An efficient solution of Liouville-von Neumann equation that is applicable to zero and finite temperatures

Abstract

Application of quantum dissipation theory to electronic dynamics has been limited to model systems with few energy levels, and its numerical solutions are mostly restricted to high temperatures. A highly accurate and efficient numerical algorithm, which is based on the Chebyshev spectral method, is developed to integrate a single-particle Liouville-von Neumann equation, and the two longstanding limitations of quantum dissipation theory are resolved in the context of quantum transport. Its computational time scales to O(N3) with N being the number of orbitals involved, which leads to a reality for the quantum mechanical simulation of real open systems containing hundreds or thousands of atomic orbitals. More importantly, the algorithm spans both finite and zero temperatures. Numerical calculations are carried out to simulate the transient current through a metallic wire containing up to 1000 orbitals. © 2012 American Institute of Physics.