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

^*Corresponding author

Faculty of Mathematical, Physical and Natural Sciences

Czech Technical University in Prague
Institut de Mathématiques de Marseille

Research output: Contribution to journal › Article › 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.

Original language	English
Pages (from-to)	N/A-N/A
Journal	Annales Henri Poincare
Volume	2022
Issue number	N/A
DOIs	https://doi.org/10.1007/s00023-022-01179-9
Publication status	Published - 2022

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Nuclear and High Energy Physics
Mathematical Physics

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

Cite this

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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.",

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T1 - Spectral Properties of Relativistic Quantum Waveguides

AU - Borrelli, William

AU - Briet, Philippe

AU - Krejčiřík, David

AU - Ourmières-Bonafos, Thomas

PY - 2022

Y1 - 2022

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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SN - 1424-0637

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SP - N/A-N/A

JO - Annales Henri Poincare

JF - Annales Henri Poincare

IS - N/A

ER -

Spectral Properties of Relativistic Quantum Waveguides

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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