Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Exact Formulation of the Time-Ordered Exponential using Path-Sums   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 representation of the time-ordered
exponential as the inverse of an operator, the mapping of this inverse to sums
of walks on 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.

20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an