Time evolution of nanoscale systems by finite difference method

Abstract

Using finite difference method, time evolution of a typical metal-moleculemetal system is studied by introducing a new method to solve general related Volterra integro−di f f erential equation (IDE). Discretization in time domain is applied for one dimensional chain tight binding model in several cases by defining a matrixintegro− di f f erential equation (MIDE). Results are compatible with their analytical counterparts and show more accuracy than other numerical methods like Runge Kutta (RK). Charge transport properties in a trans-polyacetylene chain are found by studying the time evolution of charge density in it and current-voltage diagram is calculated.