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Positive Commutators and the Spectrum¶of Pauli--Fierz Hamiltonian of Atoms and Molecules |
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| Authors: | Volker Bach Jürg Fröhlich Israek Michael Sigal Avy Soffer |
| Affiliation: | FB Mathematik MA 7-2, TU Berlin, Str. d. 17 Juni 136, 10623 Berlin, Germany.?E-mail: bach@math.tu-berlin.de, DE Institut für Theoretische Physik, ETH H?nggerberg, 8093 Zürich, Switzerland.?E-mail: juerg@itp.phys.ethz.ch, CH Department of Mathematics, University of Toronto, Toronto, M5S 3G3, Canada. E-mail: sigal@math.toronto.edu, CA Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USA. E-mail: soffer@math.rutgers.edu, US |
| Abstract: | In this paper we study the energy spectrum of the Pauli–Fierz Hamiltonian generating the dynamics of nonrelativistic electrons bound to static nuclei and interacting with the quantized radiation field. We show that, for sufficiently small values of the elementary electric charge, and under weaker conditions than those required in [3], the spectrum of this Hamiltonian is absolutely continuous, except possibly in small neighbourhoods of the ground state energy and the ionization thresholds. In particular, it is shown that (for a large range of energies) there are no stable excited eigenstates. The method used to prove these results relies on the positivity of the commutator between the Hamiltonian and a suitably modified dilatation generator on photon Fock space. Received: 10 April 1998 / Accepted: 12 April 1999 |
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