Quantum Institute: Visitor Schedule
The Quantum Lunch is regularly held on Thursdays in the Theoretical Division Conference Room, TA-3, Building 123, Room 121. For more information, contact Diego Dalvit.
January 22, 2008
Semiclassical Propagation in Phase Space
Constructing a semiclassical approximation to the propagator of the Wigner function has been a long-standing problem in quantum dynamics, owing to the fine "sub-Planckian" oscillations that encode quantum coherence in this phase-space representation. I present satisfactory solutions on two levels of approximation, based on the van-Vleck propaga- tor and a phase-space path-integral formalism, respectively. The interference of pairs of classical trajectories gives rise to a broadening of the Liouvillian delta function on the classical trajectory in the form of a smooth "quantum spot" with an oscillatory internal structure. The path-integral approach allows for a finer resolution of this quantum spot in terms of Airy functions. A route how to incorporate decoherence and dissipation, lifting the Feynman-Vernon influence-functional approach to phase space, is indicated. As an important application, I will show that the Wigner propagator is a suitable quantity to identify and resolve structures in phase space that contribute to the spectral form factor. They tend to localize on classical unstable periodic orbits and therefore can be interpreted as scars in the time domain. However, consistency between the trace of the propagator and the form factor even implies non-classical features in the propagator that 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 are revealed with unlimited (single-pixel) resolution. I present numerical results for standard models of quantum chaos which illustrate and confirm our theoretical analysis.