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

Physical Review A

Resonance poles in the complex-frequency domain for an oscillating barrier

R. Lefèbvre, Nimrod Moiseyev

Published Jun 14, 2004• 10 citations
Publisher

Abstract

The transmissivity calculated as a function of the frequency of oscillation for a particle meeting an oscillating barrier presents a resonant structure, as shown by Hagmann [Appl. Phys. Lett. 66, 789 (1995)]. The origin of this structure is explained with the help of the expression giving the scattering amplitudes in the Floquet picture applied to a periodic Hamiltonian. It is possible to interpret it as due to the poles of the scattering amplitudes in the complex-frequency domain. For a moderate modulation amplitude the analysis makes use of the data obtained for the static barrier. The existence of these poles is not limited to the present model.

DOI
10.1103/physreva.69.062105

Related papers

Scattering by an oscillating resonance

R. Lefèbvre, Osman Atabek

We consider the scattering of a particle by an oscillating rectangular barrier at energies matching with the above barrier resonances. A resonance associated with the barrier has an energy which oscillates in time. With appropriately defined parameters it is possible, using a calculation entirely based on the time-independent scattering amplitudes, to show that the transmission probability is enhanced when the wave packet describing the particle arrives on the device at a time when the resonance energy matches the energy of the particle.

Molecular Physics•Jun 10, 2007•0 citations

Collapse of transmissivity in a triple barrier

Roland Lefebvre, Osman Atabek, R. Lefèbvre +1 more

Abstract One generally expects that the transmissivity through a symmetric arrangement of barriers and wells should go to unity when the energy of the incident particle coincides with a resonance energy of the system. It has been noticed before that for a symmetric triple barrier, there are conditions that lead to a merging of the two lowest unit transmissivity peaks, accompanied by a collapse of the transmissivity profile. This feature has been interpreted as meaning that there is a reduction of the number of resonances under these conditions. We reanalyze this situation with the help of a model that involves the same number of bound and continuum states, but which possesses an analytic solution. Because the transition probability in this case is expressed entirely in terms of resonance parameters (positions and widths), it is possible to calculate with the expression derived from the model a profile that agrees completely with that calculated with the transfer matrix method. The resonance parameters are obtained from the poles of the transition amplitude. This shows that the merging of the peaks and the collapse of the transmissivity occurs without a reduction in the number of resonances.

Israel Journal of Chemistry•Dec 1, 2003•0 citations

Application of Green’s-Function techniques to quantum barrier penetration problems

Rahul K Singh, Durgesh Dixena, Dwas Lal +1 more

We obtain a mathematical and algebraic expression of the Green-function method in treating quantum tunnelling in one-dimensional barrier systems. The retarded Green's function of the free-particle resolvent is then obtained consistently to obtain scattering amplitudes using the Lippmann-Schwinger equation. The technique is used to apply to the d-function barrier, the finite square barrier, and the double-barrier quantum-well structure in order to describe the transmission, penetration of the barrier, and resonance. With the Green, the pole structure in the case of the double-barrier directly traces the quasi-bound and the Breit-Wigner-type resonances.

International Journal of Physics and Mathematics•Jul 1, 2025•0 citations

Stabilizing quantum metastable states in a time-periodic potential

Choon-Lin Ho, Chung‐Chieh Lee

Metastability of a particle trapped in a well with a time-periodically oscillating barrier is studied in the Floquet formalism. It is shown that the oscillating barrier causes the system to decay faster in general. However, avoided crossings of metastable states can occur with the less stable states crossing over to the more stable ones. If in the static well there exists a bound state, then it is possible to stabilize a metastable state by adiabatically increasing the oscillating frequency of the barrier so that the unstable state will eventually cross over to the stable bound state. It is also found that increasing the amplitude of the oscillating field may change a direct crossing of states into an avoided one.

arXiv:quant-ph/0404150•Physical Review A•Jan 7, 2005•11 citations

Resonance scattering in a waveguide with identical thick barriers

A. L. Delitsyn, Denis S. Grebenkov

We consider wave propagation across an infinite waveguide of an arbitrary bounded cross-section, whose interior is blocked by two identical thick barriers with holes. When the holes are small, the waves over a broad range of frequencies are almost fully reflected. However, we show the existence of a resonance frequency at which the wave is almost fully transmitted, even for very small holes. This resonance scattering, which is known as tunneling effect in quantum mechanics, is demonstrated in a constructive way by rather elementary tools, in contrast to commonly used abstract methods such as searching for complex-valued poles of the scattering matrix or non-stationary scattering theory. In particular, we derived an explicit equation that determines the resonance frequency. The employed elementary tools make the paper accessible to non-experts and educationally appealing.

arXiv:2001.07060•Jan 20, 2020•1 citation

Modulated barrier approach to the interaction time in tunneling for arbitrary potentials

Th. Martin, Rolf W. Landauer

The time that a transmitted particle interacts with a tunneling barrier is evaluated in one of the principal existing approaches by considering a small oscillatory perturbation added to the static barrier. The modulation frequency, at which a serious deviation from quasistatic behavior appears, is indicative of the traversal time. This approach is extended here, to a long region including the barrier, and utilizing a modulation potential which is spatially uniform throughout this region, except in the incident region ahead of the actual barrier, where it is made sufficiently smooth to avoid reflections. The resulting traversal time is \ensuremath{\Elzxh}\ensuremath{\partial} ln[\ensuremath{\partial}t/\ensuremath{\partial}E]/\ensuremath{\partial}E, where the complex transmission coefficient t(E) is defined as the ratio of the wave function at the far end to that at the point of incidence. This answer applies to arbitrary potentials and to all energies, including both propagation and tunneling in a single framework. This result is closely related to, but not identical to, that obtained by another earlier approach in which the potential is fixed, but the incident amplitude is modulated.

