degenerate ground states. This theory is applicable, for example, to models of matter with static nuclei and non-relativistic electrons that are coupled to the UV-cutoff quantized radiation field in the dipole approximation. If the lowest point of the energy spectrum is a non-degenerate eigenvalue of the Hamiltonian, we show that this eigenvalue is an analytic function of the nuclear coordinates and of $α^{3/2}$, $α$ being the fine structure constant. A suitably chosen ground state vector depends analytically on $α^{3/2}$ and it is twice continuously differentiable with respect to the nuclear coordinates.

math-ph↗

arXiv2004

Non-relativistic Matter and Quantized Radiation

This is a didactic review of spectral and dynamical properties of atoms and molecules at energies below the ionization threshold, the focus being on recent work in which the author was involved. As far as possible, the results are described using a simple model with \emph{one} electron only, and with \emph{scalar} bosons. The main ideas are explained but no complete proofs are given. The full-fledged standard model of non-relativistic QED and various of its aspects are described in the appendix.

math-ph↗

arXiv2003

Exponential Decay and Ionization Thresholds in Non-Relativistic Quantum Electrodynamics

Spatial localization of the electrons of an atom or molecule is studied in models of non-relativistic matter coupled to quantized radiation. We give two definitions of the ionization threshold. One in terms of spectral data of cluster Hamiltonians, and one in terms of minimal energies of non-localized states. We show that these two definitions agree, and that the electrons described by a state with energy below the ionization threshold are localized in a small neighborhood of the nuclei with a probability that approaches 1 exponentially fast with increasing radius of the neighborhood. The latter result is derived from a new, general result on exponential decay tailored to fit our problem, but applicable to many non-relativistic quantum systems outside quantum electrodynamics as well.

math-ph↗

arXiv2001

Ground States in Non-relativistic Quantum Electrodynamics

The excited states of a charged particle interacting with the quantized electromagnetic field and an external potential all decay, but such a particle should have a true ground state--one that minimizes the energy and satisfies the Schrödinger equation. We prove quite generally that this state exists for {\it all values} of the fine-structure constant and ultraviolet cutoff. We also show the same thing for a many-particle system under physically natural conditions.

math-ph↗

arXiv1998

Instability of a Pseudo-Relativistic Model of Matter with Self-Generated Magnetic Field

For a pseudo-relativistic model of matter, based on the no-pair Hamiltonian, we prove that the inclusion of the interaction with the self-generated magnetic field leads to instability for all positive values of the fine structure constant. This is true no matter whether this interaction is accounted for by the Breit potential, by an external magnetic field which is chosen to minimize the energy, or by the quantized radiation field.

math-ph↗