Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2001-08-17
Nonlinear Sciences
Chaotic Dynamics
24 pages, 3 figures, submitted to PRE
Scientific paper
10.1103/PhysRevE.65.036201
We study the spatial autocorrelation of energy eigenfunctions $\psi_n({\bf q})$ corresponding to classically chaotic systems in the semiclassical regime. Our analysis is based on the Weyl-Wigner formalism for the spectral average $C_{\epsilon}({\bf q^{+}},{\bf q^{-}},E)$ of $\psi_n({\bf q}^{+})\psi_n^*({\bf q}^{-})$, defined as the average over eigenstates within an energy window $\epsilon$ centered at $E$. In this framework $C_{\epsilon}$ is the Fourier transform in momentum space of the spectral Wigner function $W({\bf x},E;\epsilon)$. 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 formulae in the literature and find expressions for $C_{\epsilon}({\bf q^{+}}, {\bf q^{-}},E)$ valid for any separation size $|{\bf q^{+}}-{\bf q^{-}}|$.
Lewenkopf Caio H.
Toscano Fabricio
No associations
LandOfFree
Semiclassical spatial correlations in chaotic wave functions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Semiclassical spatial correlations in chaotic wave functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Semiclassical spatial correlations in chaotic wave functions will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-544273