Level Rearrangement in Exotic Atoms and Quantum Dots

Combescure, Monique; Khare, Avinash; Raina, A.; Richard, Jean‐Marc; Weydert, C.

doi:10.1142/s0217979207037855

Cited by 20 publications

(30 citation statements)

References 23 publications

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“…By looking at the above graph, it is crucial to realize that, differently from the plots in [17,19] and because of our renormalization, the manifestation of the Zeldovich effect occurs in the vicinity of β = 0 whilst the left boundary of the graph is instead β = −∞.…”

Section: Manifestation Of the Zeldovich Effect (Level Rearrangement)mentioning

confidence: 99%

“…Although we might return to the issue in a separate paper in the near future, we cannot help anticipating here that it is possible to reinterpret the results of the spectral analysis carried out in this note from a slightly different point of view in order to discuss the manifestation of the Zeldovich effect (see [18]) in the case of the three lowest eigenvalues of the self-adjoint operator being analyzed in this note taking account of the results outlined in [17,19].…”

Section: Manifestation Of the Zeldovich Effect (Level Rearrangement)mentioning

confidence: 99%

“…By citing [17] In their paper, the authors extend their analysis from exotic atoms to quantum dots which are mathematically modelled by Hamiltonians with the harmonic confinement perturbed by an attractive interaction whose action is strong only in the short range.…”

Section: Manifestation Of the Zeldovich Effect (Level Rearrangement)mentioning

confidence: 99%

“…Although only attractive perturbations of the 3D-isotropic harmonic oscillator represented by square wells are considered, the authors of [17] observe, in addition to the aforementioned level rearrangement (Zeldovich effect), the same remarkable spectral phenomenon noticed by us in this note and its predecessor [1] dealing with point perturbations, namely the double level crossing because of which the level ordering becomes 1S < 2S < 2P over a certain range of values of the appropriate parameter, the coupling constant (resp. the extension parameter) in the case of [17] (resp.…”

Section: Manifestation Of the Zeldovich Effect (Level Rearrangement)mentioning

confidence: 99%

“…Our main motivation for this further analysis has been the fact that, following [17], the latter parameter is the conventional one used to study the manifestation of the Zeldovich effect (see [18]), widely known also as level rearrangement. We are going to show that the phenomenon, studied by the authors of that article when the perturbation of the three-dimensional isotropic harmonic oscillator is represented by a potential whose range is physically very short but different from zero, does manifest itself also in the case of point perturbations.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Spectral properties of a symmetric three-dimensional quantum dot with a pair of identical attractive δ-impurities symmetrically situated around the origin II

Albeverio¹,

Fassari²,

Rinaldi³

2016

Nanosystems: Phys. Chem. Math.

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In this note, we continue our analysis (started in [1]) of the isotropic three-dimensional harmonic oscillator perturbed by a pair of identical attractive point interactions symmetrically situated with respect to the origin, that is to say, the mathematical model describing a symmetric quantum dot with a pair of point impurities. In particular, by making the coupling constant (to be renormalized) dependent also upon the separation distance between the two impurities, we prove that it is possible to rigorously define the unique self-adjoint Hamiltonian that, differently from the one introduced in [1], behaves smoothly as the separation distance between the impurities shrinks to zero. In fact, we rigorously prove that the Hamiltonian introduced in this note converges in the norm-resolvent sense to that of the isotropic three-dimensional harmonic oscillator perturbed by a single attractive point interaction situated at the origin having double strength, thus making this threedimensional model more similar to its one-dimensional analog (not requiring the renormalization procedure) as well as to the three-dimensional model involving impurities given by potentials whose range may even be physically very short but different from zero. Moreover, we show the manifestation of the Zeldovich effect, known also as level rearrangement, in the model investigated herewith. More precisely, we take advantage of our renormalization procedure to demonstrate the possibility of using the concept of 'Zeldovich spiral', introduced in the case of perturbations given by rapidly decaying potentials, also in the case of point perturbations.

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Section: Manifestation Of the Zeldovich Effect (Level Rearrangement)mentioning

confidence: 99%

Section: Manifestation Of the Zeldovich Effect (Level Rearrangement)mentioning

confidence: 99%

Section: Manifestation Of the Zeldovich Effect (Level Rearrangement)mentioning

confidence: 99%