Time behaviour near to spectral singularities
National Institute for Theoretical Physics, Stellenbosch Institute for Advanced Study, and Institute of Theoretical Physics, University of Stellenbosch, 7602 Matieland, South Africa
Corresponding author: a email@example.com
Revised: 30 July 2010
Published online: 28 September 2010
Spectral singularities such as exceptional points invoke specific physical effects. The present paper focuses upon the time dependent solutions of the Schrödinger equation. In a simple model it is demonstrated that – depending on initial conditions – within close proximity of exceptional points the time behaviour of the wave function displays characteristic features such as very fast decay or the opposite, i.e. very long life time. At the exceptional point the wave function typically has a linear term in time besides the usual exponential behaviour.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2010