Time-Domain Scars: Resolving the Spectral Form Factor in Phase Space

Leonardo Pachon, Universidad nacional de Colombia and 
                 Universitaet Augsburg.

Abstract: 

We study the relationship of the spectral form factor with 
quantum as well as classical probabilities to return. Defining a 
quantum return probability in phase space as a trace over the
propagator of the Wigner function allows us to identify and 
resolve manifolds in phase space that contribute to the form
factor. They can be associated with classical invariant manifolds 
such as periodic orbits, but also to non-classical structures 
such as sets of midpoints between periodic points. In contrast 
to scars in wave functions, these features are not subject to
the uncertainty relation and therefore need not show any smearing. 
They constitute important exceptions from a continuous convergence 
in the classical limit of the Wigner towards the Liouville 
propagator. We support our theory with numerical results for the 
quantum cat map and the harmonically driven quartic oscillator.