Trace formulae for stochastic evolution operators: smooth conjugation method
Trace formulae for stochastic evolution operators: smooth conjugation method
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随机演化算子的迹公式：平滑共轭法
DOI：
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
Budapešť
中科院分区：
文献类型：
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作者：
P. Cvitanović;C. Dettmann;R. Mainieri;Gabor Vattay Niels Bohr Institute;Copenhagen;L. Laboratory;E. University;Budapešť
在路径积分形式下给出了带弱加性噪声的非线性随机流的发展算子的迹公式。我们集成了一个给定的鞍点的邻域正是通过一个光滑的共轭，一个局部分析的非线性变化的字段变量。微扰校正转移到相应的雅可比矩阵，我们展开的共轭函数，而不是在定义路径积分的行动。新的微扰展开，随后由导数的递归评估出现比标准的费曼图微扰理论更紧凑。其结果是一个随机模拟的Gutzwiller跟踪公式与"校正计算的顺序高于迄今为止在随机和量子力学应用中所能达到的。
The trace formula for the evolution operator associated with nonlinear stochastic flows with weak additive noise is cast in the path integral formalism. We integrate over the neighbourhood of a given saddlepoint exactly by means of a smooth conjugacy, a locally analytic nonlinear change of field variables. The perturbative corrections are transferred to the corresponding Jacobian, which we expand in terms of the conjugating function, rather than the action used in defining the path integral. The new perturbative expansion which follows by a recursive evaluation of derivatives appears more compact than the standard Feynman diagram perturbation theory. The result is a stochastic analogue of the Gutzwiller trace formula with the `' corrections computed an order higher than what has so far been attainable in stochastic and quantum mechanical applications.