TY - JOUR
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
UR - http://hdl.handle.net/10807/200161
U2 - 10.1007/s00023-022-01179-9
DO - 10.1007/s00023-022-01179-9
M3 - Article
SN - 1424-0637
VL - 2022
SP - N/A-N/A
JO - Annales Henri Poincare
JF - Annales Henri Poincare
ER -