RESUMO
We discover that quantum dynamical tunneling, occurring between phase space regions in a classically forbidden way, can break conserved quantities. We rigorously prove that a conserved quantity in a class of typical pseudointegrable systems can be broken quantum mechanically. We then numerically compute the uncertainties of this broken conserved quantity, which remain nonzero for up to 10^{5} eigenstates and exhibit universal distributions similar to energy level statistics. Furthermore, all the eigenstates with large uncertainties show the superpositions of regular orbits with different values of the conserved quantity, showing definitive manifestation of dynamical tunneling. A random matrix model is constructed to successfully reproduce the level statistics of pseudointegrable systems.
