Times of arrival and gauge invariance

Das, Siddhant and Nöth, Markus (2021): Times of arrival and gauge invariance. In: Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, Vol. 477, No. 2250, 20210101

Abstract

We revisit the arguments underlying two well-known arrival-time distributions in quantum mechanics, viz., the Aharonov-Bohm-Kijowski (ABK) distribution, applicable for freely moving particles, and the quantum flux (QF) distribution. An inconsistency in the original axiomatic derivation of Kijowski's result is pointed out, along with an inescapable consequence of the 'negative arrival times' inherent to this proposal (and generalizations thereof). The ABK free-particle restriction is lifted in a discussion of an explicit arrival-time set-up featuring a charged particle moving in a constant magnetic field. A natural generalization of the ABK distribution is in this case shown to be critically gauge-dependent. A direct comparison to the QF distribution, which does not exhibit this flaw, is drawn (its acknowledged drawback concerning the quantum backflow effect notwithstanding).

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 1364-5021
• Language: English