CENTRAL EUROPEAN JOURNAL OF PHYSICS, vol.11, no.12, pp.1674-1679, 2013 (SCI-Expanded)
In this paper, we have provided a matrix Hamiltonian model for honeycomb lattices and subsequently obtained the dispersion relation. Furthermore, we have constructed the C operator for the given non-Hermitian Hamiltonian model. The quadratic surfaces are sketched and the quantum Brachistochrone problem is discussed for the given honeycomb lattice model.