arXiv subjects

Isa Kh. Zharekeshev

Publications and source records attributed to Isa Kh. Zharekeshev.

3 recordsLinked to original sources

arXiv2000

Advanced Lanczos diagonalization for models of quantum disordered systems

An application of an effective numerical algorithm for solving eigenvalue problems which arise in modelling electronic properties of quantum disordered systems is considered. We study the electron states at the localization-delocalization transition induced by a random potential in the framework of the Anderson lattice model. The computation of the interior of the spectrum and corresponding wavefunctions for very sparse, hermitian matrices of sizes exceeding 10^6 x 10^6 is performed by the Lanczos-type method especially modified for investigating statistical properties of energy levels and eigenfunction amplitudes.

physics.comp-ph↗

arXiv1997

Asymptotics of Universal Probability of Neighboring Level Spacings at the Anderson Transition

The nearest-neighbor level spacing distribution is numerically investigated by directly diagonalizing disordered Anderson Hamiltonians for systems of sizes up to 100 x 100 x 100 lattice sites. The scaling behavior of the level statistics is examined for large spacings near the delocalization-localization transition and the correlation length exponent is found. By using high-precision calculations we conjecture a new interpolation of the critical cumulative probability, which has size-independent asymptotic form \ln I(s) \propto -s^α with α= 1.0 \pm 0.1.

cond-mat.dis-nn↗

arXiv1995

Universal Fluctuations in Spectra of Disordered Systems at the Anderson Transition

Using the level--spacing distribution and the total probability function of the numbers of levels in a given energy interval we analyze the crossover of the level statistics between the delocalized and the localized regimes. By numerically calculating the electron spectra of systems of up to $32^3$ lattice sites described by the Anderson Hamiltonian it is shown that the distribution $P(s)$ of neighboring spacings is {\em scale- independent} at the metal-insulator transition. For large spacings it has a Poisson-like asymptotic form $P(s)\propto \exp (- A\,s/Δ)$, where $A \approx 1.9$. At the critical point we obtain a linear relationship between the variance of the number of levels $\langle [δn(\varepsilon)]^2 \rangle $ and their average number $\langle n(\varepsilon)\rangle $ within the interval $\varepsilon$. The constant of proportionality is less than unity due to the repulsion of the levels. Both $P(s)$ and $\langle [δn(\varepsilon)]^2 \rangle $ are determined by the probability density $Q_{n}(\varepsilon)$ of having exactly $n$ levels in the energy interval $\varepsilon $. The distribution $Q_{n}(\varepsilon)$ at the critical point is found to be size--independent and to obey a Gaussian law near its maximum, where $n\sim \langle n \rangle $.

cond-mat↗