Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Time-ordering and a generalized Magnus expansion   Both the classical time-ordering and the Magnus expansion are well-known in
the context of linear initial value problems. Motivated by the noncommutativity
between time-ordering and time derivation, and related problems raised recently
in statistical physics, we introduce a generalization of the Magnus expansion.
Whereas the classical expansion computes the logarithm of the evolution
operator of a linear differential equation, our generalization addresses the
same problem, including however directly a non-trivial initial condition. As a
by-product we recover a variant of the time ordering operation, known as
T*-ordering. Eventually, placing our results in the general context of
Rota-Baxter algebras permits us to present them in a more natural algebraic
setting. It encompasses, for example, the case where one considers linear
difference equations instead of linear differential equations.

25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci