Adaptive Numerical Solution of Kadanoff-Baym Equations

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.

37 pages, 17 figures

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Cited by in corpus (13)

• Time-linear quantum transport simulations with correlated nonequilibrium Green's functions
• Excitations and spectra from equilibrium real-time Green's functions
• Adaptive Time Stepping for the Two-Time Integro-Differential Kadanoff-Baym Equations
• Chirped amplitude mode in photo-excited superconductors
• Memory-Efficient Nonequilibrium Green's Function Framework Built On Quantics Tensor Trains
• Non-Markovian Dynamics of Open Quantum Systems via Auxiliary Particles with Exact Operator Constraint
• Prethermalization of light and matter in cavity-coupled Rydberg arrays
• Thermalization of a Closed Sachdev-Ye-Kitaev System in the Thermodynamic Limit
• The Two-Particle Irreducible Effective Action for Classical Stochastic Processes
• Schwinger-Keldysh non-perturbative field theory of open quantum systems beyond the Markovian regime: Application to spin-boson and spin-chain-boson models
• Compact representation and long-time extrapolation of real-time data for quantum systems using the ESPRIT algorithm
• Symmetry adaptation for self-consistent many-body calculations
• Quantum anomalous Hall domains in a Quenched Topological Mott Insulator