Toscano Fabricio, Lewenkopf Caio H
Instituto de Física, Universidade do Estado do Rio de Janeiro, R. São Francisco Xavier 524, 20559-900 Rio de Janeiro, Brazil.
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Mar;65(3 Pt 2A):036201. doi: 10.1103/PhysRevE.65.036201. Epub 2002 Feb 8.
We study the spatial autocorrelation of energy eigenfunctions psi(n)(q) corresponding to classically chaotic systems in the semiclassical regime. Our analysis is based on the Weyl-Wigner formalism for the spectral average C(epsilon)(q(+),q(-),E) of psi(n)(q(+))psi(*)(n)(q(-)), defined as the average over eigenstates within an energy window epsilon centered at E. In this framework C(epsilon) is the Fourier transform in the momentum space of the spectral Wigner function W(x,E;epsilon). Our study reveals the chord structure that C(epsilon) inherits from the spectral Wigner function showing the interplay between the size of the spectral average window, and the spatial separation scale. We discuss under which conditions is it possible to define a local system independent regime for C(epsilon). In doing so, we derive an expression that bridges the existing formulas in the literature and find expressions for C(epsilon)(q(+),q(-),E) valid for any separation size /q(+)-q(-)/.
我们研究了在半经典区域中与经典混沌系统相对应的能量本征函数ψ(n)(q)的空间自相关。我们的分析基于魏尔 - 维格纳形式体系，用于ψ(n)(q(+))ψ*(n)(q(-))的谱平均C(ε)(q(+),q(-),E)，其定义为以E为中心的能量窗口ε内本征态的平均值。在此框架下，C(ε)是谱维格纳函数W(x,E;ε)在动量空间中的傅里叶变换。我们的研究揭示了C(ε)从谱维格纳函数继承的弦结构，展示了谱平均窗口大小与空间分离尺度之间的相互作用。我们讨论了在哪些条件下可以为C(ε)定义一个与系统无关的局部区域。在此过程中，我们推导了一个连接文献中现有公式的表达式，并找到了对任何分离大小/q(+)-q(-)/都有效的C(ε)(q(+),q(-),E)的表达式。
