A unified theory of quasibound states

Moyer, C. A.

doi:10.1063/1.4865998

Cited by 6 publications

(11 citation statements)

References 28 publications

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“…was derived previously with the help of the Green functions without any detailed analysis. The same configuration was discussed by C. A. Moyer , who concentrated on finding the energy and associated polarization of its lowest level only, which at the vanishing electric intensities tends to the zero‐field bound state:

E_{0} = - 1 - \frac{5}{16} {scriptE}^{2}, E ≪ 1 .

In addition, for either the δ‐well or barrier, Eq. has two infinite sets of positive solutions that will be denoted below by the superscripts A or B corresponding to their behavior at low voltages; namely, for the weak fields,

E ≪ 1

, one finds:

\begin{matrix} true \\ right E_{n}^{A \pm} & left = - a_{n} E^{2 / 3} \mp \frac{1}{2} scriptE + \frac{1}{4} \frac{{Bi}^{'} (a_{n})}{Bi false(a_{n} false)} E^{4 / 3}, \end{matrix}

\begin{matrix} true \\ right E_{n}^{B \pm} & left = - b_{n} E^{2 / 3} \pm \frac{1}{2} scriptE + \frac{1}{4} \frac{{Ai}^{'} (b_{n})}{Ai false(b_{n} false)} E^{4 / 3}, \end{matrix}

n = 1, 2, \dots

.…”

Section: δ‐Potentialmentioning

confidence: 76%

“…Amalgamation of the levels is accompanied by the divergence of the associated dipole moments. This phenomenon, previously predicted only for the ground state , is calculated and analyzed in subsection 2.2 for all quasibound levels. It should be noted that the corresponding eigenvalue equation has, at intensities

scriptE

greater than the breakdown voltage, a pair of complex conjugate solutions that can be a mathematical indication of the formation in the electric field of a composite electron‐hole‐like structure.…”

Section: Introductionmentioning

confidence: 81%

“…and asymptote of the Airy function. Nevertheless, in the recent analysis of the lowest level evolution in the field this orbital was called the quasibound state and was defined broadly as the level having a connectedness to the true bound state through the variation of some physical parameter. In our extension to all the solutions (including those with

E \geq 0

), we found it relevant to call them real energy quasibound (REQB) states.…”

Section: δ‐Potentialmentioning

confidence: 99%

“…As a result, the corresponding scattering matrix has poles only at the complex energies. A great deal of attention has been devoted to the analysis of the finite‐width QW and its δ counterpart subjected to a dc electric field with the outcome that one approach is sometimes completely at odds to the predictions of another scheme; in particular, the peculiarities of the transformation of the resonances into the true bound states at

E \to 0

were scrutinized and the formation of new field‐induced complex energy quasibound states and resonances was predicted.…”

Section: Introductionmentioning

confidence: 99%

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Evolution of electric‐field‐induced quasibound states and resonances in one‐dimensional open quantum systems

Olendski

2016

Annalen der Physik

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A comparative analysis of three different time-independent approaches to studying open quantum structures in a uniform electric field E was performed using the example of a one-dimensional attractive or repulsive δ-potential and the surface that supports the Robin boundary condition. The three considered methods exploit different properties of the scattering matrix S(E ; E ) as a function of energy E : its poles, real values, and zeros of the second derivative of its phase. The essential feature of the method of zeroing the resolvent, which produces complex energies, is the unlimited growth of the wave function at infinity, which is, however, eliminated by the time-dependent interpretation. The real energies at which the unitary scattering matrix becomes real correspond to the largest possible distortion, S = +1, or its absence at S = −1 which in either case leads to the formation of quasibound states. Depending on their response to the increasing electric intensity, two types of field-induced positive energy quasibound levels are identified: electron-and hole-like states. Their evolution and interaction in the enlarging field lead ultimately to the coalescence of pairs of opposite states, with concomitant divergence of the associated dipole moments in what is construed as an electric breakdown of the structure. The characteristic features of the coalescence fields and energies are calculated and the behavior of the levels in their vicinity is analyzed. Similarities between the different approaches and their peculiarities are highlighted; in particular, for the zerofield bound state in the limit of the vanishing E , all three methods produce the same results, with their outcomes deviating from each other according to growing electric intensity. The significance of the zero-field spatial symmetry for the formation, number, and evolution of the electron-and hole-like states, and the interaction between them, is underlined by comparing outcomes for the symmetric δ geometry and asymmetric Robin

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E_{0} = - 1 - \frac{5}{16} {scriptE}^{2}, E ≪ 1 .

