  Using finite difference method, time evolution of a typical metal molecule
metal system is studied by introducing a new method to solve general related
Volterra integro differential equation (IDE). Discretization in time domain is
applied for one dimentional chain tight binding model in several cases by
defining a matrix integro-differential 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.

Mesoscale and Nanoscale Physics;Other Condensed Matter