OPTICAL REALIZATION OF THE BAKERS TRANSFORMATION

The quantization of a completely chaotic system-the baker's transforma tion-is investigated using the fact that the relationship between clas sical and quantum mechanics is directly analogous to the one between r ay and wave optics. A class of optical systems is constructed for whic h the ray dynamics is governed by the baker map. Applying wave-optical methods to these physical systems then gives, in the standard way, th eir corresponding quantum dynamics. The result is that in certain case s the quantum propagator is identical to that found previously using a n ad hoc mathematical quantization procedure. However, this is not alw ays so-for other systems with the same classical (ray) limit there are important differences. In particular, the propagator need not be bloc k-diagonal in its q-p' representation, as had previously been assumed, although it always tends to this basic form in the semiclassical limi t.