Quantum tunneling in the real-time path integral by the Lefschetz thimble method

Abstract

Quantum tunneling is mostly discussed in the Euclidean path integral formalism using instantons. On the other hand, it is difficult to understand quantum tunneling based on the real-time path integral due to its oscillatory nature, which causes the notorious sign problem. We show that recent development of the Lefschetz thimble method enables us to investigate this issue numerically. In particular, we find that quantum tunneling occurs due to complex trajectories, which are actually observable experimentally by using the so-called weak measurement.