DINAMICA DE UNA PARTÍCULA EN UNA RED DE ENLACE FUERTE BAJO UN POTENCIAL COULOMBIANO

Abstract

We study the tight-binding dynamics of a charged particle by the hopping mechanism in a one - dimensional lattice under the action of a Coulomb potential due to another fixed particle (impurity). The quantum dynamics is studied using the pseudo-spectral method applied to a tight-binding Hamiltonian with nearest neighbors interactions. The resulting expected values for position and velocity are then compared with those deduced by the semi-classical method invoking the effective potential in the lattice. These results are notably similar when the particle is located far from the impurity position since the Coulomb field is approximately uniform, while when near to the impurity the results are different due to the quantum dispersion of the particle’s wavepacket under a highly inhomogeneous field. Interestingly, however, the quantum and semiclassical results coincide in the continuous regime (parabolic dispersion relation) due to the transmission of the particle’s wavepacket through the impurity.