Generating Particlelike Scattering States in Wave Transport

We introduce a procedure to generate scattering states which display trajectorylike wave function patterns in wave transport through complex scatterers. These deterministic scattering states feature the dual property of being eigenstates to the Wigner-Smith time-delay matrix Q and to the transmission matrix t(dagger)t with classical (noiseless) transmission eigenvalues close to 0 or 1. Our procedure to create such beamlike 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 such as secure and low-power communication.