Propagator for symmetric double delta potential using path decomposition method

Laissaoui, Aïda; Chétouani, L.

doi:10.1063/1.5008516

Cited by 3 publications

(8 citation statements)

References 31 publications

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“…Therefore, in general, the whole structure behaves as a fully reflecting wall. This is because of the bigger singularity than that of the typical double-delta potential [35]. Such a singularity occurs due to the non-zero finiteness of the arguments A j .…”

Section: Ikx Ikxmentioning

confidence: 98%

“…Within such an approach, the three-scale parametrization [31] that connects the layer parameters through the parameter ε > 0, can be used. Thus, we set (35) where a j ∈ R, j = 1, 2, and µ, ν, τ, η are arbitrary positive parameters. We denote the potential (6) parametrized by these relations by V ε (x).…”

Section: Power-connecting Three-scale Parametrizationmentioning

confidence: 99%

“…for any ϕ(x) ∈ C ∞ 0 (R). Using the parametrization (35) and expanding ϕ(εξ) = ϕ(0) + εξϕ ′ (0) + (ε 2 ξ 2 /2)ϕ ′′ (ςεξ), where ξ = x/ε and ς ∈ (0, 1) depends for a given ϕ on εξ, the integral (36) can be computed explicitly. Thus, under the condition a 1 + ηa 2 = 0 (0 < η < ∞), we get…”

Section: Power-connecting Three-scale Parametrizationmentioning

confidence: 99%

“…In general, on the whole S δ ′ -surface, the resonance condition (31) parametrized by Eqs. (35) with the amplitudes (40) becomes an equation with respect to the intensity γ. Asymptotically, in the limit as ε → 0, it takes the form…”

Section: Power-connecting Three-scale Parametrizationmentioning

confidence: 99%

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Origin of resonant tunneling through single-point barriers

Zolotaryuk

2018

Physica E: Low-dimensional Systems and Nanostructures

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The physical interpretation of the appearance of resonant transmission through single-point barriers is discussed on the basis of a double-layer heterostructure in the squeezing limit as both the thickness of the layers and the distance between them tend to zero simultaneously. In this limit, the electron transmission through a barrier-well structure is derived to be non-zero at certain discrete values of the system parameters forming the so-called resonance set, while beyond this set, the structure behaves as a perfectly reflecting wall. The origin of this phenomenon is shown to result from the reflection coefficients at the interfaces in the inter-layer space. The transmission amplitude is computed as a set function defined on the trihedral angle surface in a three-dimensional parameter space.

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Section: Ikx Ikxmentioning

confidence: 98%

Section: Power-connecting Three-scale Parametrizationmentioning

confidence: 99%

Section: Power-connecting Three-scale Parametrizationmentioning

confidence: 99%

Section: Power-connecting Three-scale Parametrizationmentioning

confidence: 99%

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Origin of resonant tunneling through single-point barriers

Zolotaryuk

2018

Physica E: Low-dimensional Systems and Nanostructures

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“…The propagator for general four parameter family of point interactions have been given in Albeverio et al [27]. Propagators for systems involving δ potentials are also studied from various points of view in references [28][29][30][31][32][33][34]. The propagator for derivatives of Dirac delta distribution for constant strengths has been recently studied in Lange [11].…”

Section: Introductionmentioning

confidence: 99%

The Propagators for δ and δ′ Potentials With Time-Dependent Strengths

2020

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We study the time-dependent Schrödinger equation with finite number of Dirac δ and δ ′ potentials with time dependent strengths in one dimension. We obtain the formal solution for generic time dependent strengths and then we study the particular cases for single delta potential and limiting cases for finitely many delta potentials. Finally, we investigate the solution of time dependent Schrödinger equation for δ ′ potential with particular forms of the strengths.

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Buildup and decay dynamics of exponentially modulated quantum waves in resonant structures

Amador-Bartolini¹,

Villavicencio²,

Romo³

et al. 2020

Phys. Scr.

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We derive an exact analytic solution of time-dependent Schrödinger’s equation for cutoff quantum waves with exponential modulation to explore the dynamics along the internal region of a one-dimensional potential of arbitrary shape. The modulation of the wave packet is controlled by a single parameter given by its momentum distribution width, Δ, which allows to explore on the same footing the transient features of both cutoff spatially localized wave packets and extended plane waves. From the formal solution, we derive a simple and reliable formula that accurately describes both the buildup and decay of the probability density inside a resonant structure. The buildup-decay formula involves two exponential terms governed respectively by the resonance width Γ1 of the lowest resonance of the system and the width of a ‘virtual’ state induced by the incident wave packet. During the buildup process, we demonstrate that the contributions of both Γ1 and become essential. In the decay process, on the other hand, we find that there are two regimes characterized by a critical value Δc, such that for Δ > Δc the exponential decay is governed by Γ1, while for Δ < Δc the exponential decay is governed by . We also derive an analytic formula for a relevant timescale for the buildup-decay process, which depends in a simple fashion on the decay rates Γ1 and . Deviations from the exponential decay law at long times are also discussed.

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Propagator for symmetric double delta potential using path decomposition method

Abstract: Using the method of path decomposition, the space-time propagator for the one-dimensional symmetric double delta potential is determined and tested on the limiting cases a → 0 (single delta) and β → ∞ (infinite square well), which are exactly obtained.

Cited by 3 publications

References 31 publications

Origin of resonant tunneling through single-point barriers

Origin of resonant tunneling through single-point barriers

The Propagators for δ and δ′ Potentials With Time-Dependent Strengths

Buildup and decay dynamics of exponentially modulated quantum waves in resonant structures

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