scholarly journals Infinite mass boundary conditions for Dirac operators

2018 ◽  
Vol 9 (2) ◽  
pp. 569-600 ◽  
Author(s):  
Edgardo Stockmeyer ◽  
Semjon Vugalter
Keyword(s):  
Boundary Conditions ◽  
Dirac Operators ◽  
Infinite Mass ◽  
Infinite Mass Boundary Conditions

scholarly journals Electronic states and optical transitions in a graphene quantum dot in a normal magnetic field

2011 ◽  
Vol 8 (1) ◽  
pp. 53-62 ◽  
Author(s):  
Marko Grujic ◽  
Milan Tadic
Keyword(s):  
Magnetic Field ◽  
Quantum Dot ◽  
Boundary Conditions ◽  
Zero Energy ◽  
Graphene Quantum Dot ◽  
Infinite Mass ◽  
Infinite Mass Boundary Conditions ◽  
The Magnetic Field ◽  
Normal Magnetic Field ◽  
Weyl Equation

An analytical approach using the Dirac-Weyl equation is implemented to obtain the energy spectrum and optical absorption of a circular graphene quantum dot in the presence of an external magnetic field. The results are obtained for the infinite-mass and zigzag boundary conditions. We found that the energy spectra of a dot with zigzag boundary condition exhibit a zero energy band regardless of the value of the magnetic field, while for the infinite mass boundary conditions, the zero energy states appear only for high magnetic fields.

scholarly journals Higher spectral flow for Dirac operators with local boundary conditions

2016 ◽  
Vol 27 (08) ◽  
pp. 1650068
Author(s):  
Jianqing Yu
Keyword(s):  
Boundary Conditions ◽  
Elliptic Boundary ◽  
Dirac Operators ◽  
Spectral Flow ◽  
Local Boundary ◽  
Manifold With Boundary ◽  
Index Bundle ◽  
Adjoint Extension ◽  
Smooth Map ◽  
Higher Spectral Flow

We consider a one parameter family [Formula: see text] of families of fiberwise twisted Dirac type operators on a fibration with the typical fiber an even dimensional compact manifold with boundary, which verifies [Formula: see text] with [Formula: see text] being a smooth map from the fibration to a unitary group [Formula: see text]. For each [Formula: see text], we impose on [Formula: see text] a certain fixed local elliptic boundary condition [Formula: see text] and get a self-adjoint extension [Formula: see text]. Under the assumption that [Formula: see text] has vanishing [Formula: see text]-index bundle, we establish a formula for the higher spectral flow of [Formula: see text], [Formula: see text]. Our result generalizes a recent result of [A. Gorokhovsky and M. Lesch, On the spectral flow for Dirac operators with local boundary conditions, Int. Math. Res. Not. IMRN (2015) 8036–8051.] to the families case.

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