  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
conclusion that the fringes disappear in the experiments with fully chaotic
billiards. According to the results found, we are led to reassess this
remarkable effect of classical dynamics on quantum interference. Actually, we
highlight another factor which acts on interference: a symmetry condition (SC)
concerning the experimental set-up. This condition seems even to play a role
more important than classical chaos. Indeed, when the SC is verified, classical
chaos has no effect, whereas when the SC is violated classical chaos turns out
to be an additional factor that causes dephasing at the slits. We explain the
respective roles of these two factors, by specifying the physical mechanism
through which they influence the interference patterns. 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.
