Showing papers by "Jürg Fröhlich published in 2008"
TL;DR: In this article, for a model of atoms and molecules made from static nuclei and nonrelativistic electrons coupled to the quantized radiation field (the standard model of non-relative QED), the authors prove a Mourre estimate and a limiting absorption principle in a neighborhood of the ground state energy.
Abstract: For a model of atoms and molecules made from static nuclei and non-relativistic electrons coupled to the quantized radiation field (the standard model of non-relativistic QED), we prove a Mourre estimate and a limiting absorption principle in a neighborhood of the ground state energy. As corollaries we derive local decay estimates for the photon dynamics, and we prove absence of (excited) eigenvalues and absolute continuity of the energy spectrum near the ground state energy, a region of the spectrum not understood in previous investigations. The conjugate operator in our Mourre estimate is the second quantized generator of dilatations on Fock space.
58 citations
TL;DR: In this article, a quantum particle coupled to a spatial array of independent non-interacting reservoirs in thermal states (heat baths) was shown to be diffusive for small but finite energies.
Abstract: We consider a quantum particle coupled (with strength $\la$) to a spatial array of independent non-interacting reservoirs in thermal states (heat baths). Under the assumption that the reservoir correlations decay exponentially in time, we prove that the long-time behavior of the particle is diffusive for small, but finite $\la$. Our proof relies on an expansion around the kinetic scaling limit ($\la \searrow 0$, while time and space scale as $\la^{-2}$) in which the particle satisfies a Boltzmann equation. We also show an equipartition theorem: the distribution of the kinetic energy of the particle tends to a Maxwell-Boltzmann distribution, up to a correction of $O(\la^2)$.
3 citations