Dirac operators and shell interactions: a survey
作者： Thomas Ourmières-Bonafos , Fabio Pizzichillo
DOI:
关键词:
摘要: In this survey we gather recent results on Dirac operators coupled with $\delta$-shell interactions. We start by discussing advances regarding the question of self-adjointness for these operators. Afterward switch to an approximation question: can be recovered as limits squeezing potentials ? also discuss spectral features models. Namely, recall main consequences a resolvent formula and conclude commenting result asymptotic nature eigenvalues in gap operator Lorentz-scalar interaction.
arxiv.org参考文章(47)
Carleton DeTar, The Mit Bag Model Springer, Boston, MA. pp. 393- 450 ,(1980) , 10.1007/978-1-4613-3099-8_6
Bernd Thaller, Advanced visual quantum mechanics Published in <b>2005</b> in New York NY) by Springer. pp. 103- ,(2005)
Tosio Kato, Perturbation theory for linear operators ,(1966)
Sergio Albeverio, Solvable Models in Quantum Mechanics ,(1988)
Jussi Behrndt, Pavel Exner, Vladimir Lotoreichik, Essential spectrum of Schrödinger operators with δ-interactions on the union of compact Lipschitz hypersurfaces PAMM. ,vol. 13, pp. 523- 524 ,(2013) , 10.1002/PAMM.201310254
William Charles Hector McLean, Strongly Elliptic Systems and Boundary Integral Equations ,(2000)
V Duchêne, N Raymond, Spectral asymptotics of a broken delta interaction arXiv: Analysis of PDEs. ,(2013) , 10.1088/1751-8113/47/15/155203
J.F. Brasche, P. Exner, Y.A. Kuperin, P. Seba, Schrödinger-Operators with Singular Interactions Journal of Mathematical Analysis and Applications. ,vol. 184, pp. 112- 139 ,(1994) , 10.1006/JMAA.1994.1188
Naiara Arrizabalaga, Albert Mas, Luis Vega, Shell Interactions for Dirac Operators: On the Point Spectrum and the Confinement Siam Journal on Mathematical Analysis. ,vol. 47, pp. 1044- 1069 ,(2015) , 10.1137/14097759X
Anne-Sophie Bonnet-Bendhia, Monique Dauge, Karim Ramdani, Analyse spectrale et singularités d'un problème de transmission non coercif Comptes Rendus de l'Académie des Sciences - Series I - Mathematics. ,vol. 328, pp. 717- 720 ,(1999) , 10.1016/S0764-4442(99)80241-9