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Transmission of wave packets through open mesoscopic systems

N. A. Ivanov, V. V. Skalozub

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

Tunneling of the wave packets having rectangular and Gaussian forms through a quantum diode is investigated. By using the potential of the system the S-matrix for this structure is obtained and the analytic expressions describing the form of the transmitted pulse are calculated. These analytic solutions are compared with the numeric ones. An excellent coincidence is detected. The time-delay for the Gaussian pulse tunneling through the quantum dot is investigated in details.

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Tunneling of the wave packets having rectangular and Gaussian forms through a quantum diode is investigated. By using the potential of the system the S-matrix for this structure is obtained and the analytic expressions describing the form of the transmitted pulse are calculated. These analytic solutions are compared with the numeric ones. An excellent coincidence is detected. The time-delay for the Gaussian pulse tunneling through the quantum dot is investigated in details.
Tunneling of wave packages through resonant quantum systems presented in an S-matrix form is investigated. An arbitrary incident wave package can be written as the superposition of the Gaussian-form pulses and for latter ones the exact analytic solution was obtained already. As a practically interesting case, the transition of the rectangular wave package through the one-resonant level system is considered. Using developed recently modified saddle-points method the time-delay (Δt) of the wave pulses having Gaussian and rectangular form transmitted through a quantum system with resonance level is investigated. The time delay, argument and amplitude of the outgoing wave are calculated. The dependency Δt from width and energy of resonance levels, and the momentum of incident wave-package are illustrated. The results are compared with the ones obtained for tunneling of the one Gaussian package. Possible applications are discussed.
A modified saddle-point method is used to investigate the process of propagation of a wave packet through a quantum diode. A scattering matrix is constructed for the structure in question. The case of tunnelling of a packet with a Gaussian envelope through the diode is considered in detail. The time delay and the shape of the wave packet transmitted are calculated. The dependence of the delay time on the characteristics of the input packet and the internal characteristics of the quantum diode is studied. Possible applications of the results obtained are discussed.
Tunneling of wave packages through resonant quantum systems presented in an S-matrix form is investigated. An arbitrary incident wave package can be written as the superposition of the Gaussian-form pulses and for latter ones the exact analytic solution was obtained already. As a practically interesting case, the transition of the rectangular wave package through a one-resonant level system is considered. Using developed recently modified saddle-points method the transition of the wave package having a Gaussian and a rectangular form is investigated. The time delay, argument and amplitude of the outgoing wave are calculated. The dependence of tunneling time on the width and energy of resonance levels, and the momentum of incident wave-package are illustrated. The results are compared with the ones obtained for tunneling of the one Gaussian package. Possible applications are discussed.
In this paper, we discuss the tunneling time of a quantum particle through a rectangular barrier. The reflection and transmission times associated with the wave packets representing the particle are discussed. By using an initial Gaussian momentum distribution, we carry out a comparative analysis of the stationary phases of the incident, reflected, and transmitted wave packets leading to the reflection and transmission times $\ensuremath{\Delta}{t}_{R}$ and $\ensuremath{\Delta}{t}_{T},$ respectively. In the present treatment of this old and very known problem we take into account the deformations of the reflected and transmitted momentum distributions. These deformations produce a dependence of the reflection and transmission times on the location of the initial wave packet. In a parallel calculation, by numerically monitoring the time evolution of the system, we characterize a reflection and a transmission time. Such times agree with the ones obtained via the stationary phase method.
A formal analytic solution of the time-dependent Schr\"odinger equation is obtained for cutoff Gaussian wavepackets incident on finite range potentials of arbitrary shape. We derive closed analytical expressions for transmitted wavepackets with a small cutoff and the solutions are applied to investigate the dynamics of wavepacket tunneling. We showed that the analytic solutions satisfy a useful rescaling property that was applied to study and characterize the delay time in delta potential barriers.
Abstract We examine the tunnelling process of incident Hermite-Gaussian wavepackets which feature several nodes and peaks. An analytic formula for the transmitted wave function is developed which applies to arbitrary incident wave functions and potential barriers with known transmission amplitudes. This formula permits the accurate numerical calculation of the transmitted wave packet, even when the transmission probability is extremely small. For square potential barriers, the shape of the transmitted packet, its relationship to the shape of the incident packet, the momentum of the transmitted packet, and the duration of the tunnelling process are investigated. The shape of the reconstructed transmitted wave packet is also studied for the smooth repulsive Pöschl-Teller potential.