Delay time and tunneling transient phenomena

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 $\alpha$, 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 $\alpha <{\alpha }_c$. The critical opacity ${\alpha }_c$ 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}

To be published in Physical Review A

Cited by in corpus (4)

• Time Delay Plots of Unflavoured Baryons
• Time delays and advances in classical and quantum systems
• Transient time-domain resonances and the time scale for tunneling
• Semiclassical Tunneling of Wavepackets with Real Trajectories