Mathematical Theory of the Wigner-Weisskopf Atom

Vojkan Jaksic (1) , Eugene Kritchevski (1) , Claude-Alain Pillet (2, 3, 4, 5)

1 Department of Mathematics and Statistics [Montréal]
2 FRUMAM - Fédération de Recherche des Unités de MAthématiques de Marseille
3 CPT - E5 Physique statistique et systèmes complexes
4 CPT - Centre de Physique Théorique - UMR 6207
5 CPT - Centre de Physique Théorique - UMR 7332

These notes provide an introduction to the spectral theory of the Friedrichs model. This model is used in quantum physics to describe the coupling of a discrete set of energy levels to a continuum of states. We restrict ourselves to the simplest possible case of a single energy level coupled to a continuum, the so-called Wigner-Weisskopf atom. We discuss both, perturbative and non-perturbative aspects. We also consider the fermionic second quantization of this model and discuss its nonequilibrium thermodynamics: steady states, steady currents and entropy production.

Mots clés: rank one perturbations; spectral theory; Friedrichs model; nonequilibrium statistical mechanics; steady state; NESS; Kubo formula; linear response; Onsager reciprocity relations; Wigner-Weisskopf atom

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

Vojkan Jaksic, Eugene Kritchevski, Claude-Alain Pillet. Mathematical Theory of the Wigner-Weisskopf Atom. J. Derezinski, H. Siedentop. Large Coulomb Systems, Springer/Lecture Notes in Physics 695, pp.145-215, 2006, Lecture Notes in Physics 695, ⟨10.1007/b11607427⟩. ⟨hal-00009011⟩