Spectral fluctuations of multiparametric complex matrix ensembles:
evidence of a single parameter dependence
- URL: http://arxiv.org/abs/2312.08203v2
- Date: Sat, 2 Mar 2024 05:53:52 GMT
- Title: Spectral fluctuations of multiparametric complex matrix ensembles:
evidence of a single parameter dependence
- Authors: Mohd. Gayas Ansari and Pragya Shukla
- Abstract summary: We numerically analyze the spectral statistics of the multiparametric Gaussian ensembles of complex matrices with zero mean and variances with different decay routes away from the diagonals.
Such ensembles can serve as good models for a wide range of phase transitions e.g. localization to delocalization in non-Hermitian systems or Hermitian to non-Hermitian one.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We numerically analyze the spectral statistics of the multiparametric
Gaussian ensembles of complex matrices with zero mean and variances with
different decay routes away from the diagonals. As the latter mimics different
degree of effective sparsity among the matrix elements, such ensembles can
serve as good models for a wide range of phase transitions e.g. localization to
delocalization in non-Hermitian systems or Hermitian to non-Hermitian one. Our
analysis reveals a rich behavior hidden beneath the spectral statistics e.g. a
crossover of the spectral statistics from Poisson to Ginibre universality class
with changing variances for finite matrix size, an abrupt transition for
infinite matrix size and the role of complexity parameter, a single functional
of all system parameters, as a criteria to determine critical point. We also
confirm the theoretical predictions in \cite{psgs, psnh}, regarding the
universality of the spectral statistics in non-equilibrium regime of
non-Hermitian systems characterized by the complexity parameter.
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