Jump processes related to the two dimensional dirac equation

1987 ◽  
pp. 1-13 ◽  
Author(s):  
Ph. Blanchard ◽  
Ph. Combe ◽  
M. Sirugue ◽  
M. Sirugue-Collin
Keyword(s):  
Dirac Equation ◽  
Jump Processes ◽  
Two Dimensional

scholarly journals Fast forwad Adiabatic Quantum Dynamics On Two Dimensional Dirac Equation

2021 ◽  
Vol 1842 (1) ◽  
pp. 012057
Author(s):  
I Setiawan ◽  
R Sugihakim ◽  
B E Gunara
Keyword(s):  
Dirac Equation ◽  
Quantum Dynamics ◽  
Two Dimensional

scholarly journals NONCOMMUTATIVE GRAPHENE

2013 ◽  
Vol 28 (16) ◽  
pp. 1350064 ◽  
Author(s):  
CATARINA BASTOS ◽  
ORFEU BERTOLAMI ◽  
NUNO COSTA DIAS ◽  
JOÃO NUNO PRATA
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Dirac Equation ◽  
Energy Levels ◽  
Dirac Fermions ◽  
Two Dimensional ◽  
Dirac System ◽  
Noncommutative Parameter

We consider a noncommutative description of graphene. This description consists of a Dirac equation for massless Dirac fermions plus noncommutative corrections, which are treated in the presence of an external magnetic field. We argue that, being a two-dimensional Dirac system, graphene is particularly interesting to test noncommutativity. We find that momentum noncommutativity affects the energy levels of graphene and we obtain a bound for the momentum noncommutative parameter.

De la combinatoire du modèle de l'échiquier de Feynman et des fonctions spéciales

1984 ◽  
Vol 62 (7) ◽  
pp. 632-638
Author(s):  
J. G. Williams
Keyword(s):  
Exact Solution ◽  
Dirac Equation ◽  
Hypergeometric Series ◽  
Jacobi Polynomials ◽  
Dimensional Space ◽  
Space Time ◽  
Continuous Limit ◽  
Two Dimensional ◽  
Dimensional Space Time

The exact solution of the Feynman checkerboard model is given both in terms of the hypergeometric series and in terms of Jacobi polynomials. It is shown how this leads, in the continuous limit, to the Dirac equation in two-dimensional space-time.

scholarly journals Higher-order Darboux transformations for two-dimensional Dirac systems with diagonal matrix potential

2021 ◽  
Vol 2090 (1) ◽  
pp. 012038
Author(s):  
A Schulze-Halberg
Keyword(s):  
Dirac Equation ◽  
Explicit Form ◽  
Higher Order ◽  
Diagonal Matrix ◽  
Two Dimensional ◽  
Darboux Transformations ◽  
Dirac Systems ◽  
Matrix Potential ◽  
De Vries ◽  
The Matrix

Abstract We construct the explicit form of higher-order Darboux transformations for the two-dimensional Dirac equation with diagonal matrix potential. The matrix potential entries can depend arbitrarily on the two variables. Our construction is based on results for coupled Korteweg-de Vries equations [27].

CHIRAL ZEROMODES ON VORTEX-TYPE INTERSECTING FIVE-BRANE IN HETEROTIC STRING

2013 ◽  
Vol 21 ◽  
pp. 191-192
Author(s):  
MASAYA YATA
Keyword(s):  
Dirac Equation ◽  
String Theory ◽  
Boundary Conditions ◽  
Heterotic String ◽  
The Other ◽  
Two Dimensional ◽  
Complete Spectrum ◽  
Heterotic String Theory ◽  
Brane Solution ◽  
Opposite Chirality

We solve the gaugino Dirac equation on a smeared intersecting five-brane solution in E8 × E8 heterotic string theory to search for localized chiral zeromodes on the intersection. The background is chosen to depend on the full two-dimensional overall transverse coordinates to the branes. Under some appropriate boundary conditions, we compute the complete spectrum of zeromodes to find that, among infinite towers of Fourier modes, there exist only three localized normalizable zeromodes, one of which has opposite chirality to the other two.

scholarly journals Darboux partners of Heun-class potentials for the two-dimensional massless Dirac equation

2020 ◽  
Vol 421 ◽  
pp. 168273 ◽  
Author(s):  
Axel Schulze-Halberg ◽  
Artur M. Ishkhanyan
Keyword(s):  
Dirac Equation ◽  
Two Dimensional

scholarly journals The Landau-Zener Transition and the Surface Hopping Method for the 2D Dirac Equation for Graphene

2017 ◽  
Vol 21 (2) ◽  
pp. 313-357 ◽  
Author(s):  
Ali Faraj ◽  
Shi Jin
Keyword(s):  
Dirac Equation ◽  
Electrostatic Potential ◽  
Numerical Experiments ◽  
Transition Probabilities ◽  
Energy Levels ◽  
Two Dimensional ◽  
Lagrangian Surface ◽  
Surface Hopping ◽  
Asymptotic Models ◽  
Semiclassical Regime

AbstractA Lagrangian surface hopping algorithm is implemented to study the two dimensional massless Dirac equation for Graphene with an electrostatic potential, in the semiclassical regime. In this problem, the crossing of the energy levels of the system at Dirac points requires a particular treatment in the algorithm in order to describe the quantum transition—characterized by the Landau-Zener probability— between different energy levels. We first derive the Landau-Zener probability for the underlying problem, then incorporate it into the surface hopping algorithm. We also show that different asymptotic models for this problem derived in [O. Morandi, F. Schurrer, J. Phys. A:Math. Theor. 44 (2011) 265301]may give different transition probabilities. We conduct numerical experiments to compare the solutions to the Dirac equation, the surface hopping algorithm, and the asymptotic models of [O. Morandi, F. Schurrer, J. Phys. A: Math. Theor. 44 (2011) 265301].

scholarly journals CHIRAL ZERO MODES ON VORTEX-TYPE INTERSECTING HETEROTIC FIVE-BRANES

2012 ◽  
Vol 27 (12) ◽  
pp. 1250072 ◽  
Author(s):  
MASAYA YATA
Keyword(s):  
Dirac Equation ◽  
Zero Mode ◽  
The Other ◽  
Two Dimensional ◽  
Complete Spectrum ◽  
Type Solution ◽  
Heterotic String Theory ◽  
Zero Modes ◽  
Brane Solution ◽  
Opposite Chirality

We solve the gaugino Dirac equation on a smeared intersecting five-brane solution in E8×E8 heterotic string theory to search for localized chiral zero modes on the intersection. The background is chosen to depend on the full two-dimensional overall transverse coordinates to the branes. Under some appropriate boundary conditions, we compute the complete spectrum of zero modes to find that, among infinite towers of Fourier modes, there exist only three localized normalizable zero modes, one of which has opposite chirality to the other two. This agrees with the result previously obtained in the domain-wall type solution, supporting the claim that there exists one net chiral zero mode localized on the heterotic five-brane system.

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