E ≪ 1

, one finds:

\begin{matrix} true \\ right E_{n}^{A \pm} & left = - a_{n} E^{2 / 3} \mp \frac{1}{2} scriptE + \frac{1}{4} \frac{{Bi}^{'} (a_{n})}{Bi false(a_{n} false)} E^{4 / 3}, \end{matrix}

\begin{matrix} true \\ right E_{n}^{B \pm} & left = - b_{n} E^{2 / 3} \pm \frac{1}{2} scriptE + \frac{1}{4} \frac{{Ai}^{'} (b_{n})}{Ai false(b_{n} false)} E^{4 / 3}, \end{matrix}

n = 1, 2, \dots

.…”

Section: δ‐Potentialmentioning

confidence: 76%

scriptE

Section: Introductionmentioning

confidence: 81%

E \geq 0

), we found it relevant to call them real energy quasibound (REQB) states.…”

Section: δ‐Potentialmentioning

confidence: 99%

E \to 0

were scrutinized and the formation of new field‐induced complex energy quasibound states and resonances was predicted.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Evolution of electric‐field‐induced quasibound states and resonances in one‐dimensional open quantum systems

Olendski

2016

Annalen der Physik

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“…As a last application for the Green's function approach reviewed so far, we finally consider a context not usually addressed for the present quantum systems (but see [183]): quasi-bound states. For a general treatment of such problems using G -however not discussing quantum graphs -we cite [215].…”

Section: Basic Aspectsmentioning

confidence: 99%

Green’s function approach for quantum graphs: An overview

et al. 2016

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Here we review the many aspects and distinct phenomena associated to quantum dynamics on general graph structures. For so, we discuss such class of systems under the energy domain Green's function (G) framework. This approach is particularly interesting because G can be written as a sum over classical-like paths, where local quantum effects are taking into account through the scattering matrix amplitudes (basically, transmission and reflection amplitudes) defined on each one of the graph vertices. Hence, the exact G has the functional form of a generalized semiclassical formula, which through different calculation techniques (addressed in details here) always can be cast into a closed analytic expression. It allows to solve exactly arbitrary large (although finite) graphs in a recursive and fast way. Using the Green's function method, we survey many properties for open and closed quantum graphs as scattering solutions for the former and eigenspectrum and eigenstates for the latter, also considering quasi-bound states. Concrete examples, like cube, binary trees and Sierpiński-like topologies are presented. Along the work, possible distinct applications using the Green's function methods for quantum graphs are outlined.

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Spatial quasi-bound states of Dirac electrons in graphene monolayer

Miniya,

Oubram,

El Hachimi

et al. 2024

Sci Rep

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Our study investigated the emergence of spatial quasi-bound states (QBSs) in graphene monolayers induced by rectangular potential barriers. By solving the time-independent Dirac equation and using the transfer matrix formalism, we calculated the resonance energies and identify the QBSs based on probability density functions (PDF). We analyzed two types of structures: single and double barriers, and we find that the QBSs are located within the barrier region, at energies higher than the single barrier. Additionally, we observe QBSs in the double barrier and their position depends on the distance and width of the well between the two barriers. The width and height of the barrier significantly impact the QBSs while the well width influences the resonance energy levels of the QBSs in the double barrier. Interestingly, the QBSs can be manipulated in the graphene system, offering potential for optoelectronic devices. Finally, our results demonstrated that the spatial localization of these states is counter-intuitive and holds great promise for future research in optolectronic devices.

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A unified theory of quasibound states

Cited by 6 publications

References 28 publications

Evolution of electric‐field‐induced quasibound states and resonances in one‐dimensional open quantum systems

Evolution of electric‐field‐induced quasibound states and resonances in one‐dimensional open quantum systems

Green’s function approach for quantum graphs: An overview

Spatial quasi-bound states of Dirac electrons in graphene monolayer

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