An exact formulation of the time-ordered exponential using path-sums

DOI10.1063/1.4920925zbMath1316.15010arXiv1410.6637OpenAlexW1580820409MaRDI QIDQ5253093

Pierre-Louis Giscard, K. Lui, S. J. Thwaite, Dieter Jaksch

Publication date: 4 June 2015

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.6637

zbMATH Keywords

sparse matricesbranched continued fractionexponential of a time-dependent matrixpath-sum formulationwalks on a graph

Mathematics Subject Classification ID

Continued fractions and generalizations (11J70) Matrix exponential and similar functions of matrices (15A16) Random walks on graphs (05C81)

Related Items (14)

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Uses Software

• mftoolbox

Cites Work

• Unnamed Item
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• Decay bounds and \(O(n)\) algorithms for approximating functions of sparse matrices
• Bounds for the entries of matrix functions with applications to preconditioning
• Decay properties for functions of matrices over \(C^\ast\)-algebras
• Bounds on the number of closed walks in a graph and its applications
• On the finite section method for computing exponentials of doubly-infinite skew-Hermitian matrices
• Evaluating Matrix Functions by Resummations on Graphs: The Method of Path-Sums
• Decomposition of time-ordered products and path-ordered exponentials
• Decay Properties of Spectral Projectors with Applications to Electronic Structure
• Functions of Matrices

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