Classical billiards and double-slit quantum interference

We carry out a numerical simulation about the occurrence of interference fringes in experiments where an initial Gaussian wave packet evolves inside a billiard domain with two slits on the boundary. Our simulation extends a previous work by Casati and Prosen and it is aimed to test their surprising result that the classical chaos of the billiards causes the disappearance of the fringes. Our investigation reveals a more complex phenomenon. Actually, we find out another factor that influences the interference patterns as well: a symmetry condition concerning the experimental set-up. This condition plays a very important role on its own. Indeed, irrespective of the classical integrability of the billiards, when it is verified the phase difference of the wave function at the slits is always zero, whereas when it is violated a varied dephasing at the slits is always present. We explain the respective roles of our symmetry condition and of classical chaos, by specifying the physical mechanism through which they influence the interference patterns. In particular, this mechanism depends both on the position and direction of the initial wave packet and on certain its recurrences which occur especially in the regular billiards.