918 research outputs found
Symmetry deduction from spectral fluctuations in complex quantum systems
The spectral fluctuations of complex quantum systems, in appropriate limit,
are known to be consistent with that obtained from random matrices. However,
this relation between the spectral fluctuations of physical systems and random
matrices is valid only if the spectra are desymmetrized. This implies that the
fluctuation properties of the spectra are affected by the discrete symmetries
of the system. In this work, it is shown that in the chaotic limit the
fluctuation characteristics and symmetry structure for any arbitrary sequence
of measured or computed levels can be inferred from its higher-order spectral
statistics without desymmetrization. In particular, we consider a spectrum
composed of independent level sequences with each sequence having the
same level density. The -th order spacing ratio distribution of such a
composite spectrum is identical to its nearest neighbor counterpart with
modified Dyson index . This is demonstrated for the spectra obtained from
random matrices, quantum billiards, spin chains and experimentally measured
nuclear resonances with disparate symmetry features.Comment: Revised text and new figures. Final versio
Spectral fluctuations and 1/f noise in the order-chaos transition regime
Level fluctuations in quantum system have been used to characterize quantum
chaos using random matrix models. Recently time series methods were used to
relate level fluctuations to the classical dynamics in the regular and chaotic
limit. In this we show that the spectrum of the system undergoing order to
chaos transition displays a characteristic noise and is
correlated with the classical chaos in the system. We demonstrate this using a
smooth potential and a time-dependent system modeled by Gaussian and circular
ensembles respectively of random matrix theory. We show the effect of short
periodic orbits on these fluctuation measures.Comment: 4 pages, 5 figures. Modified version. To appear in Phys. Rev. Let
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