# Application of the shift-invert Lanczos algorithm to a non-equilibrium Green function for transport problems

Source: [Application of the shift-invert Lanczos algorithm to a non-equilibrium Green function for transport problems](<https://www.sota2.com/research/paper/68fa490a1e209131ce9342b4>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T07:08:35.105Z

Authors: K. Uzawa, K. Hagino

Published: 2024-08-13T01:34:37.000Z

## Abstract

Non-equilibrium Green's function theory and related methods are widely used to describe transport phenomena in many-body systems, but they often require a costly inversion of a large matrix. We show here that the shift-invert Lanczos method can dramatically reduce the computational effort. We apply the method to two test problems, namely a simple model Hamiltonian and to a more realistic Hamiltonian for nuclear fission. For a Hamiltonian of dimension 66103 we find that the computation time is reduced by a factor of 33 compared to the direct calculation of the Green's function.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2408.06554>)

[PDF](<https://arxiv.org/pdf/2408.06554.pdf>)