Spectral Properties of Relativistic Quantum Waveguides

William Borrelli; Philippe Briet; David Krejčiřík; Thomas Ourmières-Bonafos

doi:10.1007/s00023-022-01179-9

Spectral Properties of Relativistic Quantum Waveguides

William Borrelli^*
, Philippe Briet
, David Krejčiřík
, Thomas Ourmières-Bonafos

^*Autore corrispondente per questo lavoro

Facoltà di Scienze Matematiche, Fisiche e Naturali

Czech Technical University in Prague
Institut de Mathématiques de Marseille

Risultato della ricerca: Contributo in rivista › Articolo › peer review

Abstract

We make a spectral analysis of the massive Dirac operator in a tubular neighbourhood of an unbounded planar curve, subject to infinite mass boundary conditions. Under general assumptions on the curvature, we locate the essential spectrum and derive an effective Hamiltonian on the base curve which approximates the original operator in the thin-strip limit. We also investigate the existence of bound states in the non-relativistic limit and give a geometric quantitative condition for the bound states to exist.

Lingua originale	Inglese
pagine (da-a)	N/A-N/A
Rivista	Annales Henri Poincare
Volume	2022
Numero di pubblicazione	N/A
DOI	https://doi.org/10.1007/s00023-022-01179-9
Stato di pubblicazione	Pubblicato - 2022

All Science Journal Classification (ASJC) codes

Fisica Statistica e Non Lineare
Fisica Nucleare e ad Alta Energia
Fisica Matematica

Keywords

Dirac operator
infinite mass boundary conditions
non-relativistic limit
norm-resolvent convergence
quantum waveguides
thin-waveguide limit

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10.1007/s00023-022-01179-9

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AU - Borrelli, William

AU - Briet, Philippe

AU - Krejčiřík, David

AU - Ourmières-Bonafos, Thomas

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N2 - We make a spectral analysis of the massive Dirac operator in a tubular neighbourhood of an unbounded planar curve, subject to infinite mass boundary conditions. Under general assumptions on the curvature, we locate the essential spectrum and derive an effective Hamiltonian on the base curve which approximates the original operator in the thin-strip limit. We also investigate the existence of bound states in the non-relativistic limit and give a geometric quantitative condition for the bound states to exist.

AB - We make a spectral analysis of the massive Dirac operator in a tubular neighbourhood of an unbounded planar curve, subject to infinite mass boundary conditions. Under general assumptions on the curvature, we locate the essential spectrum and derive an effective Hamiltonian on the base curve which approximates the original operator in the thin-strip limit. We also investigate the existence of bound states in the non-relativistic limit and give a geometric quantitative condition for the bound states to exist.

KW - Dirac operator

KW - infinite mass boundary conditions

KW - non-relativistic limit

KW - norm-resolvent convergence

KW - quantum waveguides

KW - thin-waveguide limit

KW - Dirac operator

KW - infinite mass boundary conditions

KW - non-relativistic limit

KW - norm-resolvent convergence

KW - quantum waveguides

KW - thin-waveguide limit

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Spectral Properties of Relativistic Quantum Waveguides

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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