Instantaneous tunneling time within the theory of time-of-arrival operators
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| Format: | Preprint |
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2024
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| _version_ | 1866913601876393984 |
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| author | Flores, Philip Caesar Pablico, Dean Alvin Galapon, Eric |
| author_facet | Flores, Philip Caesar Pablico, Dean Alvin Galapon, Eric |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_12389 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Instantaneous tunneling time within the theory of time-of-arrival operators Flores, Philip Caesar Pablico, Dean Alvin Galapon, Eric Quantum Physics Mathematical Physics 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. |
| title | Instantaneous tunneling time within the theory of time-of-arrival operators |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2409.12389 |