2004/10/20 by Pedro Carpena, Pedro Bernaola‐Galván, Pedro Bernaola-Galvan +1
Mathematics · Physics and Astronomy · #Distribution (mathematics) #Limit (mathematics) #Mathematical analysis #Mathematics #Physics #Poisson distribution #Quantum chaos and dynamical systems #Range (aeronautics) #Standard deviation #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Uncorrelated #cond-mat.dis-nn
paper · pdf · doi:10.1103/physrevlett.93.176804
published as Physical Review Letters 93, 176804 (2004) · 5 pages and 4 figures. RevTeX 4
openalex publication_date 2004/10/20 · arxiv created 2004/12/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the properties of the level statistics of 1D disordered systems with long-range spatial correlations. We find a threshold value in the degree of correlations below which in the limit of large system size the level statistics follows a Poisson distribution (as expected for 1D uncorrelated-disordered systems), and above which the level statistics is described by a new class of distribution functions. At the threshold, we find that with increasing system size, the standard deviation of the function describing the level statistics converges to the standard deviation of the Poissonian distribution as a power law. Above the threshold we find that the level statistics is characterized by different functional forms for different degrees of correlations.