Tuesday, June 19, 2012

1206.3990 (Michel Bauer et al.)

Time-ordering and a generalized Magnus expansion    [PDF]

Michel Bauer, Raphael Chetrite, Kurusch Ebrahimi-Fard, Frederic Patras
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.
View original: http://arxiv.org/abs/1206.3990

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