In case of a double well potential, particle can tunnel from one well to another and this process is known as quantum tunneling or tunneling in general. I want to know about dynamical tunneling and how it is different from the simple tunneling.
Quantum tunneling through a barrier is described here
Note that the energy of the tunneling particle stays constant, it is the probability amplitude that changes.
For dynamical tunneling I found this abstract clear:
The divergence of quantum and classical descriptions of particle motion is clearly apparent in quantum tunnelling1, between two regions of classically stable motion. An archetype of such non-classical motion is tunnelling through an energy barrier. In the 1980s, a new process, ‘dynamical’ tunnelling was predicted, involving no potential energy barrier; however, a constant of the motion (other than energy) still forbids classically the quantum-allowed motion. This process should occur, for example, in periodically driven, nonlinear hamiltonian systems with one degree of freedom. Such systems may be chaotic, consisting of regions in phase space of stable, regular motion embedded in a sea of chaos. Previous studies predicted dynamical tunnelling between these stable regions. Here we observe dynamical tunnelling of ultracold atoms from a Bose–Einstein condensate in an amplitude-modulated optical standing wave. Atoms coherently tunnel back and forth between their initial state of oscillatory motion (corresponding to an island of regular motion) and the state oscillating 180° out of phase with the initial state.
And here is a review.