Time-ordering and a generalized Magnus expansion

Abstract : 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.
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Contributor : Patras Frédéric <>
Submitted on : Saturday, November 17, 2012 - 3:26:14 PM
Last modification on : Tuesday, October 16, 2018 - 2:26:02 PM

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Michel Bauer, Raphael Chetrite, Kurusch Ebrahimi-Fard, Frederic Patras. Time-ordering and a generalized Magnus expansion. Letters in Mathematical Physics, Springer Verlag, 2013, 103 (3), pp.331-350. ⟨10.1007/s11005-012-0596-z⟩. ⟨hal-00753116⟩

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