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Time of arrival in the presence of interactions

J. Leon·J. Julve·P. Pitanga·F. J. de Urries
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Abstract

We introduce a formalism for the calculation of the time of arrival t at a space point for particles traveling through interacting media. We develop a general formulation that employs quantum canonical transformations from the free to the interacting cases to construct t in the context of the Positive Operator Valued Measures. We then compute the probability distribution in the times of arrival at a point for particles that have undergone reflection, transmission or tunneling off finite potential barriers. For narrow Gaussian initial wave packets we obtain multimodal time distributions of the reflected packets and a combination of the Hartman effect with unexpected retardation in tunneling. We also employ explicitly our formalism to deal with arrivals in the interaction region for the step and linear potentials.

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J. Leon, J. Julve, P. Pitanga, F. J. de Urries. 2000-02-02. Time of arrival in the presence of interactions. https://doi.org/10.1103/physreva.61.062101

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