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

TL;DR

This paper demonstrates that the Lefschetz thimble method allows for numerical investigation of quantum tunneling in real-time path integrals, revealing complex trajectories as observable phenomena through weak measurements.

Contribution

It introduces a novel application of the Lefschetz thimble method to analyze quantum tunneling in real-time path integrals, overcoming the sign problem.

Findings

Quantum tunneling occurs via complex trajectories.

Complex trajectories are observable with weak measurements.

The Lefschetz thimble method enables numerical study of real-time tunneling.

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.