Application of the Perturbative Renormalization Group Method Based on the Lie Group to Pulse Dynamics(Condensed Matter and Statistical Physics)

概要

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Pulse dynamics are studied using the perturbative renormalization group method based on the Lie group. The method is explained with several examples, and its similarities and dissimilarities with other methods are discussed. An interacting pulse is composed of a superposition of a single pulse solution (that is, the zero-th order solution) and its corrections. In the present method, the corrections are assumed to be expansions in terms of the zero eigenfunctions of a linear operator, whose coefficients are time-dependent variables. Unlike in other methods, in the present method, the time-dependence of the position of a pulse is introduced a posteriori in order to avoid the divergence of the corrections obtained in the naive perturbation expansion. The time-dependence of the position of a pulse is easily obtained by taking the inner product with the zero eigenfunction of the adjoint operator. It is shown that the present method based on the Lie group is a first-order approximation of interacting pulses. However, the truncated renormalization transformation reproduces the results obtained with other methods. It is necessary to use the zero-th order solutions of the linear operator and its adjoint operator in order to perform actual calculations.
理論物理学刊行会の論文
2005-04-25