Energy splitting in dynamical tunneling

Abstract

We propose an operator method for calculating the semiclassical asymptotic form of the energy splitting value in the general case of tunneling between symmetric orbits in the phase space. We use this approach in the case of a particle on a circle to obtain the asymptotic form of the energy tunneling splitting related to the over-barrier reflection from the potential. As an example, we consider the quantum pendulum in the rotor regime.