Localization-delocalization transition in one-dimensional electron systems with long-range correlated disorder

Abstract

We investigate localization properties of electron eigenstates in one-dimensional (1D) systems with longrange correlated diagonal disorder. Numerical studies on the localization length of eigenstates demonstrate the existence of the localization-delocalization transition in 1D systems and elucidate nontrivial behavior of as a function of the disorder strength. The critical exponent for localization length is extracted for various values of parameters characterizing the disorder, revealing that every disobeys the Harris criterion Ͼ 2/d.

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

“…However, it was demonstrated later on that ␣ c = 2 is the universal critical value for the LDT to occur in this model, independently of . 19 Another peculiarity of this model, having a direct relationship to the specific form of the random potential ͑2͒ as well as to its localization properties, is that the absorption spectrum at ␣ Ͼ ␣ c = 2, i.e., in the presence of the phase of extended states, reveals a double-peaked structure ͑see Ref. 66 and Sec.…”

Absence of extended states in a ladder model of DNA

“…[3][4][5][6][7][8] Those models are based on the fact that random sequences, having a power-law spectral density S͑k͒ϳ1/k ␣ with ␣ Ͼ 0, result in a phase of extended states at the band center, provided ␣ is larger than a critical value ␣ c . [9][10][11][12] As a consequence, long range charge transport might be feasible even at very low temperature, provided the chemical potential lies within the band of extended states.…”

Emergence of self-similarity in football dynamics

“…If C j (τ ) follows a power law such as: then the corresponding process u j (t) is said to be fBm with a Hurst exponent of H [16]. If H > 1/2, the interincremental correlation will be positive [18], indicating a strong trend in the time series marked by a rather smooth data profile with a memory effect [16]. Because the correlation between the increments disappears at a large time scale, in practice, equation (5) is valid only at τ < η j , where η j is a characteristic time scale, in which case C j (τ ) for τ > η j approaches a constant value.…”