Quantum Dot with Attached Wires: Resonant States Completeness

Popov, I. Yu.; Попов, Антон Юрьевич

doi:10.1016/s0034-4877(17)30054-x

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Cited by 5 publications

(2 citation statements)

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“…Rigorous mathematical theory of quantum graphs was constructed last decades [12][13][14]. Hybrid manifolds were studied in less extent [3,15,16]. It was shown that such models are effective for description of spectral properties of operators.…”

Section: Introductionmentioning

confidence: 99%

Spectral gaps for star-like quantum graph and for two coupled rings

Blinova¹,

Popov²,

Bosova³

2022

Nanosystems: Phys. Chem. Math.

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The spectral problems for two types of quantum graphs are considered. We deal with star-like graph and a graph consisting of two rings connected through a segment. The spectral gap, i.e. the difference between the second and the first eigenvalues of the free Schr ödinger operator, is studied. The dependence of the gap on the geometric parameters of the graph is investigated. Particularly, it is shown that the maximal gap is observed for the symmetric quantum graph.

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Section: Introductionmentioning

confidence: 99%

Spectral gaps for star-like quantum graph and for two coupled rings

Blinova¹,

Popov²,

Bosova³

2022

Nanosystems: Phys. Chem. Math.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Resonances have attracted great attention over time. There are a number of works concerning the problem of resonances, particularly the completeness of resonance states which is related to the resonance asymptotics (see, e.g., [7][8][9][10][11][12][13][14][15][16][17]). The purpose of this paper is to investigate the asymptotics of the resonances of the Dirac operator on a quantum graph.…”

Section: Introductionmentioning

confidence: 99%