Unraveling the bounce: a real time perspective on tunneling
- URL: http://arxiv.org/abs/2309.07585v1
- Date: Thu, 14 Sep 2023 10:35:39 GMT
- Title: Unraveling the bounce: a real time perspective on tunneling
- Authors: Kfir Blum and Omri Rosner
- Abstract summary: We study tunneling in one-dimensional quantum mechanics using the path integral in real time, where solutions of the classical equation of motion live in the complex plane.
We show explicitly how the imaginary time bounce arises as a parameterization of the lowest order term in the energy expansion.
- Score: 0.0
- License: http://creativecommons.org/publicdomain/zero/1.0/
- Abstract: We study tunneling in one-dimensional quantum mechanics using the path
integral in real time, where solutions of the classical equation of motion live
in the complex plane. Analyzing solutions with small (complex) energy, relevant
for constructing the wave function after a long time, we unravel the analytic
structure of the action, and show explicitly how the imaginary time bounce
arises as a parameterization of the lowest order term in the energy expansion.
The real time calculation naturally extends to describe the wave function in
the free region of the potential, reproducing the usual WKB approximation. The
extension of our analysis to the semiclassical correction due to fluctuations
on the saddle is left for future work.
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