PMID: 11909206Mar 23, 2002Paper

Semiclassical spatial correlations in chaotic wave functions

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Fabricio Toscano, Caio H Lewenkopf

Abstract

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(-)/.

References

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Jan 3, 2001·Physical Review Letters·F Toscano Ozorio De Almeida AM

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Citations

May 15, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·F M CucchiettiR O Vallejos
Jan 20, 2018·Physical Review. E·Rodolfo A JalabertDietmar Weinmann
Apr 12, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Alexei Akolzin, Richard L Weaver
Oct 30, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Rodolfo A JalabertDietmar Weinmann
May 21, 2005·Physical Review Letters·Holger Schanz
Aug 25, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Juan Diego Urbina, Klaus Richter

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