Instantaneous tunneling time within the theory of time-of-arrival operators

• URL: http://arxiv.org/abs/2409.12389v1
• Date: Thu, 19 Sep 2024 01:26:40 GMT
• Title: Instantaneous tunneling time within the theory of time-of-arrival operators
• Authors: Philip Caesar Flores, Dean Alvin Pablico, Eric Galapon,
• Abstract summary: Quantum tunneling is instantaneous using a time-of-arrival operator constructed by Weyl quantization of the classical TOA. But there are infinitely many possible quantum images of the classical TOA, leaving it unclear if one is uniquely preferred over the others. Here, we demonstrate that tunneling time vanishes for all possible quantum images of the classical arrival time, irrespective of the ordering rule between the position and momentum observables.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: It has been shown in \href{https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.108.170402}{\textit{Phys. Rev. Lett.}, \textbf{108} 170402 (2012)}, that quantum tunneling is instantaneous using a time-of-arrival (TOA) operator constructed by Weyl quantization of the classical TOA. However, there are infinitely many possible quantum images of the classical TOA, leaving it unclear if one is uniquely preferred over the others. This raises the question on whether instantaneous tunneling time is simply an artifact of the chosen ordering rule. Here, we demonstrate that tunneling time vanishes for all possible quantum images of the classical arrival time, irrespective of the ordering rule between the position and momentum observables. The result still holds for TOA-operators that are constructed independent of canonical quantization, while still imposing the correct algebra defined by the time-energy canonical commutation relation.

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