Time evolution of nanoscale systems by finite difference method

TL;DR

This paper introduces a novel finite difference method for simulating the time evolution of nanoscale systems, specifically metal-molecule-metal junctions, by solving Volterra integro-differential equations with higher accuracy than traditional methods.

Contribution

The paper presents a new finite difference approach to solve Volterra integro-differential equations for nanoscale system dynamics, improving accuracy over existing numerical methods.

Findings

Results align with analytical solutions

Method demonstrates higher accuracy than Runge Kutta

Charge transport properties are effectively modeled

Abstract

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.