We investigate the semiclassical mechanism of tunneling process in
non-integrable systems. The significant role of complex-phase-space chaos in
the description of the tunneling process is elucidated by studying a simple
scattering map model. Behaviors of tunneling orbits are encoded into symbolic
sequences based on the structure of complex homoclinic tanglement. By means of
the symbolic coding, the phase space itineraries of tunneling orbits are
related with the amounts of imaginary parts of actions gained by the orbits, so
that the systematic search of significant tunneling orbits becomes possible.Comment: 26 pages, 28 figures, submitted to Physical Review
