SPECTRAL THEORETIC CHARACTERIZATION OF THE MASSLESS DIRAC ACTION

Spectral theoretic characterization of the massless Dirac operator

We consider an elliptic self-adjoint first-order differential operator acting on pairs (2-columns) of complex-valued half-densities over a connected compact three-dimensional manifold without boundary. The principal symbol of our operator is assumed to be trace-free. We study the spectral function which is the sum of squares of Euclidean norms of eigenfunctions evaluated at a given point of the...

Collective modes of the massless dirac plasma.

We develop a theory for the long-wavelength plasma oscillation of a collection of charged massless Dirac particles in a solid, as occurring, for example, in doped graphene layers, interacting via the long-range Coulomb interaction. We find that the long-wavelength plasmon frequency in such a doped massless Dirac plasma is explicitly nonclassical in all dimensions with the plasma frequency being...

Spectral analysis of the massless Dirac operator on a 3-manifold

The talk will give an overview of our further development of the paper [7] by Robert Downes, Michael Levitin and Dmitri Vassiliev and it will also give an insight how spectrum of massless Dirac operator on a 3-manifold interplays with geometric contents of the manifold. In contrast to the Riemann flat manifold studied in [7], 3-torus, we study the massless Dirac operator on a 3-sphere equipped ...

Spectral asymmetry of the massless Dirac operator on a 3 - torus

Quantum transport of massless Dirac fermions.

Motivated by recent graphene transport experiments, we undertake a numerical study of the conductivity of disordered two-dimensional massless Dirac fermions. Our results reveal distinct differences between the cases of short-range and Coulomb randomly distributed scatterers. We speculate that this behavior is related to the Boltzmann transport theory prediction of dirty-limit behavior for Coulo...