New Class of Level Statistics in Correlated Disordered Chains

Carpena, Pedro; Bernaola‐Galván, Pedro; Ivanov, Plamen Ch.

doi:10.1103/physrevlett.93.176804

Cited by 37 publications

(23 citation statements)

References 20 publications

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“…It has been observed that the strength of the long-range correlations in such systems can control their electronic properties, as the localization length [30–32] or the level statistics [33]. For 1D binary systems, α = 0.5 corresponds to the random binary alloy [34], where the electronic states are exponentially localized.…”

Section: Implications To Correlated-disordered Systemsmentioning

confidence: 99%

Phase transitions in the first-passage time of scale-invariant correlated processes

et al. 2012

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A key quantity describing the dynamics of complex systems is the first-passage time (FPT). The statistical properties of FPT depend on the specifics of the underlying system dynamics. We present a unified approach to account for the diversity of statistical behaviors of FPT observed in real-world systems. We find three distinct regimes, separated by two transition points, with fundamentally different behavior for FPT as a function of increasing strength of the correlations in the system dynamics: stretched exponential, power-law, and saturation regimes. In the saturation regime, the average length of FPT diverges proportionally to the system size, with important implications for understanding electronic delocalization in one-dimensional correlated-disordered systems.

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Section: Implications To Correlated-disordered Systemsmentioning

confidence: 99%

Phase transitions in the first-passage time of scale-invariant correlated processes

et al. 2012

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“…10,18,20,36 The 1 / k ␣ law has also its trace in energy level statistics. 15 All said above unambiguously testifies that studying the properties of disordered systems with long-range-correlated disorder is an attention grabbing task.…”

Section: Introductionmentioning

confidence: 99%

Wannier-Stark ladder in the linear absorption of a random system with scale-free disorder

et al. 2006

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We study numerically the linear optical response of a quasiparticle moving on a one-dimensional disordered lattice in the presence of a linear bias. The random site potential is assumed to be long-range correlated with a power-law spectral density S͑k͒ϳ1/k ␣ , ␣ Ͼ 0. This type of correlation results in a phase of extended states at the band center, provided ␣ is larger than a critical value ␣ c ͓F. A. B. F. de Moura and M. L. Lyra, Phys. Rev. Lett. 81, 3735 ͑1998͔͒. The width of the delocalized phase can be tested by applying an external electric field: Bloch-like oscillations of a quasiparticle wave packet are governed by the two mobility edges, playing now the role of band edges ͓F. Domínguez-Adame et al., Phys. Rev. Lett. 91, 197402 ͑2003͔͒. We demonstrate that the frequency-domain counterpart of these oscillations, the so-called Wannier-Stark ladder, also arises in this system. When the phase of extended states emerges in the system, this ladder turns out to be a comb of doublets, for some range of disorder strength and bias. Linear optical absorption provides a tool to detect this level structure.

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“…8 At the end of the 1980s and beginning of the 1990s it was realized, however, that correlations in disorder may give rise to extended states in low dimensions. [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] Thus, short-range correlated on-site disorder was found to cause the appearance of extended states at special resonance energies in 1D. They form a set of null measure in the density of states in the thermodynamic limit, [9][10][11][12][13][14] implying the absence of mobility edges in those models.…”

Section: Introductionmentioning

confidence: 99%

Localization properties of a one-dimensional tight-binding model with nonrandom long-range intersite interactions

et al. 2005

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We perform both analytical and numerical studies of the one-dimensional tight-binding Hamiltonian with stochastic uncorrelated on-site energies and nonfluctuating long-range hopping integrals J mn = J / ͉m − n͉ . It was argued recently ͓A. Rodríguez et al., J. Phys. A 33, L161 ͑2000͔͒ that this model reveals a localizationdelocalization transition with respect to the disorder magnitude provided 1 Ͻ Ͻ 3 / 2. The transition occurs at one of the band edges ͑the upper one for J Ͼ 0 and the lower one for J Ͻ 0͒. The states at the other band edge are always localized, which hints at the existence of a single mobility edge. We analyze the mobility edge and show that, although the number of delocalized states tends to infinity, they form a set of null measure in the thermodynamic limit, i.e., the mobility edge tends to the band edge. The critical magnitude of disorder for the band edge states is computed versus the interaction exponent by making use of the conjecture on the universality of the normalized participation number distribution at the transition.

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New Class of Level Statistics in Correlated Disordered Chains

Cited by 37 publications

References 20 publications

Phase transitions in the first-passage time of scale-invariant correlated processes

Phase transitions in the first-passage time of scale-invariant correlated processes

Wannier-Stark ladder in the linear absorption of a random system with scale-free disorder

Localization properties of a one-dimensional tight-binding model with nonrandom long-range intersite interactions

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