Quantum waveguides

Exner, Pavel; Šeba, P.; Šťovı́ček, P.

doi:10.1007/bfb0022953

Cited by 69 publications

(109 citation statements)

References 10 publications

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“…This applies, in particular, to the so-called leaky quantum graphs and similar structures, cf. [15,Chap. 10], describing the motion of quantum particles confined to 'thin' regions of space of a possibly nontrivial geometrical and topological character in a way which does not neglect the tunneling effect.…”

Section: Introductionmentioning

confidence: 99%

Generalized interactions supported on hypersurfaces

Exner

Rohleder

2016

Journal of Mathematical Physics

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Abstract. We analyze a family of singular Schrödinger operators with local singular interactions supported by a hypersurface Σ ⊂ R n , n ≥ 2, being the boundary of a Lipschitz domain, bounded or unbounded, not necessarily connected. At each point of Σ the interaction is characterized by four real parameters, the earlier studied case of δ-and δ ′ -interactions being particular cases. We discuss spectral properties of these operators and derive operator inequalities between those referring to the same hypersurface but different couplings and describe their implications for spectral properties.

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Section: Introductionmentioning

confidence: 99%

Generalized interactions supported on hypersurfaces

Exner

Rohleder

2016

Journal of Mathematical Physics

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“…We note that the linear wave equations on metric graphs have been extensively studied in the Refs. [30][31][32][33][34][35] and soliton dynamics in networks has been the topic for extensive research during the past decade (see, e.g., Refs. [36][37][38][39][40][41][42][43][44][45]).…”

Section: Introductionmentioning

confidence: 99%

Dynamics of polarons in branched conducting polymers

Sabirov¹,

Yusupov²,

Matyokubov³

2020

Nanosystems: Phys. Chem. Math.

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“…The mathematical analysis of nonlinear PDEs on such graphs attracted recently a lot of interest, cf. . The use of graphs is motivated for instance by nano‐technological objects with a similar geometric structure, such as nano‐tubes or graphene.…”

Section: Introductionmentioning

confidence: 99%