JonaLasinio G., Presilla C., Capasso F. Quantum Chaos Without Classical Counterpart (20K, apsTeX2.0) ABSTRACT. We describe a quantum many-body system undergoing multiple resonant tunneling which exhibits chaotic behavior in numerical simulations of a mean field approximation. This phenomenon, which has no counterpart in the classical limit, is due to effective nonlinearities in the tunneling process and can be observed in principle within a heterostructure.