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GSE spectra in uni-directional quantum systems

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 Added by Maram Akila
 Publication date 2018
  fields Physics
and research's language is English




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Generically, spectral statistics of spinless systems with time reversal invariance (TRI) and chaotic dynamics are well described by the Gaussian Orthogonal ensemble (GOE). However, if an additional symmetry is present, the spectrum can be split into independent sectors which statistics depend on the type of the groups irreducible representation. In particular, this allows the construction of TRI quantum graphs with spectral statistics characteristic of the Gaussian Symplectic ensembles (GSE). To this end one usually has to use groups admitting pseudo-real irreducible representations. In this paper we show how GSE spectral statistics can be realized in TRI systems with simpler symmetry groups lacking pseudo-real representations. As an application, we provide a class of quantum graphs with only $C_4$ rotational symmetry possessing GSE spectral statistics.



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