Delay-time distribution in the scattering of time-narrow wave packets (II) - Quantum Graphs

摘要

We apply the framework developed in the preceding paper in this series tocompute the time-delay distribution in the scattering of ultra short RF pulseson complex networks of transmission lines which are modeled by metric (quantum)graphs. We consider wave packets which are centered at high quantum number andcomprise many energy levels. In the limit of pulses of very short duration wecompute upper and lower bounds to the actual time delay distribution of theradiation emerging from the network using a simplified problem where time isreplaced by the discrete count of vertex-scattering events. The classical limitof the time-delay distribution is also discussed and we show that for finitenetworks it decays exponentially, with a decay constant which depends on thegraph connectivity and the distribution of its edge lengths. We illustrate andapply our theory to a simple model graph where an algebraic decay of thequantum time delay distribution is established.