相关论文: Single parameter scaling of one-dimensional system…
Numerical study of the scaling of transmission fluctuations in the 1-D localization problem in the presence of absorption is carried out. Violations of single parameter scaling for lossy systems are found and explained on the basis of a new…
The variance of the Lyapunov exponent is calculated exactly in the one-dimensional Anderson model with random site energies distributed according to the Cauchy distribution. We derive an exact analytical criterion for the validity of the…
A one-dimensional diagonal tight binding electronic system with correlated disorder is investigated. The correlation of the random potential is exponentially decaying with distance and its correlation length diverges as the concentration of…
Validity of the single parameter scaling (SPS) in one dimensional Anderson model with purely off-diagonal disorder is being studied. It is shown that the localized region with standard symmetry is divided into two regimes: SPS and non-SPS.…
By using dimensionless conductances as scaling variables, the conventional one-parameter scaling theory of localization fails for non-reciprocal non-Hermitian systems such as the Hanato-Nelson model. Here, we propose a one-parameter scaling…
We investigate localization properties of electron eigenstates in one-dimensional (1d) systems with long-range correlated diagonal disorder. Numerical studies on the localization length $\xi$ of eigenstates demonstrate the existence of the…
This review is intended to give a pedagogical and unified view on the subject of the statistics and scaling of physical quantities in disordered electron systems at very low temperatures. Quantum coherence at low temperatures and randomness…
We numerically investigate dynamical property in the one-dimensional tight-binding model with long-range correlated disorder having power spectrum $1/f^\alpha$ ($\alpha:$spectrum exponent) generated by Fourier filtering method. For…
The localization lengths of long-range correlated disordered chains are studied for electronic wavefunctions in the Anderson model and for vibrational states. A scaling theory close to the band edge is developed in the Anderson model and…
We investigate the three-dimensional Anderson model of localization via a modified transfer-matrix method in the presence of scale-free diagonal disorder characterized by a disorder correlation function $g(r)$ decaying asymptotically as…
Statistical and scaling properties of the Lyapunov exponent for a tight-binding model with the diagonal disorder described by a dichotomic process are considered near the band edge. The effect of correlations on scaling properties is…
The localization behavior of the one-dimensional Anderson model with correlated and uncorrelated purely off-diagonal disorder is studied. Using the transfer matrix method, we derive an analytical expression for the localization length at…
We present a perturbative approach to disordered systems in one spatial dimension that accesses the full range of phase disorder and clarifies the connection between localization and phase information. We consider a long chain of…
We study the metal-insulator transition in a tight-binding one-dimensional (1D) model with long-range correlated disorder. In the case of diagonal disorder with site energy within $[-\frac{W}{2},\frac{W}{2}]$ and having a power-law spectral…
We study the delocalisation transition which takes places in one-dimensional disordered systems when the random potential exhibits specific long-range correlations. We consider the case of weak disorder; using a systematic perturbative…
Based on the spectral statistics obtained in numerical simulations on three dimensional disordered systems within the tight--binding approximation, a new superuniversal scaling relation is presented that allows us to collapse data for the…
We numerically study the distribution function of the conductivity (transmission) in the one-dimensional tight-binding Anderson model in the region of fluctuation states. We show that while single parameter scaling in this region is not…
The scaling property of level statistics in the quantum Hall regime, i.e. 2D disordered electron systems subject to strong magnetic fields, is analyzed numerically in the light of the random matrix theory. The energy dependences of the…
The single-parameter scaling hypothesis relating the average and variance of the logarithm of the conductance is a pillar of the theory of electronic transport. We use a maximum-entropy ansatz to explore the logarithm of the energy density,…
Products of random matrices associated to one-dimensional random media satisfy a central limit theorem assuring convergence to a gaussian centered at the Lyapunov exponent. The hypothesis of single parameter scaling states that its variance…