scholarly journals Residues of the eta function for an operator of Dirac type with local boundary conditions

1992 ◽  
Vol 2 (3) ◽  
pp. 249-267 ◽  
Author(s):  
Thomas P. Branson ◽  
Peter B. Gilkey
Keyword(s):  
Boundary Conditions ◽  
Local Boundary ◽  
Dirac Type ◽  
Operator Of Dirac Type

scholarly journals Heat asymptotics with spectral boundary conditions. II

2003 ◽  
Vol 133 (2) ◽  
pp. 333-361 ◽  
Author(s):  
Peter Gilkey ◽  
Klaus Kirsten
Keyword(s):  
Riemannian Manifold ◽  
Boundary Conditions ◽  
Compact Riemannian Manifold ◽  
Smooth Boundary ◽  
Dirac Type ◽  
Heat Trace ◽  
Operator Of Dirac Type ◽  
Laplace Type

Let P be an operator of Dirac type on a compact Riemannian manifold with smooth boundary. We impose spectral boundary conditions and study the asymptotics of the heat trace of the associated operator of Laplace type.

scholarly journals BOUNDARY CONDITIONS IN THE DIRAC APPROACH TO GRAPHENE DEVICES

2012 ◽  
Vol 14 ◽  
pp. 240-249 ◽  
Author(s):  
C.G. BENEVENTANO ◽  
E.M. SANTANGELO
Keyword(s):  
Boundary Conditions ◽  
Zeta Function ◽  
Continuum Limit ◽  
Casimir Energy ◽  
Local Boundary ◽  
Graphene Devices ◽  
The Continuum

We study a family of local boundary conditions for the Dirac problem corresponding to the continuum limit of graphene, both for nanoribbons and nanodots. We show that, among the members of such family, MIT bag boundary conditions are the ones which are in closest agreement with available experiments. For nanotubes of arbitrary chirality satisfying these last boundary conditions, we evaluate the Casimir energy via zeta function regularization, in such a way that the limit of nanoribbons is clearly determined.

Elliptic problem involving non-local boundary conditions

2019 ◽  
Vol 181 ◽  
pp. 87-100
Author(s):  
Noureddine Igbida ◽  
Soma Safimba
Keyword(s):  
Boundary Conditions ◽  
Elliptic Problem ◽  
Local Boundary ◽  
Non Local
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