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

2024/09/19 by Philip Caesar Flores, Flores, Philip Caesar, Dean Alvin L. Pablico +3 · 1 citation
Physics and Astronomy · Computer Science · #Quantum optics and atomic interactions #Network Time Synchronization Technologies #Advanced Optical Sensing Technologies

paper · pdf · doi:10.48550/arxiv.2409.12389

Abstract

It has been shown in Phys. Rev. Lett., 108 170402 (2012) (https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.108.170402), 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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• Canonical pairs in finite-dimensional Hilbert space

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