Semiclassical description of chaos-assisted tunneling

We study tunneling between regular and chaotic regions in the phase space of Hamiltonian systems. We analytically calculate the transition rate and show that its variation depends only on corresponding phase space area and in this sense is universal. We derive the distribution of level splittings associated with the pairs of quasidegenerate regular eigenstates which in the general case is different from a Cauchy distribution. We show that chaos-assisted tunneling leads to level repulsion between regular eigenstates, solving the longstanding problem of level-spacing distribution in mixed systems.