Collective dynamics of unstable quantum states

• Published in: Annals of physics 1992-06, Vol.216 (2), p.323-350
• Main Authors: Sokolov, V.V, Zelevinsky, V.G
• Format: Article
• Language: English
• Subjects: Classical and quantum physics: mechanics and fields; Exact sciences and technology; Physics; Quantum mechanics
• ISSN: 0003-4916; 1096-035X
• DOI: 10.1016/0003-4916(92)90180-T

Dynamics of a complicated quantum system interacting with open decay channels is treated by means of the discretized effective non-hermitian Hamiltonian. The main subject is segregation of short-lived resonances from a background of equilibrium compound states. Broad states are created by the interaction through common decay channels similarly to the formation of Dicke states in optics when individual radiators are synchronized by the common radiation field. The analysis is carried out with the use of two complementary representations (internal and doorway). A sharp transition between regimes of weak and strong continuum coupling is considered. The weak coupling limit corresponds to well-isolated resonances, whereas at strong coupling collectivization of widths and formation of the short-lived Dicke states enveloping the fine-structure compound states occur. Effects of channel thresholds as well as a problem of ergodicity (equivalence of energy and ensemble averages) are discussed. Two simple models illustrate results, show the relationship to similar solid state problems, and display new collective phenomena for the doorways strongly coupled to the background.