Adaptive numerical solution of Kadanoff-Baym equations

Meirinhos, Francisco; Kajan, Michael; Kroha, Johann; Bode, Tim

doi:10.21468/SciPostPhysCore.5.2.030

SciPost Physics Core

Adaptive numerical solution of Kadanoff-Baym equations

Francisco Meirinhos, Michael Kajan, Johann Kroha, Tim Bode

SciPost Phys. Core 5, 030 (2022) · published 27 May 2022

doi: 10.21468/SciPostPhysCore.5.2.030
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Abstract

A time-stepping scheme with adaptivity in both the step size and the integration order is presented in the context of non-equilibrium dynamics described via Kadanoff-Baym equations. The accuracy and effectiveness of the algorithm are analysed by obtaining numerical solutions of exactly solvable models. We find a significant reduction in the number of time-steps compared to fixed-step methods. Due to the at least quadratic scaling of Kadanoff-Baym equations, reducing the amount of steps can dramatically increase the accessible integration time, opening the door for the study of long-time dynamics in interacting systems. A selection of illustrative examples is provided, among them interacting and open quantum systems as well as classical stochastic processes. An open-source implementation of our algorithm in the scientific-computing language Julia is made available.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysCore.5.2.030
TI  - Adaptive numerical solution of Kadanoff-Baym equations
PY  - 2022/05/27
UR  - https://www.scipost.org/SciPostPhysCore.5.2.030
JF  - SciPost Physics Core
JA  - SciPost Phys. Core
VL  - 5
IS  - 2
SP  - 030
A1  - Meirinhos, Francisco
AU  - Kajan, Michael
AU  - Kroha, Johann
AU  - Bode, Tim
AB  - A time-stepping scheme with adaptivity in both the step size and the integration order is presented in the context of non-equilibrium dynamics described via Kadanoff-Baym equations. The accuracy and effectiveness of the algorithm are analysed by obtaining numerical solutions of exactly solvable models. We find a significant reduction in the number of time-steps compared to fixed-step methods. Due to the at least quadratic scaling of Kadanoff-Baym equations, reducing the amount of steps can dramatically increase the accessible integration time, opening the door for the study of long-time dynamics in interacting systems. A selection of illustrative examples is provided, among them interacting and open quantum systems as well as classical stochastic processes. An open-source implementation of our algorithm in the scientific-computing language Julia is made available.
ER  -

@Article{10.21468/SciPostPhysCore.5.2.030,
	title={{Adaptive numerical solution of Kadanoff-Baym equations}},
	author={Francisco Meirinhos and Michael Kajan and Johann Kroha and Tim Bode},
	journal={SciPost Phys. Core},
	volume={5},
	pages={030},
	year={2022},
	publisher={SciPost},
	doi={10.21468/SciPostPhysCore.5.2.030},
	url={https://scipost.org/10.21468/SciPostPhysCore.5.2.030},
}

Cited by 11

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¹ Francisco Meirinhos,
¹ Michael Kajan,
¹ Johann Kroha,
² Tim Bode

Funder for the research work leading to this publication

Deutsche Forschungsgemeinschaft / German Research FoundationDeutsche Forschungsgemeinschaft [DFG]