Observing quantum tunneling in perturbation series

We apply Borel resummation to the conventional perturbation series of ground state energy in a metastable potential, V(x) = x22 − gx44. We observe numerically that the discontinuity of the Borel transform reproduces the imaginary part of the energy eigenvalue, i.e., the total decay width due to quantum tunneling. The agreement with the exact numerical value is remarkable in the whole tunneling regime 0 < g ≲ 0.7.