Abstract
My focus in this talk will be on the statistical properties of the quantum energy eigenfunctions in classically chaotic systems. Twenty years ago, Berry1 conjectured that these eigenfunctions could be treated as gaussian random variables, and that the spatial correlations would be those following from taking the expected value of the Wigner density for each eigenfunction to be microcanonical. More specifically, the probability that the actual eigenfunction ψα(q) for energy E = Eα (the corresponding energy eigenvalue) is between ψ(q) and ψ(q) +dψ(q) for all coordinate points q is given by (1)
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Srednicki, M. (1999). Spatial Correlations in Chaotic Eigenfunctions. In: Lerner, I.V., Keating, J.P., Khmelnitskii, D.E. (eds) Supersymmetry and Trace Formulae. NATO ASI Series, vol 370. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4875-1_13
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