Related papers: Single parameter scaling in 1-D localized absorbin…
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…
The single parameter scaling hypothesis is the foundation of our understanding of the Anderson transition. However, the conductance of a disordered system is a fluctuating quantity which does not obey a one parameter scaling law. It is…
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…
Advances in material growth methods have renewed the interest in localization of one-dimensional systems in the presence of scale-free long-range correlated disorder potentials. We analyze the validity of single parameter scaling for the…
We reconcile the phenomenon of mesoscopic conductance fluctuations with the single parameter scaling theory of the Anderson transition. We calculate three averages of the conductance distribution: $\exp(<\ln g>)$, $<g>$ and $1/<R>$ where…
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…
We numerically study the distribution function of the conductance (transmission) in the one-dimensional tight-binding Anderson and periodic-on-average superlattice models in the region of fluctuation states where single parameter scaling is…
We show, using detailed numerical analysis and theoretical arguments, that the normalized participation number of the stationary solutions of disordered nonlinear lattices obeys a one-parameter scaling law. Our approach opens a new way to…
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 find a new significant scaling parameter in the system, and…
We follow the temporal evolution of mesoscopic intensity fluctuations and correlation in strongly localized samples. We find an initial burst in relative transmission fluctuations in random one dimensional (1D) samples due to fluctuations…
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…
We analyse numerically the critical behavior of an absorbing phase transition in a conserved lattice gas in an external field. The external field is realized as a spontaneous creation of active particles which drives the system away from…
In most noninteracting quantum systems, the scaling theory of localization predicts one-parameter scaling flow in both ergodic and localized regimes. On the other hand, it is expected that the one-parameter scaling hypothesis breaks down…
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.…
We discuss the localization behavior of localized electronic wave functions in the one- and two-dimensional tight-binding Anderson model with diagonal disorder. We find that the distributions of the local wave function amplitudes at fixed…
Many fluctuating systems consist of macroscopic structures in addition to noisy signals. Thus, for this class of fluctuating systems, the scaling behaviors are very complicated. Such phenomena are quite commonly observed in Nature, ranging…
The one parameter scaling theory is a powerful tool to investigate Anderson localization effects in disordered systems. In this paper we show this theory can be adapted to the context of quantum chaos provided that the classical phase space…
We investigate the scaling properties of eigenstates of a one-dimensional (1D) Anderson model in the presence of a constant electric field. The states show a transition from exponential to factorial localization. For infinite systems this…
In one dimension very general results from conformal field theory and exact calculations for certain quantum spin systems have established universal scaling properties of the entanglement entropy between two parts of a critical system.…