## Mathematical theory of the Wigner-Weisskopf atom.(English)Zbl 1108.81054

Dereziński, Jan (ed.) et al., Large Coulomb systems. Lecture notes on mathematical aspects of QED. Selected papers based on the presentations at the summer school on large quantum systems – QED, Nordfjordeid, Norway, August 11–18, 2003, and the summer school ”Quantum field theory – from Hamiltonian point of view”, Sandbjerg Manor, Denmark, August 2–9, 2000. Berlin: Springer (ISBN 3-540-32578-6/hbk). Lecture Notes in Physics 695, 145-215 (2006).
In the lectures an “atom” known as the Wigner-Weisskopf atom (1930) (WWA) is studied in detail. In general case the WWA is described by finitely many energy levels, coupled to a “radiation” field, which is defined by an another set of energy levels. The presented consideration is restricted to the case of WWA with a single energy level. The paper is organized as follows: 1. Introduction. 2. Non-perturbative theory. (Basic facts. Aronszajn-Donoghue theorem. The spectral theorem. Scattering theory. Spectral averaging. Simon-Wolff theorem. Fixing real number $$\omega$$. Examples. Digression: the semi-circle law). 3. The perturbative theory. (The radiating WWA. Perturbation theory of embedded eigenvalues. Complex deformations. Weak coupling limit. Examples). 4. Fermionic quantization. (Basic notions. Fermionic quantization of the WWA. Spectral theory. Scattering theory). 5. Quantum statistical mechanics of SEBB (simple electronic black box) model. (Quasi-free states. Nonequilibrium stationary states. Subsystem structure. Nonequilibrium thermodynamics. The effect of eigenvaluaes. Thermodynamics in the nonequilibrium regime. Properties of the fluxes. Examples). 65 references are given.
For the entire collection see [Zbl 1094.81005].

### MSC:

 81V70 Many-body theory; quantum Hall effect 82B10 Quantum equilibrium statistical mechanics (general) 81V10 Electromagnetic interaction; quantum electrodynamics