Transmission properties of the oscillating δ-function potential

Martinez, Dario; Reichl, L. E.

doi:10.1103/physrevb.64.245315

Cited by 55 publications

(42 citation statements)

References 18 publications

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“…A continued fraction representation of t 0 ðEÞ for the classical case has been derived recently by Martinez and Reichl [6]. The corresponding matrix defining the transmission amplitudes t cl ¼ ð. .…”

Section: Comparison To the Classical Casementioning

confidence: 99%

Transmission through a Quantum Dynamical Delta Barrier

Brandes

Robinson

2002

phys. stat. sol. (b)

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We discuss electron scattering in a one-dimensional delta barrier potential with either a time-dependent coupling constant (classical model) or a coupling constant that is linear in a boson coordinate (quantum model). We find an exact continued fraction solution and Fano like resonances in the transmission coefficient. In the quantum model, energies for perfect transmission exist below the first sideband threshold. Introduction and ModelSimple models for the interaction between fermions and bosons continue to be fascinating, as often very non-trivial results can be obtained from even the most primitive Hamiltonians. Exactly solvable models for the interaction of photons or phonons with electrons in quantum dots [1] or quasi-one-dimensional systems [2, 3] provide the best examples, as they often provide a deep insight into rich and complex physics.In this contribution, we re-consider a simple model for a single electron of mass m in one dimension that interacts with a delta-barrier through a coupling parameter that itself is a dynamical quantity. The Hamiltonian is written as

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Section: Comparison To the Classical Casementioning

confidence: 99%

Transmission through a Quantum Dynamical Delta Barrier

Brandes

Robinson

2002

phys. stat. sol. (b)

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“…Transport through a time-dependent (mostly periodically oscillating) potential is also a subject of increasing importance, with a growing number of applications [14][15][16][17][18][19][20][21]. One of the important features here is that an oscillating potential can transfer an incoming electron of energy E with finite probability to 'Floquet' sidebands at E ± nhω, where n is an integer and ω is the angular frequency of the oscillation.…”

Section: Introductionmentioning

confidence: 99%

Quasibound states at thresholds in multichannel impurity scattering

Kim

Park

Sim

et al. 2003

J. Phys. A: Math. Gen.

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We investigate the threshold behavior of transmission resonances and quasibound states in the multichannel scattering problems of a one dimensional (1D) time-dependent impurity potential, and the related problem of a single impurity in a quasi 1D wire. It was claimed before in the literature that a quasibound state disappears when a transmission zero collides with the subband boundary. However, the transmission line shape, the Friedel sum rule, and the delay time show that the quasibound states still survive and affect the physical quantities. We discuss the relation between threshold behavior of transmission resonances, and quasibound states and their boundary conditions in the general context of multichannel scatterings. PACS number(s): 03.65.Ge, 73.50.Bk

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“…The scattering problem of a single δ-function impurity with sinusoidal time dependence has been investigated by several authors [15,42,43]. We would like to summarize how to construct its Floquet scattering matrix in this Appendix.…”

Section: Appendix A: Floquet Scattering Matrix In a Single Oscillatinmentioning

confidence: 99%

Floquet Formalism of Quantum Pumps

Kim

2004

Int. J. Mod. Phys. B

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We review Floquet formalism of quantum electron pumps. In the Floquet formalism the quantum pump is regarded as a time dependent scattering system, which allows us to go beyond the adiabatic limit. It can be shown that the well-known adiabatic formula given by Brouwer can be derived from the adiabatic limit of Floquet formalism. We compare various physical properties of the quantum pump both in the adiabatic and in the non-adiabatic regime using the Floquet theory.

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Transmission properties of the oscillating δ-function potential

Cited by 55 publications

References 18 publications

Transmission through a Quantum Dynamical Delta Barrier

Transmission through a Quantum Dynamical Delta Barrier

Quasibound states at thresholds in multichannel impurity scattering

Floquet Formalism of Quantum Pumps

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