Quantum Chaos in Quantum Wells

We develop a quantitative semiclassical theory for the resosnant tunneling through a quantum well in a tilted magnetic field. It is shown, that in the leading semiclassical approximation the tunneling current depends only on periodic orbits within the quantum well. Further corrections (due to e.g. "ghost" effect) can be expressed in terms of closed, but non-periodic orbits, started at the "injection point". The results of the semiclassical theory are shown to be in good agreement with both the experimental data and numerical calculations.