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

Journal article

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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Authors: Giscard, P; Lui, K; Thwaite, S; Jaksch, D

• Publication date: 2014-10-24
• Keywords: math.CA; math.MP; math-ph