SOBRE UN TIPO DE EFECTO RETICULAR DURANTE LA PROPAGACIÓN LIBRE DE UN ELECTRÓN DE BLOCH
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Revista Boliviana de Física
Abstract
Se investiga una de las formas cómo podría manifiestarse físicamente la estructura de red periódica en la propagación unidimensional de un electrón de Bloch. Los efectos dinámicos de esta propagación en presencia de ciertos potenciales externos son conocidos: la oscilación de Bloch en presencia de un potencial lineal y localización dinámica en presencia de potenciales armónicos. En ausencia de un potencial externo (propagación "libre"), la teoría semiclásica y la teoría cuántica predicen una velocidad constante de propagación, lo que se verifica en la simulación numérica de la ecuación de Schrödinger. En este caso se puede apreciar que el paquete de ondas gaussiano que simula al electrón en el instante inicial, evoluciona deformándose como una gaussiana asimétrica; si bien el centro de masa (centroide) del paquete se propaga con velocidad constante, el valor máximo del paquete se propaga con una velocidad constante mayor, por lo que se puede concluir que el centro efectivo de interacción eléctrica del paquete se "adelanta" al centro de masa. Se propone un escenario experimental en el que una consecuencia física interesante (y eventualmente medible) de dicho "adelanto" se manifiesta en un cristal ideal en 2D.
A study is carried out of an effect due to the structure of the lattice in the propagation of a one-dimensional Bloch electron. The dynamics of this propagation in the presence of certain external potentials are well known: the Bloch oscillation in the presence of a lineal potential and the dynamic localization in the presence of harmonic potentials. In the absence of an external potential (free propagation), both the semi classic theory and the quantum theory predict a constant propagation velocity which is verified by numerical simulations of the Schrdinger equation. In this case, the Gaussian wavepacket that simulates the electron in its initial state, evolves itself into an asymmetrical gaussian maintaining the centre of mass at a constant velocity. However the wavepackets peak propagates with greater velocity, indicating that the center of mass lags behind the effective center of the electrical interaction. We propose an experimental scenario in which an interesting physical consequence of such a lag would manifest itself in an ideal 2D crystal.
A study is carried out of an effect due to the structure of the lattice in the propagation of a one-dimensional Bloch electron. The dynamics of this propagation in the presence of certain external potentials are well known: the Bloch oscillation in the presence of a lineal potential and the dynamic localization in the presence of harmonic potentials. In the absence of an external potential (free propagation), both the semi classic theory and the quantum theory predict a constant propagation velocity which is verified by numerical simulations of the Schrdinger equation. In this case, the Gaussian wavepacket that simulates the electron in its initial state, evolves itself into an asymmetrical gaussian maintaining the centre of mass at a constant velocity. However the wavepackets peak propagates with greater velocity, indicating that the center of mass lags behind the effective center of the electrical interaction. We propose an experimental scenario in which an interesting physical consequence of such a lag would manifest itself in an ideal 2D crystal.
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Vol. 15, No. 15