Digitalisierung und Prosuming in der Gastronomie: Potenziale und Herausforderungen

Ziesen, Nenja; Yildiz-Ziesen, Nazim Baris

doi:10.1007/978-3-658-36514-1_14

Cited by 1 publication

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“…Since it is computationally costly to work with a 3D lattice, [ 4 ] a fully 2D formulation is preferable. In what follows we will review the options developed by particle physicists, with one key criterion in mind: If we add disorder to the Dirac Hamiltonian, as is unavoidable in a real material, will the Dirac cone remain gapless?…”

Section: Introductionmentioning

confidence: 99%

Tangent Fermions: Dirac or Majorana Fermions on a Lattice Without Fermion Doubling

et al. 2023

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Methods to discretize the Hamiltonian of a topological insulator or topological superconductor, without giving up on the topological protection of the massless excitations (respectively, Dirac fermions or Majorana fermions) are reviewed. The method of tangent fermions, pioneered by Richard Stacey, is singled out as being uniquely suited for this purpose. Tangent fermions propagate on a 2+1${2\bm {+}1}$ dimensional space‐time lattice with a tangent dispersion: tan2(bold-italicε/2)=tan2(kx/2)+tan2(ky/2)${\text{tan}^2 (\bm {\varepsilon }/2) \bm {=} \text{tan}^2 (k_x/2) \bm {+}\text{tan}^2 (k_y/2)}$ in dimensionless units. They avoid the fermion doubling lattice artefact that will spoil the topological protection, while preserving the fundamental symmetries of the Dirac Hamiltonian. Although the discretized Hamiltonian is nonlocal, as required by the fermion‐doubling no‐go theorem, it is possible to transform the wave equation into a generalized eigenproblem that is local in space and time. Applications that are discussed include Klein tunneling of Dirac fermions through a potential barrier, the absence of localization by disorder, the anomalous quantum Hall effect in a magnetic field, and the thermal metal of Majorana fermions.

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Section: Introductionmentioning

confidence: 99%