Effects of two successive parity-invariant point interactions on one-dimensional quantum transmission: Resonance conditions for the parameter space

Konno, Kohkichi; Nagasawa, Tomoaki; Takahashi, Rohta

doi:10.1016/j.aop.2016.09.012

Cited by 7 publications

(13 citation statements)

References 63 publications

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“…(98), we find that the perfect reflection (F = 0) occurs if and only if the condition e 2ik(ξ 1 −ξ 2 ) = 1 (103) holds except the trivial cases of s 21 = 0 or s 31 = 0. It should be emphasized that this phenomenon never happen when we consider one-dimensional quantum systems with double point interactions of degree 2 (see [13,14]).…”

Section: An Anti-symmetric Ring System With Double Y-junctionsmentioning

confidence: 99%

Quantum reflection and transmission in ring systems with double Y-junctions: occurrence of perfect reflection

Fujimoto¹,

Konno²,

Nagasawa³

et al. 2020

J. Phys. A: Math. Theor.

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We consider the scattering problems of a quantum particle in a system with a single Y-junction and in ring systems with double Yjunctions. We provide new formalism for such quantum mechanical problems. Based on a path integral approach, we find compact formulas for probability amplitudes in the ring systems. We also discuss quantum reflection and transmission in the ring systems under scale-invariant junction conditions. It is remarkable that perfect reflection can occur in an anti-symmetric ring system, in contrast with the one-dimensional quantum systems having singular nodes of degree 2.

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Section: An Anti-symmetric Ring System With Double Y-junctionsmentioning

confidence: 99%

Quantum reflection and transmission in ring systems with double Y-junctions: occurrence of perfect reflection

Fujimoto¹,

Konno²,

Nagasawa³

et al. 2020

J. Phys. A: Math. Theor.

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“…In the unbiased case (b = 0, k R = k) this formula reduces to T = [1 + (α/2k) 2 ] −1 with α = ad, the well known expression for the constant potential. Equation (69) has been obtained for any a ∈ R. However, for negative values of a, i.e., for a δ-like well, it does not describe the oscillating behavior with respect to the constant α that takes place under tunneling across a well with finite thickness l.…”

Section: Realization Of Point Interactions In the Zero-thickness Limimentioning

confidence: 99%

“…The resonant tunneling through double-barrier scatters is still an active area of research for the applications to nanotechnology. In the context of the Cheon-Fülöp-Tsutsui approach [19,20], the conditions for the parameter space under which the perfect resonant transmission occurs through two point interactions, each of which is described by four parameters, have been found by Konno, Nagasawa and Takahashi [69,70].…”

Section: Introductionmentioning

confidence: 99%

Point Interactions With Bias Potentials

2019

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We develop an approach on how to define single-point interactions under the application of external fields. The essential feature relies on an asymptotic method based on the one-point approximation of multi-layered heterostructures that are subject to bias potentials. In this approach , the zero-thickness limit of the transmission matrices of specific structures is analyzed and shown to result in matrices connecting the two-sided boundary conditions of the wave function at the origin. The reflection and transmission amplitudes are computed in terms of these matrix elements as well as biased data. Several one-point interaction models of two-and three-terminal devices are elaborated. The typical transistor in the semiconductor physics is modeled in the "squeezed limit" as a δ-and a δ -potential and referred to as a "point" transistor. The basic property of these one-point interaction models is the existence of several extremely sharp peaks as an applied voltage tunes, at which the transmission amplitude is non-zero, while beyond these resonance values, the heterostructure behaves as a fully reflecting wall. The location of these peaks referred to as a "resonance set" is shown to depend on both system parameters and applied voltages. An interesting effect of resonant transmission through a δ-like barrier under the presence of an adjacent well is observed. This transmission occurs at a countable set of the well depth values.

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“…This paper aims to explain how the resonant tunneling of this type happens in the simplest case of a double-layer structure. For this purpose we use the interference mechanism, similarly to that used in the works [33,34], where instead of the description of point interactions in terms of the limiting transmission matrix Λ := lim ε→0 Λ ε , an alternative way for identifying the whole family of point interactions has been used. This approach has been suggested in the works [11,12], according to which the boundary conditions are written via the two-component vectors…”

Section: Introductionmentioning

confidence: 99%

“…The U-matrix can be parametrized in an appropriate way and the relationship between its elements and the Λ-matrix elements can be established (for more details see [11]). Using this approach in [33,34], the scattering of a quantum particle by two independent point interactions has been investigated in one dimension. As a result, the resonance conditions for perfect transmission through this twopoint system have been found.…”

Section: Introductionmentioning

confidence: 99%

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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Effects of two successive parity-invariant point interactions on one-dimensional quantum transmission: Resonance conditions for the parameter space

Cited by 7 publications

References 63 publications

Quantum reflection and transmission in ring systems with double Y-junctions: occurrence of perfect reflection

Quantum reflection and transmission in ring systems with double Y-junctions: occurrence of perfect reflection

Point Interactions With Bias Potentials

Origin of resonant tunneling through single-point barriers

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