Search results for "impur"
showing 10 items of 349 documents
Statistical properties of the eigenvalue spectrum of the three-dimensional Anderson Hamiltonian
1993
A method to describe the metal-insulator transition (MIT) in disordered systems is presented. For this purpose the statistical properties of the eigenvalue spectrum of the Anderson Hamiltonian are considered. As the MIT corresponds to the transition between chaotic and nonchaotic behavior, it can be expected that the random matrix theory enables a qualitative description of the phase transition. We show that it is possible to determine the critical disorder in this way. In the thermodynamic limit the critical point behavior separates two different regimes: one for the metallic side and one for the insulating side.
Shape analysis of the level-spacing distribution around the metal-insulator transition in the three-dimensional Anderson model
1995
We present a new method for the numerical treatment of second order phase transitions using the level spacing distribution function $P(s)$. We show that the quantities introduced originally for the shape analysis of eigenvectors can be properly applied for the description of the eigenvalues as well. The position of the metal--insulator transition (MIT) of the three dimensional Anderson model and the critical exponent are evaluated. The shape analysis of $P(s)$ obtained numerically shows that near the MIT $P(s)$ is clearly different from both the Brody distribution and from Izrailev's formula, and the best description is of the form $P(s)=c_1\,s\exp(-c_2\,s^{1+\beta})$, with $\beta\approx 0.…
Relation between Energy Level Statistics and Phase Transition and its Application to the Anderson Model
1994
A general method to describe a second-order phase transition is discussed. It starts from the energy level statistics and uses of finite-size scaling. It is applied to the metal-insulator transition (MIT) in the Anderson model of localization, evaluating the cumulative level-spacing distribution as well as the Dyson-Metha statistics. The critical disorder $W_{c}=16.5$ and the critical exponent $\nu=1.34$ are computed.
Numerical investigations of complex nano-systems
2005
The nature of the melting transition for a system of hard disks with translational degrees of freedom in two spatial dimensions has been analysed by a combination of computer simulation methods and a finite size scaling technique. The behaviour of the system is consistent with the predictions of the Kosterlitz–Thouless–Halperin–Nelson–Young (KTHNY) theory. The structural and elastic properties of binary colloidal mixtures in two and three spatial dimensions are discussed as well as those of colloidal systems with quenched point impurities. Hard and soft disks in external periodic (light) fields show rich phase diagrams, including freezing and melting transitions when the density of the syst…
Entanglement controlled single- electron transmittivity
2006
We consider a system consisting of single electrons moving along a 1D wire in the presence of two magnetic impurities. Such system shows strong analogies with a Fabry - Perot interferometer in which the impurities play the role of two mirrors with a quantum degree of freedom: the spin. We have analysed the electron transmittivity of the wire in the presence of entanglement between the impurity spins. The main result of our analysis is that, for suitable values of the electron momentum, there are two maximally entangled state of the impurity spins the first of which makes the wire transparent whatever the electron spin state while the other strongly inhibits the electron transmittivity. Such…
Macroscopic conductivity of free fermions in disordered media
2014
We conclude our analysis of the linear response of charge transport in lattice systems of free fermions subjected to a random potential by deriving general mathematical properties of its conductivity at the macroscopic scale. The present paper belongs to a succession of studies on Ohm and Joule's laws from a thermodynamic viewpoint. We show, in particular, the existence and finiteness of the conductivity measure $\mu _{\mathbf{\Sigma }}$ for macroscopic scales. Then we prove that, similar to the conductivity measure associated to Drude's model, $\mu _{\mathbf{\Sigma }}$ converges in the weak$^{\ast } $-topology to the trivial measure in the case of perfect insulators (strong disorder, compl…
Strong quantum scarring by local impurities
2016
We discover and characterize strong quantum scars, or eigenstates resembling classical periodic orbits, in two-dimensional quantum wells perturbed by local impurities. These scars are not explained by ordinary scar theory, which would require the existence of short, moderately unstable periodic orbits in the perturbed system. Instead, they are supported by classical resonances in the unperturbed system and the resulting quantum near-degeneracy. Even in the case of a large number of randomly scattered impurities, the scars prefer distinct orientations that extremize the overlap with the impurities. We demonstrate that these preferred orientations can be used for highly efficient transport of…
Determination of the mobility edge in the Anderson model of localization in three dimensions by multifractal analysis.
1995
We study the Anderson model of localization in three dimensions with different probability distributions for the site energies. Using the Lanczos algorithm we calculate eigenvectors for different model parameters like disorder and energy. From these we derive the singularity spectrum typically used for the characterization of multifractal objects. We demonstrate that the singularity spectrum at the critical disorder, which determines the mobility edge at the band center, is independent of the employed probability distribution. Assuming that this singularity spectrum is universal for the metal-insulator transition regardless of specific parameters of the model we establish a straightforward …
Dimensionality Dependence of the Metal-Insulator Transition in the Anderson Model of Localization
1996
The metal-insulator transition is investigated by means of the transfer-matrix method to describe the critical behavior close to the lower critical dimension 2. We study several bifractal systems with fractal dimensions between 2 and 3. Together with 3D and 4D results, these data give a coherent description of the dimensionality dependence of the critical disorder and the critical exponent in terms of the spectral dimension of the samples. We also show that the upper critical dimension is probably infinite, certainly larger than 4.
MULTIFRACTAL ELECTRONIC WAVE FUNCTIONS IN THE ANDERSON MODEL OF LOCALIZATION
1992
Investigations of the multifractal properties of electronic wave functions in disordered samples are reviewed. The characteristic mass exponents of the multifractal measure, the generalized dimensions and the singularity spectra are discussed for typical cases. New results for large 3D systems are reported, suggesting that the multifractal properties at the mobility edge which separates localized and extended states are independent of the microscopic details of the model.