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Gaussian fluctuations in chaotic eigenstates

Mark Srednicki and Frank Stiernelof

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We study the fluctuations that are predicted in the autocorrelation function of an energy eigenstate of a chaotic, two-dimensional billiard by the conjecture (due to Berry) that the eigenfunction is a Gaussian random variable. We find an explicit formula for the root-mean-square amplitude of the expected fluctuations in the autocorrelation function. These fluctuations turn out to be in the small (high energy) limit. For comparison, any corrections due to scars from isolated periodic orbits would also be . The fluctuations take on a particularly simple form if the autocorrelation function is averaged over the direction of the separation vector. We compare our various predictions with recent numerical computations of Li and Robnik for the Robnik billiard, and find good agreement. We indicate how our results generalize to higher dimensions.


PACS

05.45.Pq Numerical simulations of chaotic systems

05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion

MSC

65P20 Numerical chaos

Subjects

Statistical physics and nonlinear systems

Dates

Issue 18 (21 September 1996)

Received 10 April 1996



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