A new picture of quantum tunneling in the real-time path integral from Lefschetz thimble calculations

A bstract It is well known that quantum tunneling can be described by instantons in the imaginary-time path integral formalism. However, its description real-time formalism has been elusive. Here we establish a statement characterized general contribution of complex saddle points, which identified using Picard-Lefschetz theory. We demonstrate this explicitly performing Monte Carlo simulations simple mechanical systems, overcoming sign problem generalized Lefschetz thimble method. confirm numerically points manifests itself “weak value” Hermitian coordinate operator $$ \hat{x} x ̂ evaluated at time t , physical quantity measured experiments principle. also discuss transition to classical dynamics based on our picture.