KadanoffBaym

The KadanoffBaym package is a state-of-the-art computational framework for simulating the non-equilibrium strongly correlated electron systems. It provides some useful application programming interfaces to manipulate the non-equilibrium Green's functions defined on the 𝐿-shape Kadanoff-Baym contour, including:

• Basic integration and differentiation rules
• Basic operations for Contour Green's functions
• Basic diagrammatic algorithms based on many-body perturbation theory
• Solve Volterra integral equations
• Solve Volterra integro-differential equations
• Convolution between two contour Green's functions

This package is inspired by the NESSi (The Non-Equilibrium Systems Simulation package) code, which was developed and maintained by Martin Eckstein et al. Actually, it can be regarded as a replacement of the NESSi package for those peoples who don't like or aren't familiar with C++.

References

[NESSi] Martin Eckstein, et al., NESSi: The Non-Equilibrium Systems Simulation package, Computer Physics Communications 257, 107484 (2020)

[REVIEW] Philipp Werner, et al., Nonequilibrium dynamical mean-field theory and its applications, Reviews of Modern Physics 86, 779 (2014)

[MABOOK] Johan de Villiers, Mathematics of Approximation, Atlantis Press (2012)

[MATABLE] Dan Zwillinger (editor), CRC Standard Mathematical Tables and Formulas (33rd edition), CRC Press (Taylor & Francis Group) (2018)

[QUADRATURE] Ruben J. Espinosa-Maldonado and George D. Byrne, On the Convergence of Quadrature Formulas, SIAM J. Numer. Anal. 8, 110 (1971)

_precompile()

Here, we would like to precompile the whole KadanoffBaym toolkit to reduce the runtime latency and speed up the successive calculations.

__init__()

This function would be executed immediately after the module is loaded at runtime for the first time. It works at the REPL mode only.