Chaos-assisted instanton tunneling in one-dimensional perturbed periodic potential

For the system with a one-dimensional spatially periodic potential we demonstrate that small periodic in-time perturbation results in the appearance of chaotic instanton solutions. We estimate the parameter of local instability, the width of the stochastic layer, and the correlator for perturbed instanton solutions. The application of the instanton technique enables us to calculate the amplitude of the tunneling, the form of the spectrum, and the lower bound for the width of the ground quasienergy zone.