Adaptive Time Stepping for the Two-Time Integro-Differential Kadanoff-Baym Equations

TL;DR

This paper introduces an adaptive integration scheme for the Kadanoff-Baym equations in quantum Green's function calculations, significantly improving efficiency while maintaining accuracy in simulating quantum transport phenomena.

Contribution

The paper develops an adaptive time-stepping and order control method for the Kadanoff-Baym equations, enhancing computational efficiency in non-equilibrium quantum simulations.

Findings

Achieves an order of magnitude speedup over fixed step methods.

Maintains accuracy with adaptive order and step size control.

Highlights the importance of self-consistent solutions in the method.

Abstract

The non-equilibrium Green's function gives access to one-body observables for quantum systems. Of particular interest are quantities such as density, currents, and absorption spectra which are important for interpreting experimental results in quantum transport and spectroscopy. We present an integration scheme for the Green's function's equations of motion, the Kadanoff-Baym equations (KBE), which is both adaptive in the time integrator step size and method order as well as the history integration order. We analyze the importance of solving the KBE self-consistently and show that adapting the order of history integral evaluation is important for obtaining accurate results. To examine the efficiency of our method, we compare runtimes to a state of the art fixed time step integrator for several test systems and show an order of magnitude speedup at similar levels of accuracy.