Time delay for resonances

Werner O. Amrein, Kalyan B. Sinha

We present stationary expressions for the on-shell time delay operator and for its trace in quantum-mechanical potential scattering. The trace of this operator is shown to represent the time delay for a monoenergetic and well-collimated beam of initial states. For exponentially decaying potentials the total scattering cross section and the trace of the on-shell time delay operator have analytic extensions to complex energies, with poles at most at the usual resonance poles (poles of the analytically continued S -matrix) in the lower half plane and at their mirror images with respect to the real axis. At real energies close to such a pole both the scattering cross section and the time delay are approximately of Breit–Wigner type, the sign of the time delay being related to that of the virial. These results corroborate the idea that a resonance should show up through a peak in the scattering cross section and a large (though positive) time delay.

David F. P. Pile

D. Bollé

Rajesh Patel, Rasbindu V. Mehta

Time delays in emission of resonantly trapped light in magnetite microspheres dispersed in a ferrofluid were measured for three different sphere sizes. The time delay was found to vary randomly. The effect of the size of microspheres on the probability distribution was determined. Analysis of the data showed that the statistics of the time delay is best described by a Levy distribution.

D. Klakow, M. Weber, P.‐G. Reinhard

Juan Gonzalo Muga, José P. Palao

Quantum scattering resonances are generally associated with a positive time delay. An example of anomalous negative time delay in resonance scattering is provided. The effect is due to an absorbing, negative imaginary part in the interaction potential.