Spectrum of stochastic evolution operators: local matrix representation approach.
Spectrum of stochastic evolution operators: local matrix representation approach.
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随机演化算子谱：局部矩阵表示方法。
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
C. Dettmann
中科院分区：
文献类型：
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作者：
P. Cvitanović;N. Søndergaard;G. Palla;G. Vattay;C. Dettmann
用加性噪声非线性随机流的演化算子的矩阵表示来计算其谱。在弱噪声极限下，用以经典周期轨道为中心的演化算子的局部矩阵表示来表示谱的微扰展开式。与标准的费曼图扰动理论相比，微扰修正的评估在这个框架中更容易实现。这些结果是对古兹威尔半经典谱行列式的随机模拟的微扰修正，计算结果达到了迄今为止在随机和量子力学应用中所能获得的几个数量级。
A matrix representation of the evolution operator associated with a nonlinear stochastic flow with additive noise is used to compute its spectrum. In the weak noise limit a perturbative expansion for the spectrum is formulated in terms of local matrix representations of the evolution operator centered on classical periodic orbits. The evaluation of perturbative corrections is easier to implement in this framework than in the standard Feynman diagram perturbation theory. The results are perturbative corrections to a stochastic analog of the Gutzwiller semiclassical spectral determinant computed to several orders beyond what has so far been attainable in stochastic and quantum-mechanical applications.