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.

Borrelli, W., Briet, P., Krejčiřík, D., Ourmières-Bonafos, T., Spectral Properties of Relativistic Quantum Waveguides, <<ANNALES HENRI POINCARE'>>, N/A; 2022 (N/A): N/A-N/A. [doi:10.1007/s00023-022-01179-9] [http://hdl.handle.net/10807/200161]

Spectral Properties of Relativistic Quantum Waveguides

Borrelli, William
;
2022

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.
2022
Inglese
Borrelli, W., Briet, P., Krejčiřík, D., Ourmières-Bonafos, T., Spectral Properties of Relativistic Quantum Waveguides, <<ANNALES HENRI POINCARE'>>, N/A; 2022 (N/A): N/A-N/A. [doi:10.1007/s00023-022-01179-9] [http://hdl.handle.net/10807/200161]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/200161
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