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Twin-Double

Предмет Гостиничное дело
👍 Проверено Автор24

гостиничный номер на 2 персоны с 2 двуспальными кроватями.

Научные статьи на тему «Twin-Double»

SPECTRAL PROPERTIES OF A SYMMETRIC THREE-DIMENSIONAL QUANTUM DOT WITH A PAIR OF IDENTICAL ATTRACTIVE δ-IMPURITIES SYMMETRICALLY SITUATED AROUND THE ORIGIN

In this presentation, we wish to provide an overview of the spectral features for the self-adjoint Hamiltonian of the three-dimensional isotropic harmonic oscillator perturbed by either a single attractive δ-interaction centered at the origin or by a pair of identical attractive interactions symmetrically situated with respect to the origin. Given that such Hamiltonians represent the mathematical model for quantum dots with sharply localized impurities, we cannot help having the renowned article by Brüning, Geyler and Lobanov [1] as our key reference. We shall also compare the spectral features of the aforementioned three-dimensional models with those of the self-adjoint Hamiltonian of the harmonic oscillator perturbed by an attractive δ'-interaction in one dimension, fully investigated in [2, 3], given the existence in both models of the remarkable spectral phenomenon called ”level crossing”. The rigorous definition of the self-adjoint Hamiltonian for the singular double well m...

Научный журнал

THE BEHAVIOUR OF THE THREE-DIMENSIONAL HAMILTONIAN -Δ+λ[δ(X+X0)+δ(X-X0)] AS THE DISTANCE BETWEEN THE TWO CENTRES VANISHES

In this note, we continue our analysis of the behavior of self-adjoint Hamiltonians with symmetric double wells given by twin point interactions perturbing various types of “free Hamiltonians” as the distance between the two centers shrinks to zero. In particular, by making the coupling constant to be renormalized and also dependent on 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 studied in detail by Albeverio and collaborators, 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 negative three-dimensional Laplacian perturbed by a single attractive point interaction situated at the origin having double strength, thus making this three-dimensional model more similar to its one-dimensional analog (not requi...

Научный журнал

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