Complex-time approach for semi-classical quantum tunneling
Hideaki Aoyama, Toshiyuki Harano
TL;DR
This paper develops a complex-time method for analyzing quantum tunneling in one-dimensional systems, deriving a Green function reduction formula based on WKB approximation that sums over complex-time paths.
Contribution
It introduces a novel reduction formula for Green functions in quantum tunneling, connecting complex-time paths with WKB approximation.
Findings
Derived a Green function reduction formula for tunneling
Interpreted the series as a sum over complex-time paths
Determined weights for the complex-time paths
Abstract
The complex-time method for quantum tunneling is studied. In one-dimensional quantum mechanics, we construct a reduction formula for a Green function in the number of turning points based on the WKB approximation. This formula yields a series, which can be interpreted as a sum over the complex-time paths. The weights of the paths are determined.
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