TY  - JOUR
A1  - Klein, Markus
A1  - Rama, Juliane
T1  - Time asymptotics of e(-ith(kappa)) for analytic matrices and analytic perturbation theory
JF  - Asymptotic analysis
N2  - In quantum mechanics the temporal decay of certain resonance states is associated with an effective time evolution e(-ith(kappa)), where h(.) is an analytic family of non-self-adjoint matrices. In general the corresponding resonance states do not decay exponentially in time. Using analytic perturbation theory, we derive asymptotic expansions for e(-ith(kappa)), simultaneously in the limits kappa -> 0 and t -> infinity, where the corrections with respect to pure exponential decay have uniform bounds in one complex variable kappa(2)t.
 In the Appendix we briefly review analytic perturbation theory, replacing the classical reference to the 1920 book of Knopp [Funktionentheorie II, Anwendungen und Weiterfuhrung der allgemeinen Theorie, Sammlung Goschen, Vereinigung wissenschaftlicher Verleger Walter de Gruyter, 1920] and its terminology by standard modern references. This might be of independent interest.
KW  - resonances
KW  - exponential decay
KW  - long-time corrections
KW  - Fermi golden rule
KW  - analytic perturbation theory
Y1  - 2014
U6  - https://doi.org/10.3233/ASY-141226
SN  - 0921-7134
SN  - 1875-8576
VL  - 89
IS  - 3-4
SP  - 189
EP  - 233
PB  - IOS Press
CY  - Amsterdam
ER  -