## next Q-MAC meetings in 2018:

3^{rd} Q-MAC symposium in Venice, May 22-25, 2018.

Next regular meeting in Paris, November 27-28, 2018.

Read more## Antoine Georges leads the CCQ in New York

at the newly founded Flatiron Institute of the Simons Foundation.

Read more# Publication Detail / Abstract

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

published in the Journal of Mathematical Physics on May 11, 2015

> Full text via publisher
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.

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