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). 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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
W. Amrein, A. Boutet de Monvel, and V. Georgescu, C 0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians(Birkhäuser, Basel-Boston-Berlin, 1996).
H. Araki and E. Woods, Representations of the canonical commutation relations describing a non-relativistic infinite free bose gas, J. Math. Phys. 4:637–662 (1963).
V. Bach, J. Fröhlich, and I. M. Sigal, Quantum electrodynamics of confined nonrelativistic particles, Adv. Math. 137:299–395 (1995).
V. Bach, J. Fröhlich, I. M. Sigal, and A. Soffer, Positive commutators and the spectrum of Pauli-Fierz hamiltonians of atoms and molecules, Comm. Math. Phys. 207:557–587 (1999).
O. Bratteli and D. Robinson, Operator Algebras and Quantum Statistical Mechanics I, II, 2nd ed., Texts and Monographs in Physics (Springer-Verlag, Berlin, 1987).
J. Fröhlich, Application of commutator theorems to the integration of representations of lie algebras and commutation relations, Comm. Math. Phys. 54:135–150 (1977).
J. Fröhlich and M. Merkli, Thermal Ionization, to appear in Math. Phys., Anal. Geom.(2004).
V. Georgescu and C. Gérard, On the virial theorem in quantum mechanics, Comm. Math. Phys. 208:275–281 (1999).
V. Jakšić and C.-A. Pillet, On a model for quantum friction III. Ergodic properties of the Spin-Boson system, Comm. Math. Phys. 178:627–651 (1996).
M. Merkli, Positive commutators in non-equilibrium quantum statistical mechanics, Comm. Math. Phys. 223:327–362 (2001).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Fröhlich, J., Merkli, M. & Sigal, I.M. Ionization of Atoms in a Thermal Field. Journal of Statistical Physics 116, 311–359 (2004). https://doi.org/10.1023/B:JOSS.0000037226.16493.5e
Issue Date:
DOI: https://doi.org/10.1023/B:JOSS.0000037226.16493.5e