# Journal article

## An Exact Formulation of the Time-Ordered Exponential using Path-Sums

Abstract:

We present the path-sum formulation for $\mathsf{OE}[\mathsf{H}](t',t)=\mathcal{T}\,\text{exp}\big(\int_{t}^{t'}\!\mathsf{H}(\tau)\,d\tau\big)$, the time-ordered exponential of a time-dependent matrix $\mathsf{H}(t)$. The path-sum formulation gives $\mathsf{OE}[\mathsf{H}]$ 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 representatio...

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Publication date:
2014-10-24
Keywords:
Pubs id:
pubs:488575
UUID:
uuid:11a91dbf-31ba-413d-a32a-2c573715a5a1
Local pid:
pubs:488575
Source identifiers:
488575
Deposit date:
2014-11-11