Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE International Conference Nanomaterials: Applications & Properties (NAP)

Tunneling of wave packages through resonant quantum systems

N. A. Ivanov, Natalia Yu. Filonenko

Published Sep 1, 2017• 0 citations
Publisher

Abstract

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.

DOI
10.1109/nap.2017.8190291

Related papers

Tunneling of rectangular wave packages through resonant quantum systems

N. A. Ivanov, V. V. Skalozub

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.

International Conference on Mathematical Methods in Electromagnetic Theory•Aug 1, 2014•0 citations

Transmission of wave packets through open mesoscopic systems

N. A. Ivanov, V. V. Skalozub

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.

•Jan 1, 2012•0 citations

Time delay of wave packets during their tunnelling through a quantum diode

N. A. Ivanov, V. V. Skalozub

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.

Quantum Electronics•Apr 28, 2014•0 citations

Tunneling time through a rectangular barrier

Verissimo Manoel de Aquino, Valdir C. Aguilera-Navarro, Mário Goto +1 more

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.

Physical Review A•Dec 1, 1998•28 citations

Tunneling and delay time of cutoff Gaussian wave packets

Jorge Villavicencio, Roberto Romo, Elmer Cruz

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.

Physical Review A•Jan 23, 2007•17 citations

Reflection of wave packets from a quantum well with a tunneling transmission resonance

A Gomez Edgar

The reflection of wave packets from a quantum well bounded by rectangular potential barriers, and which has a tunneling transmission resonance, is discussed. Numeric solutions to Schrödinger’s time-dependent equation show that the shape of the probability function ψψ* for a reflected wave packet can be quite different from that of the incident packet. Either a symmetric double hump or an asymmetric shape are possible for the reflected ψψ*, depending on the sharpness of the resonance. These shapes are explained analytically in terms of the reflection coefficient.

American Journal of Physics•Feb 1, 1995•8 citations
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.
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.
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.
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.
The reflection of wave packets from a quantum well bounded by rectangular potential barriers, and which has a tunneling transmission resonance, is discussed. Numeric solutions to Schrödinger’s time-dependent equation show that the shape of the probability function ψψ* for a reflected wave packet can be quite different from that of the incident packet. Either a symmetric double hump or an asymmetric shape are possible for the reflected ψψ*, depending on the sharpness of the resonance. These shapes are explained analytically in terms of the reflection coefficient.