标题： 从激发态的量子隧道效应：从实时间分析中恢复虚时间瞬子 显示英文标题

标题： Quantum tunneling from excited states: Recovering imaginary-time instantons from a real-time analysis

摘要： 我们重新审视量子隧穿的路径积分描述，并展示如何将其推广到激发态。为了清晰起见，我们将注意力集中在单势垒粒子的简单玩具模型上，并明确执行所有步骤。我们没有采用从物理时间到虚时间的熟悉维克旋转（这种旋转在处理激发态隧穿时与必要的边界条件不一致），而是通过在哈密顿量中加入一个无穷小的复贡献来正则化路径积分，同时保持时间严格为实数。我们发现这会引出一个复数的驻相解，这与最近来自皮卡-莱夫谢茨理论的见解一致。然后，我们证明了对于相应的运动方程存在一类解析解，这些解可以在调节参数趋于零且物理时间趋于无穷大的物理相关极限下满足适当的边界条件。我们详细讨论了这一非平凡的极限。我们发现，对于没有显式时间依赖性的系统，我们的方法再现了有限欧几里得时间间隔上的类似瞬子解的图像。最后，我们讨论了将这种方法推广到更广泛的系统类别的可能性，对于这些系统，它作为一个可靠的高精度计算框架。 显示英文摘要

摘要： We revisit the path integral description of quantum tunneling and show how it can be generalized to excited states. For clarity, we focus on the simple toy model of a point particle in a double-well potential, for which we perform all steps explicitly. Instead of performing the familiar Wick rotation from physical to imaginary time - which is inconsistent with the requisite boundary conditions when treating tunneling from excited states - we regularize the path integral by adding an infinitesimal complex contribution to the Hamiltonian, while keeping time strictly real. We find that this gives rise to a complex stationary-phase solution, in agreement with recent insights from Picard-Lefshitz theory. We then show that there exists a class of analytic solutions for the corresponding equations of motion, which can be made to match the appropriate boundary conditions in the physically relevant limits of a vanishing regulator and an infinite physical time. We provide a detailed discussion of this non-trivial limit. We find that, for systems without an explicit time-dependence, our approach reproduces the picture of an instanton-like solution defined on a finite Euclidean-time interval. Lastly, we discuss the generalization of our approach to broader classes of systems, for which it serves as a reliable framework for high-precision calculations.