Physical Review A•Mar 1, 1993•33 citations
The transmissivity calculated as a function of the frequency of oscillation for a particle meeting an oscillating barrier presents a resonant structure, as shown by Hagmann [Appl. Phys. Lett. 66, 789 (1995)]. The origin of this structure is explained with the help of the expression giving the scattering amplitudes in the Floquet picture applied to a periodic Hamiltonian. It is possible to interpret it as due to the poles of the scattering amplitudes in the complex-frequency domain. For a moderate modulation amplitude the analysis makes use of the data obtained for the static barrier. The existence of these poles is not limited to the present model.
We consider the scattering of a particle by an oscillating rectangular barrier at energies matching with the above barrier resonances. A resonance associated with the barrier has an energy which oscillates in time. With appropriately defined parameters it is possible, using a calculation entirely based on the time-independent scattering amplitudes, to show that the transmission probability is enhanced when the wave packet describing the particle arrives on the device at a time when the resonance energy matches the energy of the particle.
Abstract One generally expects that the transmissivity through a symmetric arrangement of barriers and wells should go to unity when the energy of the incident particle coincides with a resonance energy of the system. It has been noticed before that for a symmetric triple barrier, there are conditions that lead to a merging of the two lowest unit transmissivity peaks, accompanied by a collapse of the transmissivity profile. This feature has been interpreted as meaning that there is a reduction of the number of resonances under these conditions. We reanalyze this situation with the help of a model that involves the same number of bound and continuum states, but which possesses an analytic solution. Because the transition probability in this case is expressed entirely in terms of resonance parameters (positions and widths), it is possible to calculate with the expression derived from the model a profile that agrees completely with that calculated with the transfer matrix method. The resonance parameters are obtained from the poles of the transition amplitude. This shows that the merging of the peaks and the collapse of the transmissivity occurs without a reduction in the number of resonances.
We obtain a mathematical and algebraic expression of the Green-function method in treating quantum tunnelling in one-dimensional barrier systems. The retarded Green's function of the free-particle resolvent is then obtained consistently to obtain scattering amplitudes using the Lippmann-Schwinger equation. The technique is used to apply to the d-function barrier, the finite square barrier, and the double-barrier quantum-well structure in order to describe the transmission, penetration of the barrier, and resonance. With the Green, the pole structure in the case of the double-barrier directly traces the quasi-bound and the Breit-Wigner-type resonances.
Metastability of a particle trapped in a well with a time-periodically oscillating barrier is studied in the Floquet formalism. It is shown that the oscillating barrier causes the system to decay faster in general. However, avoided crossings of metastable states can occur with the less stable states crossing over to the more stable ones. If in the static well there exists a bound state, then it is possible to stabilize a metastable state by adiabatically increasing the oscillating frequency of the barrier so that the unstable state will eventually cross over to the stable bound state. It is also found that increasing the amplitude of the oscillating field may change a direct crossing of states into an avoided one.
We consider wave propagation across an infinite waveguide of an arbitrary bounded cross-section, whose interior is blocked by two identical thick barriers with holes. When the holes are small, the waves over a broad range of frequencies are almost fully reflected. However, we show the existence of a resonance frequency at which the wave is almost fully transmitted, even for very small holes. This resonance scattering, which is known as tunneling effect in quantum mechanics, is demonstrated in a constructive way by rather elementary tools, in contrast to commonly used abstract methods such as searching for complex-valued poles of the scattering matrix or non-stationary scattering theory. In particular, we derived an explicit equation that determines the resonance frequency. The employed elementary tools make the paper accessible to non-experts and educationally appealing.
The time that a transmitted particle interacts with a tunneling barrier is evaluated in one of the principal existing approaches by considering a small oscillatory perturbation added to the static barrier. The modulation frequency, at which a serious deviation from quasistatic behavior appears, is indicative of the traversal time. This approach is extended here, to a long region including the barrier, and utilizing a modulation potential which is spatially uniform throughout this region, except in the incident region ahead of the actual barrier, where it is made sufficiently smooth to avoid reflections. The resulting traversal time is \ensuremath{\Elzxh}\ensuremath{\partial} ln[\ensuremath{\partial}t/\ensuremath{\partial}E]/\ensuremath{\partial}E, where the complex transmission coefficient t(E) is defined as the ratio of the wave function at the far end to that at the point of incidence. This answer applies to arbitrary potentials and to all energies, including both propagation and tunneling in a single framework. This result is closely related to, but not identical to, that obtained by another earlier approach in which the potential is fixed, but the incident amplitude is modulated.