Quantized Alternate Current on Curved Graphene

Abstract

Based on the numerical solution of the quantum lattice Boltzmann method in curved space, we predict the onset of a quantized alternating current on curved graphene sheets. Such numerical prediction is verified analytically via a set of semi-classical equations relating the Berry curvature to real space curvature. The proposed quantised oscillating current on curved graphene could form the basis for the implementation of quantum information processing algorithms.

Photonic realization of the kappa-deformed Dirac equation

“…It is also obvious that the undeformed Dirac equation is obtained in the limit a → 0. However, we underscore the fact that, experimentally, the deformation parameter a is greatly limited by an upper bound of the order of a < 10 −29 m [31]. Several effects can be investigated using this new Hamiltonian.…”

“…The calculation of x(t) for the more general case α = 0 is, however, straightforward and we shall proceed in this direction. In the Heisenberg picture, we have [31]: where H = −ασ z + ξσ x p x . To see the dependence on the deformation parameter more clearly, we focus now on the width of wave packets (∆x) 2 = x 2 − x 2 .…”

“…Such table-top experiments provide flexible configurations and easy tuning of parameters, including recent constructions of effective relativistic systems. Examples of condensed matter realizations and their emulations also abound [30][31][32][33][34][35][36]. The success of dynamical analogies between quantum mechanical equations and electromagnetic waves in various important subjects -quantum graphs, chaotic scattering and billiards, tight-binding arrays and crystals, including graphene and phosphorene-has led us to consider new experimental challenges towards high-energy extensions of the Dirac equation, ruling the motion of ultra relativistic fermions.…”