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- W2977966210 abstract "We point out that by the ``smoothness means fast decay'' principle in Fourier analysis, it is possible to infer the smoothness (or nonsmoothness) of the autocorrelation function from a mere glimpse of the initial state. Specifically, for a generic system with smooth eigenstates, the smoother an initial state is, the faster its decomposition coefficients with respect to the eigenstates of the system decay, and in turn the smoother the autocorrelation function is. The idea is illustrated with three increasingly smooth functions in an infinite square well. By using the Mellin transform, we also find that the nonsmoothness or singularity of the initial state affects the short-time behavior of its autocorrelation function. In particular, a sufficiently nonsmooth or singular initial state could decay in a nonquadratic power law, with the exponent continuously tunable. We now understand the periodic cusps of the autocorrelation function in the quench dynamics of a Bloch state, which was observed previously [Zhang and Yang, EPL 114, 60001 (2016)]." @default.
- W2977966210 created "2019-10-10" @default.
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- W2977966210 date "2018-11-28" @default.
- W2977966210 modified "2023-09-27" @default.
- W2977966210 title "From the smoothness of the initial state to that of the autocorrelation function" @default.
- W2977966210 hasPublicationYear "2018" @default.
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