The MIT Bag Model as an infinite mass limit

2018/08/29 by Arrizabalaga, Naiara, Treust, Loïc Le, Mas, Albert +1 · 3 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1808.09746

Abstract

The Dirac operator, acting in three dimensions, is considered. Assuming that a large mass m>0 lies outside a smooth and bounded open set Ω⊂\R³, it is proved that its spectrum is approximated by the one of the Dirac operator on Ω with the MIT bag boundary condition. The approximation, which is developed up to and error of order o(1/√ m), is carried out by introducing tubular coordinates in a neighborhood of ∂Ω and analyzing the corresponding one dimensional optimization problems in the normal direction.

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• Congruence of Dirac operators with applications to generalized MIT bag models
• MIT bag in non-smooth convex domains
• Semi-Dirac semi-metals quantum dots

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