Controllable resonant tunnelling through single-point potentials: A point triode

Zolotaryuk, A. V.; Zolotaryuk, Yaroslav

doi:10.1016/j.physleta.2014.12.016

Cited by 20 publications

(19 citation statements)

References 40 publications

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“…Solving the eigenvalue problem for this kind of Hamiltonians is not, in general, an easy task and often requires rather sophisticated tools. One of the most widely used is the Birman-Schwinger operator, namely the integral operator 5) and the related technique: as in most applications B E can be shown to be compact, the solutions of the eigenvalue problem for the Hamiltonian are given by those values of E for which B E has an eigenvalue equal to -1 (see [22,37,38] and references therein as well as [39], p. 99). Therefore, the detailed study of the properties of the Birman-Schwinger operator arising from our model is quite relevant.…”

Section: Introductionmentioning

confidence: 99%

The Birman-Schwinger Operator for a Parabolic Quantum Well in a Zero-Thickness Layer in the Presence of a Two-Dimensional Attractive Gaussian Impurity

et al. 2019

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In this note we consider a quantum mechanical particle moving inside an infinitesimally thin layer constrained by a parabolic well in the x-direction and, moreover, in the presence of an impurity modelled by an attractive Gaussian potential. We investigate the Birman-Schwinger operator associated to a model assuming the presence of a Gaussian impurity inside the layer and prove that such an integral operator is Hilbert-Schmidt, which allows the use of the modified Fredholm determinant in order to compute the bound states created by the impurity. Furthermore, we consider the case where the Gaussian potential degenerates to a δ-potential in the x-direction and a Gaussian potential in the y-direction. We construct the corresponding self-adjoint Hamiltonian and prove that it is the limit in the norm resolvent sense of a sequence of corresponding Hamiltonians with suitably scaled Gaussian potentials. Satisfactory bounds on the ground state energies of all Hamiltonians involved are exhibited.

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Section: Introductionmentioning

confidence: 99%

The Birman-Schwinger Operator for a Parabolic Quantum Well in a Zero-Thickness Layer in the Presence of a Two-Dimensional Attractive Gaussian Impurity

et al. 2019

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“…The advantage of one-dimensional models with point perturbations is clear as they are useful for the study of a variety of qualitative properties [3][4][5][6][7][8][9][10][11][12][13]. They have been used to model several kinds of extra thin structures [14,15], to mimic point defects in materials, or to study heterostructures [16,17]. In any case, point potentials may serve as solvable or quasi solvable models that approximate results for very short range potentials.…”

Section: Introductionmentioning

confidence: 99%

Spectral properties of the two-dimensional Schrödinger Hamiltonian with various solvable confinements in the presence of a central point perturbation

et al. 2019

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We study three solvable two-dimensional systems perturbed by a point interaction centered at the origin. The unperturbed systems are the isotropic harmonic oscillator, a square pyramidal potential and a combination thereof. We study the spectrum of the perturbed systems. We show that, while most eigenvalues are not affected by the point perturbation, a few of them are strongly perturbed. We show that for some values of one parameter, these perturbed eigenvalues may take lower values than the immediately lower eigenvalue, so that level crossings occur. These level crossings are studied in some detail.

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“…They serve to model realistic physical situations with a number of practical applications. They are used to model several kinds of extra thin structures [3,4] or to model point defects in materials, so that effects like tunnelling are easily studied. They are also used in the study of heterostructures, where they may appear in connection with an abrupt effective mass change [5].…”

Section: Introductionmentioning

confidence: 99%

Spectroscopy of a one-dimensional V-shaped quantum well with a point impurity

et al. 2018

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a b s t r a c tWe consider the one-dimensional Hamiltonian with a V-shaped, decorated with a point impurity of either δ-type, or local δ ′ -type or even nonlocal δ ′ -type, thus yielding three exactly solvable models. We analyse the behaviour of the change in the energy levels when an interaction of the type −λ δ(x) or −λ δ(x − x 0 ) is switched on. In the first case, even energy levels, pertaining to antisymmetric bound states, remain invariant with respect to λ even though odd energy levels, pertaining to symmetric bound states, decrease as λ increases. In the second, all energy levels decrease when the factor λ increases. A similar study has been performed for the so-called nonlocal δ ′ interaction, requiring a coupling constant renormalisation, which implies the replacement of the form factor λ by a renormalised form factor β. In terms of β, odd energy levels are unchanged. However, we show the existence of level crossings: after a fixed value of β the energy of each even level, with the natural exception of the first one, becomes lower than the constant energy of the previous odd level. Finally, we consider an interaction of the type −λδ(x)+µδ ′ (x), and analyse in detail the discrete spectrum of the resulting selfadjoint Hamiltonian.

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Controllable resonant tunnelling through single-point potentials: A point triode

Cited by 20 publications

References 40 publications

The Birman-Schwinger Operator for a Parabolic Quantum Well in a Zero-Thickness Layer in the Presence of a Two-Dimensional Attractive Gaussian Impurity

The Birman-Schwinger Operator for a Parabolic Quantum Well in a Zero-Thickness Layer in the Presence of a Two-Dimensional Attractive Gaussian Impurity

Spectral properties of the two-dimensional Schrödinger Hamiltonian with various solvable confinements in the presence of a central point perturbation

Spectroscopy of a one-dimensional V-shaped quantum well with a point impurity

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