Related Experiment Video
Updated: Jul 16, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
Published on: July 19, 2016
Stochastic resolution of identity second-order Matsubara Green's function theory
Tyler Y Takeshita1, Wenjie Dou2, Daniel G A Smith3
1Mercedes-Benz Research and Development North America, Sunnyvale, California 94085, USA.
Abstract:
We develop a stochastic resolution of identity representation to the second-order Matsubara Green's function (sRI-GF2) theory. Using a stochastic resolution of the Coulomb integrals, the second order Born self-energy in GF2 is decoupled and reduced to matrix products/contractions, which reduces the computational cost from O(N5) to O(N3) (with N being the number of atomic orbitals). The current approach can be viewed as an extension to our previous work on stochastic resolution of identity second order Møller-Plesset perturbation theory [T. Y. Takeshita et al., J. Chem. Theory Comput. 13, 4605 (2017)] and offers an alternative to previous stochastic GF2 formulations [D. Neuhauser et al., J. Chem. Theory Comput. 13, 5396 (2017)]. We show that sRI-GF2 recovers the deterministic GF2 results for small systems, is computationally faster than deterministic GF2 for N > 80, and is a practical approach to describe weak correlations in systems with 103 electrons and more.
Related Concept Videos
Second Uniqueness Theorem
In contrast, consider that the electric field is non-unique and apply Gauss's law in divergence form in the region between the conductors and the integral form to the surface...
Second Derivatives and Laplace Operator
Consider a scalar function. The curl of its...
Divergence and Stokes' Theorems
Second Order systems II
If ζ...
Green’s Theorem
Extended Versions of Green’s Theorem

