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Delay time and tunneling transient phenomena

Gaston Garcia-Calderon·Jorge Villavicencio
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Abstract

Analytic solutions to the time-dependent Schrödinger equation for cutoff wave initial conditions are used to investigate the time evolution of the transmitted probability density for tunneling. For a broad range of values of the potential barrier opacity $α$, we find that the probability density exhibits two evolving structures. One refers to the propagation of a {\it forerunner} related to a {\it time domain resonance} [Phys. Rev. A {\bf 64}, 0121907 (2001)], while the other consists of a semiclassical propagating wavefront. We find a regime where the {\it forerunners} are absent, corresponding to positive {\it time delays}, and show that this regime is characterized by opacities $α< α_c$. The critical opacity $α_c$ is derived from the analytical expression for the {\it delay time}, that reflects a link between transient effects in tunneling and the {\it delay time}

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Gaston Garcia-Calderon, Jorge Villavicencio. 2002-10-01. Delay time and tunneling transient phenomena. https://doi.org/10.1103/physreva.66.032104

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