New class of level statistics in correlated disordered chains

• Published in: Physical review letters 2004-10, Vol.93 (17), p.176804.1-176808.4, Article 176804
• Main Authors: CARPENA, Pedro, BERNAOLA-GALVAN, Pedro, IVANOV, Plamen Ch
• Format: Article
• Language: English
• Subjects: Condensed matter: electronic structure, electrical, magnetic, and optical properties; Electron states and collective excitations in multilayers, quantum wells, mesoscopic, and nanoscale systems; Electron states and collective excitations in thin films, multilayers, quantum wells, mesoscopic and nanoscale systems; Electronic structure and electrical properties of surfaces, interfaces, thin films and low-dimensional structures; Exact sciences and technology; Physics
• ISSN: 0031-9007; 1079-7114
• DOI: 10.1103/PhysRevLett.93.176804

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.