Journal
PHYSICS LETTERS A
Volume 456, Issue -, Pages -Publisher
ELSEVIER
DOI: 10.1016/j.physleta.2022.128548
Keywords
Quantum scattering; One-dimensional tunneling; Time delay; Dwell time; Quantum trajectories
Categories
Funding
- French Agence Nationale de la Recherche (ANR-HYTRAJ)
- Robert A. Welch Foundation
- [ANR-19-CE30-0039-01]
- [D-1523]
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In this paper, an exact trajectory-ensemble reformulation of quantum mechanics is used to study the evolution of tunneling and reflection over time in a one-dimensional rectangular potential barrier. The quantum trajectory approach provides a robust, accurate, and efficient method for directly computing dwell time and time delay, and offers interesting physical insights into the tunneling process.
Among the numerous concepts of time in quantum scattering, Smith's dwell time (Smith, 1960 [7]) and Eisenbud & Wigner's time delay (Wigner, 1955 [12]) are the most well established. The dwell time represents the amount of time spent by the particle inside a given coordinate range (typically a potential barrier interaction region), while the time delay measures the excess time spent in the interaction region because of the potential. In this paper, we use the exact trajectory-ensemble reformulation of quantum mechanics, recently proposed by one of the authors (Poirier), to study how tunneling and reflection unfold over time, in a one-dimensional rectangular potential barrier. Among other dynamical details, the quantum trajectory approach provides an extremely robust, accurate, and straightforward method for directly computing the dwell time and time delay, from a single quantum trajectory. The resultant numerical method is highly efficient, and in the case of the time delay, completely obviates the traditional need to energy-differentiate the scattering phase shift. In particular, the trajectory variables provide a simple expression for the time delay that disentangles the contribution of the self-interference delay. More generally, quantum trajectories provide interesting physical insight into the tunneling process.(c) 2022 Elsevier B.V. All rights reserved.
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