期刊
JOURNAL OF MATHEMATICAL PHYSICS
卷 56, 期 5, 页码 -出版社
AMER INST PHYSICS
DOI: 10.1063/1.4920925
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资金
- EPSRC [EP/K038311/1]
- ERC under the European Unions Seventh Framework Programme/ERC [FP7/2007-2013, 319286 Q-MAC]
- Bechtel Fund Summer Internship Award
- Alexander von Humboldt Foundation
- Engineering and Physical Sciences Research Council [EP/K038311/1, EP/M013243/1] Funding Source: researchfish
- EPSRC [EP/K038311/1, EP/M013243/1] Funding Source: UKRI
We present the path-sum formulation for the time-ordered exponential of a time-dependent matrix. The path-sum formulation gives the time-ordered exponential as a branched continued fraction of finite depth and breadth. The terms of the path-sum have an elementary interpretation as self-avoiding walks and self-avoiding polygons on a graph. Our result is based on a representation of the time-ordered exponential as the inverse of an operator, the mapping of this inverse to sums of walks on a graphs, and the algebraic structure of sets of walks. We give examples demonstrating our approach. We establish a super-exponential decay bound for the magnitude of the entries of the time-ordered exponential of sparse matrices. We give explicit results for matrices with commonly encountered sparse structures. (C) 2015 AIP Publishing LLC.
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