CLASSICAL STRUCTURES IN THE QUANTIZED BAKER TRANSFORMATION

We study the role of periodic trajectories and other classical structures on single eigenfunctions of the quantized version of the baker's transformation. Due to the simplicity of both the classical and the quantum description a very detailed comparison is possible, which is made in phase space by means of a special positive definite representation adapted to the discreteness of the map. A slight but essential modification of the original version described by Balasz and Voros (Ann. Phys. 190 (1989), 1) restores the classical phase space symmetry. In particular, we are able to observe how the whole hyperbolic neighborhood of the fixed points appears in the eigenfunctions. New scarring mechanisms related to the homoclinic and heteroclinic trajectories are observed and discussed. © 1990.