Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Localization landscape for Dirac fermions   In the theory of Anderson localization, a landscape function predicts where
wave functions localize in a disordered medium, without requiring the solution
of an eigenvalue problem. It is known how to construct the localization
landscape for the scalar wave equation in a random potential, or equivalently
for the Schr\"{o}dinger equation of spinless electrons. Here we generalize the
concept to the Dirac equation, which includes the effects of spin-orbit
coupling and allows to study quantum localization in graphene or in topological
insulators and superconductors. The landscape function $u(r)$ is defined on a
lattice as a solution of the differential equation $\overline{{H}}u(r)=1$,
where $\overline{{H}}$ is the Ostrowsky comparison matrix of the Dirac
Hamiltonian. Random Hamiltonians with the same (positive definite) comparison
matrix have localized states at the same positions, defining an equivalence
class for Anderson localization. This provides for a mapping between the
Hermitian and non-Hermitian Anderson model.

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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: chem-ph
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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: math
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The categories of this paper are: math-ph