  It is not widely appreciated that an acoustic wave can "jump" or "tunnel"
across a vacuum gap between two piezoelectric solids, nor has the general case
been formulated or studied in detail. Here, we remedy that situation, by
presenting a general formalism and approach to study such an acoustic tunneling
effect between two arbitrarily oriented anisotropic piezoelectric semi-infinite
crystals. The approach allows one to solve for the reflection and transmission
coefficients of all the partial wave modes, and is amenable to practical
numerical or even analytical implementation, as we demonstrate by a few chosen
examples. The formalism can be used in the future for quantitative studies of
the tunneling effect in connection not only with the manipulation of acoustic
waves, but with many other areas of physics of vibrations such as heat
transport, for example.
