Critical statistics in a power-law random-banded matrix ensemble
We investigate the statistical properties of the eigenvalues and eigenvectors in a random
matrix ensemble with H ij∼| i− j|− μ. It is known that this model shows a localization-
delocalization transition (LDT) as a function of the parameter μ. The model is critical at μ= 1
and the eigenstates are multifractals. Based on numerical simulations we demonstrate that
the spectral statistics at criticality differs from semi-Poisson statistics which is expected to be
a general feature of systems exhibiting a LDT or “weak chaos.”
matrix ensemble with H ij∼| i− j|− μ. It is known that this model shows a localization-
delocalization transition (LDT) as a function of the parameter μ. The model is critical at μ= 1
and the eigenstates are multifractals. Based on numerical simulations we demonstrate that
the spectral statistics at criticality differs from semi-Poisson statistics which is expected to be
a general feature of systems exhibiting a LDT or “weak chaos.”
Abstract
We investigate the statistical properties of the eigenvalues and eigenvectors in a random matrix ensemble with H ij∼| i− j|− μ. It is known that this model shows a localization-delocalization transition (LDT) as a function of the parameter μ. The model is critical at μ= 1 and the eigenstates are multifractals. Based on numerical simulations we demonstrate that the spectral statistics at criticality differs from semi-Poisson statistics which is expected to be a general feature of systems exhibiting a LDT or “weak chaos.”
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