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.

scholarly journals The Casimir effect for thick pistons

2016 ◽  
Vol 31 (06) ◽  
pp. 1650012
Author(s):  
Guglielmo Fucci
Keyword(s):  
Boundary Conditions ◽  
Zeta Function ◽  
Regularization Method ◽  
Casimir Force ◽  
Casimir Effect ◽  
Casimir Energy ◽  
Numerical Results ◽  
Spectral Zeta Function

In this work, we analyze the Casimir energy and force for a thick piston configuration. This study is performed by utilizing the spectral zeta function regularization method. The results we obtain for the Casimir energy and force depend explicitly on the parameters that describe the general self-adjoint boundary conditions imposed. Numerical results for the Casimir force are provided for specific types of boundary conditions and are also compared to the corresponding force on an infinitely thin piston.

scholarly journals DISCRETIZED LAPLACIANS ON AN INTERVAL AND THEIR RENORMALIZATION GROUP

1994 ◽  
Vol 09 (25) ◽  
pp. 4485-4509 ◽  
Author(s):  
E. ERCOLESSI ◽  
P. TEOTONIO-SOBRINHO ◽  
G. BIMONTE
Keyword(s):  
Boundary Conditions ◽  
Laplace Operator ◽  
Continuum Limit ◽  
Wave Functions ◽  
The Other ◽  
Scale Invariant ◽  
Dimensional Parameter ◽  
Finite Dimensional ◽  
The Laplace Operator ◽  
The Continuum

The Laplace operator admits infinite self-adjoint extensions when considered on a segment of the real line. They have different domains of essential self-adjointness characterized by a suitable set of boundary conditions on the wave functions. In this paper we show how these extensions can be recovered by studying the continuum limit of certain discretized versions of the Laplace operator on a lattice. Associated to this limiting procedure, there is a renormalization flow in the finite-dimensional parameter space describing the discretized operators. This flow is shown to have infinite fixed points, corresponding to the self-adjoint extensions characterized by scale-invariant boundary conditions. The other extensions are recovered by looking at the other trajectories of the flow.

scholarly journals Casimir Energy in a Bounded Gross-Neveu model

2018 ◽  
Vol 64 (6) ◽  
pp. 577
Author(s):  
Juan Cristóbal Rojas
Keyword(s):  
Boundary Conditions ◽  
Zeta Function ◽  
Casimir Effect ◽  
Beta Function ◽  
Spatial Dimension ◽  
Casimir Energy ◽  
The Other ◽  
Effective Theory ◽  
Different Boundary Conditions ◽  
Complex Picture

In this letter, we study some relevant parameters of the massless Gross-Neveu (GN) model in afinite spatial dimension for different boundary conditions. It is considered the standard homogeneousHartree-Fock solution using zeta function regularization for the study the mass dynamically generated and its respective beta function. It is found that the beta function does not depend on the boundary conditions. On the other hand, it was considered the Casimir effect of the resulting effective theory. There appears a complex picture where the sign of the generated forces depends on the parameters used in the study.

scholarly journals Zero point fluctuations for magnetic spirals and Skyrmions, and the fate of the Casimir energy in the continuum limit

2018 ◽  
Vol 399 ◽  
pp. 239-257
Author(s):  
Benoit Douçot ◽  
Dmitry L. Kovrizhin ◽  
Roderich Moessner
Keyword(s):  
Continuum Limit ◽  
Zero Point ◽  
Casimir Energy ◽  
The Continuum

scholarly journals HEISENBERG SPINS ON A CYLINDER SECTION

2000 ◽  
Vol 14 (19n20) ◽  
pp. 2093-2100 ◽  
Author(s):  
J. BENOIT ◽  
R. DANDOLOFF ◽  
A. SAXENA
Keyword(s):  
Boundary Conditions ◽  
Finite Length ◽  
Continuum Limit ◽  
Elastic Cylinder ◽  
Physical Realization ◽  
Topological Soliton ◽  
Geometric Effect ◽  
Rigidity Constraint ◽  
Cylinder Model ◽  
The Continuum

Classical Heisenberg spins in the continuum limit (i.e. the nonlinear σ-model) are studied on an elastic cylinder section with homogeneous boundary conditions. The latter may serve as a physical realization of magnetically coated microtubules and cylindrical membranes. The corresponding rigid cylinder model exhibits topological soliton configurations with geometrical frustration due to the finite length of the cylinder section. Assuming small and smooth deformations allows to find shapes of the elastic support by relaxing the rigidity constraint: an inhomogeneous Lamé equation arises. Finally, this leads to a novel geometric effect: a global shrinking of the cylinder section with swellings.

scholarly journals Towards the continuum limit with improved Wilson fermions employing open boundary conditions

2017 ◽  
Author(s):  
Wolfgang Soeldner ◽  
Gunnar S. Bali ◽  
Sara Collins ◽  
Fabian Hutzler ◽  
Meinulf Gockeler ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Continuum Limit ◽  
Open Boundary ◽  
Open Boundary Conditions ◽  
The Continuum ◽  
Wilson Fermions

Instability and Collapse in Discrete Wave Equations

2005 ◽  
Vol 5 (3) ◽  
pp. 223-241
Author(s):  
A. Carpio ◽  
G. Duro
Keyword(s):  
Continuum Limit ◽  
Wave Equations ◽  
Numerical Solutions ◽  
Blow Up ◽  
Theoretical Predictions ◽  
Initial States ◽  
The Impact ◽  
The Continuum

AbstractUnstable growth phenomena in spatially discrete wave equations are studied. We characterize sets of initial states leading to instability and collapse and obtain analytical predictions for the blow-up time. The theoretical predictions are con- trasted with the numerical solutions computed by a variety of schemes. The behavior of the systems in the continuum limit and the impact of discreteness and friction are discussed.

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