Resonance-assisted tunneling in three degrees of freedom without discrete symmetry.

We study dynamical tunneling in a near-integrable Hamiltonian with three degrees of freedom. Despite the absence of discrete symmetry we show that the mixing of near-degenerate quantum states is due to dynamical tunneling mediated by the nonlinear resonances in the classical phase space. Identifying the key resonances allows us to selectively suppress the dynamical tunneling by adding weak counter-resonant terms.