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Positive commutators and the spectrum of Pauli-Fierz Hamiltonian of atoms and molecules. (English) Zbl 0962.81011

Summary: 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 [the first three authors, Adv. Math. 137, 205-298 (1998; Zbl 0923.47041)], 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.

MSC:

81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
47N50 Applications of operator theory in the physical sciences
81V45 Atomic physics
81V55 Molecular physics

Citations:

Zbl 0923.47041
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