We present a semiclassical approximation to the scattering wavefunction $Psi(mathbf{r},k)$ for an open quantum billiard which is based on the reconstruction of the Feynman path integral. We demonstrate its remarkable numerical accuracy for the open r
ectangular billiard and show that the convergence of the semiclassical wavefunction to the full quantum state is controlled by the path length or equivalently the dwell time. Possible applications include leaky billiards and systems with decoherence present.
We introduce a procedure to generate scattering states which display trajectory-like wave function patterns in wave transport through complex scatterers. These deterministic scattering states feature the dual property of being eigenstates to the Wign
er-Smith time-delay matrix and to the transmission matrix with classical (noiseless) transmission eigenvalues close to 0 or 1. Our procedure to create such beam-like states is based solely on the scattering matrix and successfully tested numerically for regular, chaotic and disordered cavities. These results pave the way for the experimental realization of highly collimated wave fronts in transport through complex media with possible applications like secure and low-power communication.
We investigate the effect of decoherence on Fano resonances in wave transmission through resonant scattering structures. We show that the Fano asymmetry parameter q follows, as a function of the strength of decoherence, trajectories in the complex pl
ane that reveal detailed information on the underlying decoherence process. Dissipation and unitary dephasing give rise to manifestly different trajectories. Our predictions are successfully tested against microwave experiments using metal cavities with different absorption coefficients and against previously published data on transport through quantum dots. These results open up new possibilities for studying the effect of decoherence in a wide array of physical systems where Fano resonances are present.
