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

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.

References in corpus (6)

• Real time evolution using the density matrix renormalization group
• Real-time path integral approach to nonequilibrium many-body quantum system
• Attosecond Field Emission
• Comparing the generalized Kadanoff-Baym ansatz with the full Kadanoff-Baym equations for an excitonic insulator out of equilibrium
• Time-linear quantum transport simulations with correlated nonequilibrium Green's functions
• Adaptive Numerical Solution of Kadanoff-Baym Equations

Cited by in corpus (3)

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• Schwinger-Keldysh non-perturbative field theory of open quantum systems beyond the Markovian regime: Application to spin-boson and spin-chain-boson models