Theoretical derivation of 1/ƒ noise in quantum chaos

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It was recently conjectured that 1/ƒ noise is a fundamental characteristic of spectral fluctuations in chaotic quantum systems. This conjecture is based on the power spectrum behavior of the excitation energy fluctuations, which is different for chaotic and integrable systems. Using random matrix theory, we derive theoretical expressions that explain without free parameters the universal behavior of the excitation energy fluctuations power spectrum. The theory gives excellent agreement with numerical calculations and reproduces to a good approximation the 1/ƒ (1/ƒ^(2)) power law characteristic of chaotic (integrable) systems. Moreover, the theoretical results are valid for semiclassical systems as well.
©2004 The American Physical Society. We are particularly indebted to P. Leboeuf, O. Bohigas, and M. Robnik for enlightening discussions. This work is supported in part by Spanish Government Grants No. BFM2003-04147-C02 and No. FTN2003-08337-C04-04.
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