Time dependence of the position momentum and position velocity uncertainties in gapped graphene

Abstract

We examine the time dependence of the position-momentum and position-velocity uncertainties in monolayer gapped graphene. The effect of the energy gap to the uncertainties is shown to appear via the Compton-like wavelength lambda(c). The uncertainties in the graphene are mainly contributed by two phenomena, spreading and zitterbewegung. While the former determines the uncertainties in the long range of time, the latter gives high oscillation to the uncertainties in the short range of time. The uncertainties in the graphene are compared with the corresponding values for the usual free Hamiltonian (H) over cap (free) = (p(1)(2) + p(2)(2))/2M. It is shown that the uncertainties can be under control within the quantum mechanical laws if one can choose the gap parameter lambda(c) freely.