Short-time Chebyshev propagator for the Liouville–von Neumann equation

A Chebyshev interpolation scheme is proposed for the short-time Liouville–von Neumann propagator. For each propagation step, a small number of Chebyshev polynomials is used to construct the propagator. The method involves only matrix-vector multiplication and is memory efficient since the three-term Chebyshev recursion needs only two vectors stored. It is also numerically stable since neither matrix diagonalization nor inversion is involved. The short Chebyshev recursion ensures that the divergence due to the complex eigenvalues of the Liouville superoperator is kept under control. Numerical tests carried out for the Redfield equation of a one-dimensional dissipative harmonic system demonstrate that the short-time Chebyshev propagator is accurate and significantly more efficient than the commonly used fourth-order Runge–Kutta scheme.