Juerg Froehlich, Marco Merkli, Israel Michael Sigal
Ionization of atoms in a thermal field
(491K, postscript)
ABSTRACT. We study the stationary states of a quantum mechanical system describing an
atom coupled to black-body radiation at positive temperature. The
stationary states of the non-interacting system are given by product states,
where the particle is in a
bound state corresponding to an eigenvalue of the particle Hamiltonian, and
the field is in its equilibrium state.
We show that if Fermi's Golden Rule predicts that a stationary state
disintegrates after coupling to the radiation field then it is unstable,
provided the coupling constant is sufficiently small (depending on the
temperature). \\
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The result is proven by analyzing the spectrum of the thermal Hamiltonian
(Liouvillian) of the system within the framework of $W^*$-dynamical systems. A
key element of our spectral analysis is the positive commutator method.