Title:  A Stochastic Approach to Time-of-Arrival in Quantum Mechanics and its Applications to Free-Falling Systems

Speaker: Mathieu Beau

Date: Tuesday, November 5th, 2024
Time: 12:00 pm-1:00 pm
Location: EXP-610A

Abstract: The concept of time in quantum mechanics presents unique challenges, particularly concerning the measurement of time-of-arrival (TOA), which lacks a formal mathematical treatment within the standard quantum theory. In this presentation, we propose a stochastic approach to TOA, employing the Born rule and probabilistic techniques to rigorously derive TOA distributions for both Gaussian and non-Gaussian quantum systems.

We begin by addressing the underlying mathematical problem of time in quantum mechanics, focusing on why time cannot be treated as an observable within the conventional framework. We then introduce an experimental protocol for measuring TOA and present a mathematical formulation of TOA using a random variable. A general formula for the TOA distribution is derived, first in the Gaussian case and then extended to more complex non-Gaussian systems. As a case study, we apply this approach to a free-falling quantum particle, demonstrating how quantum corrections introduce a measurable delay in comparison to classical free-fall times. Furthermore, we demonstrate the existence of a novel uncertainty relation between TOA and position measurements, underscoring their mutual exclusiveness. Finally, we explore the broader mathematical implications of these results and extensions to more abstract systems such as spin systems and open quantum systems


Bio: Mathieu Beau is a research associate at the University of Massachusetts Boston and a mathematics teacher at the International School of Boston. He earned his Ph.D. in Theoretical and Mathematical Physics from the University of Marseille, France, in 2010. He held postdoctoral positions at the Dublin Institute for Advanced Studies and the University of Massachusetts Boston before transitioning to high school teaching in 2017. While teaching at the high school level, Mathieu Beau has continued to publish articles in international journals on quantum physics and mathematical physics.