Eur. Phys. J. D 60, 257-261 (2010)
https://doi.org/10.1140/epjd/e2010-00243-0

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 This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 7 June 2010
Revised: 30 July 2010
Published online: 28 September 2010

Abstract

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.