| In recent years, semiclassical approximations to the propagator of the Wigner function have become available which are based on pairs of classical trajectories. As an important application, I will show that the diagonal Wigner propagator (initial and final arguments coinciding) is a suitable quantity to identify and resolve structures in quantum-mechanical phase space that contribute to the spectral form factor. They tend to localize on classical unstable periodic orbits when the time argument coincides with the respective period and therefore can be interpreted as scars in the time domain. Consistency between the trace of the propagator and the form factor requires the existence of additional non-classical features in the propagator which are of the same order of magnitude as the classical ones and take the form of phase-space manifolds in regions that are void of classical structures. As the propagator, by contrast to eigenstates, is not restricted by the uncertainty relation, these features can be revealed in principle with unlimited (single-pixel) resolution. I present numerical results for standard models of quantum chaos which illustrate and confirm the theoretical analysis. |
|