Work

Adaptive time stepping for the two-time integro-differential Kadanoff-Baym equations

Year: 2024

Type: article

Abstract: The nonequilibrium 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. Published by the American Physical Society 2024

Source: Physical review. B./Physical review. B

DOI: 10.1103/physrevb.110.205134

Authors: Thomas Blommel, David J. Gardner, Carol S. Woodward, Emanuel Gull

Institutions: University of Michigan, Lawrence Livermore National Laboratory

Language: English

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid