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- W1990382847 abstract "It is shown that expectation values and transition matrix elements in classically chaotic quantum systems may not fluctuate randomly, since features of the short-time classical dynamics significantly affect the fluctuations. We analyze semiclassical sum rules constraining expectation values and transition matrix elements in classically chaotic and integrable quantum systems. We show that these sum rules exhibit a wealth of interesting structures (resonances and oscillatory contributions) as well as interesting properties, such as their asymptotic decay. It is shown how these properties can be explained semiclassically, in terms of periodic and quasiperiodic classical motion. In particular, we analyze how phase-space inhomogeneities in chaotic systems give rise to localization of wave functions and hence to exceptionally large matrix elements. These are related to resonances in classical autocorrelation functions. As an example, we consider a family of billiards in two dimensions the classical dynamics of which ranges from integrable to chaotic." @default.
- W1990382847 created "2016-06-24" @default.
- W1990382847 creator A5074141887 @default.
- W1990382847 date "1999-01-01" @default.
- W1990382847 modified "2023-10-03" @default.
- W1990382847 title "Semiclassical sum rules for matrix elements and response functions in chaotic and in integrable quantum billiards" @default.
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- W1990382847 doi "https://doi.org/10.1103/physreve.59.390" @default.
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