Title: A new picture of quantum tunneling in the real-time path integral from Lefschetz thimble calculations Show Chinese title

Title: 勒夫谢茨流形计算中实时路径积分的量子隧道新图景

Abstract: It is well known that quantum tunneling can be described by instantons in the imaginary-time path integral formalism. However, its description in the real-time path integral formalism has been elusive. Here we establish a statement that quantum tunneling can be characterized in general by the contribution of complex saddle points, which can be identified by using the Picard-Lefschetz theory. We demonstrate this explicitly by performing Monte Carlo simulations of simple quantum mechanical systems, overcoming the sign problem by the generalized Lefschetz thimble method. We confirm numerically that the contribution of complex saddle points manifests itself in a complex ``weak value'' of the Hermitian coordinate operator $\hat{x}$ evaluated at time $t$, which is a physical quantity that can be measured by experiments in principle. We also discuss the transition to classical dynamics based on our picture. Show Chinese abstract

Abstract: 众所周知，量子隧穿可以通过虚时间路径积分形式主义中的瞬子来描述。然而，在实时间路径积分形式主义中的描述却一直难以捉摸。在这里，我们提出了一种陈述，即量子隧穿通常可以由复数驻点的贡献来表征，这些驻点可以通过使用皮卡-勒夫谢兹理论来识别。我们通过对简单的量子力学系统进行蒙特卡洛模拟来明确展示这一点，通过广义勒夫谢兹流形方法克服了符号问题。我们数值确认了在时间$t$评估的厄米算符$\hat{x}$的“弱值”的复数贡献，这是一个原则上可以通过实验测量的物理量。我们还基于我们的图景讨论了经典动力学的过渡。