Inertial effects play an important role in classical mechanics but have been largely overlooked in quantum mechanics. Nevertheless, the analogy between inertial forces on mass particles and electromagnetic forces on charged particles is not new. In this paper, we consider a rotating non-interacting planar two-dimensional electron gas with a perpendicular uniform magnetic field and investigate the effects of the rotation in the Hall conductiv

The electronic structure of a single-layer graphene with a periodic Fermi velocity modulation is investigated by using an effective Dirac-like Hamiltonian. In a gapless graphene or in a graphene with a constant energy gap the modulation of the Fermi velocity, as expected, only changes the dispersion between energy and moment, turning the minibands narrower or less narrow than in the usual graphene depending on how the Fermi velocity is modulated and the energy gap remains the same. However, with a modulated energy gap it is possible to control the energy gap of graphene by Fermi velocity engineering. This is based on a very simple idea that has never been reported so far. The results obtained here reveal a new way of controlling the energy gap of graphene, which can be used in the fabrication of graphene-based devices

In this paper, motivated by the experimental evidence of rapidly rotating C60 molecules in fullerite, we study the low-energy electronic states of rotating fullerene within a continuum model. In this model, the low-energy spectrum is obtained from an effective Dirac equation including non-Abelian gauge fields that simulate the pentagonal rings of the molecule. Rotation is incorporated into the model by solving the effective Dirac equation in the rotating referential frame. The exact analytical solution for the eigenfunctions and energy spectrum is obtained, yielding the previously known static results in the no rotation limit. Due to the coupling between rotation and total angular momentum, that appears naturally in the rotating frame, the zero modes of static C60 are shifted and also suffer a Zeeman splitting whithout the presence of a magnetic field.

The quantum dynamics of particles with mass dependent on the position is a problem of interest since the effective-mass approach to charge carriers in conductors and semiconductors began to be used. These problems have been solved using the Hamiltonian \documentclass[12pt]{minimal}\begin{document}$H=\frac{1}{2}m^\alpha (x) p m^\beta (x) p m^\alpha (x)$\end{document}H=12mα(x)pmβ(x)pmα(x), where α and β are real parameters which satisfy the condition 2α + β = −1. It has been verified that the choice α = 0, β = −1 is compatible with Galilean invariance. In this work we propose a new Hamiltonian, \documentclass[12pt]{minimal}\begin{document}$\hat{H}=\frac{1}{6}\left[\hat{m}(\hat{x})^{-1}\hat{p}^2+\hat{p}\hat{m}(\hat{x})^{-1}\hat{p}+p^2\hat{m}(\hat{x})^{-1}\right]$\end{document}Ĥ=16m̂(x̂)−1p̂2+p̂m̂(x̂)−1p̂+p2m̂(x̂)−1, to describe variable mass systems. We considered every permutation among the operators, taking into account that the mass is now an operator. We verified that this Hamiltonian is Hermitian and is compatible with Galilean invariance. For comparison, we used both Hamiltonians to calculate the band structure for a quantum particle with mass varying periodically. Although qualitatively equivalent, the results turn out to produce different numerical values.

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