Numerical studies on the anderson localization problem

Our study of Anderson's tight binding model for strongly disordered electronic systems is extended to a numerical treatment of thed c-conductivity atT=0. For 100 × 100 square lattices, 129 × 129 triangular lattices, and for diamond lattices with 27,000 sites, the behaviour of is studied as a function of the Fermi energy and the disorder. The calculations are based on the exact eigenfunction representation of the Kubo formula, which is evaluated by the systematic application of recursion algorithms. Our results are in favour of Mott's original suggestion of a minimum metallic conductivity _min, both in two and three dimensions. In two dimensions we find the universal value of _min=(0.11 ±0.02)e ²/. Based on the thesis of J. Stein, Regensburg 1979     

Numerical studies on the Anderson localization problem

The localization properties of three different gauge invariant disordered electronic systems are studied by numerical methods with the purpose to clarify their localization properties and to evaluate the dc-resistivity atT=0 K as far as possible. The three different models, two of which involve also spin-dependent scattering processes, represent three different universality classes, corresponding to orthogonal, unitary, and symplectic matrix ensembles, respectively, in a field-theoretic representation. For the symplectic case, which corresponds to a situation with dominating spin-orbit scattering, we find hints for an unconventional transition, separating weakly antilocalized from exponentially localized states, whereas in the other two cases instead of a sharp transition only a drastic crossover between weak localization and exponential localization seems to happen. For the symplectic model also the magnetoresistivity is calculated; we find a negative magnetoresistivity if the Zeeman splitting is neglected, whereas by inclusion of Zeeman splitting the magnetoresistivity is positive.     

Scaling in the one-dimensional anderson localization problem in the region of fluctuation states

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 valid, the distribution can still be described within a scaling approach based upon the ratio of two fundamental quantities, the localization length, l(loc), and a new length, l(s), related to the integral density of states. In an intermediate interval of the system's length L, l(loc)相似文献   

Periodic-orbit theory of anderson localization on graphs

We present the first quantum system where Anderson localization is completely described within periodic-orbit theory. The model is a quantum graph analogous to an aperiodic Kronig-Penney model in one dimension. The exact expression for the probability to return to an initially localized state is computed in terms of classical trajectories. It saturates to a finite value due to localization, while the diagonal approximation decays diffusively. Our theory is based on the identification of families of isometric orbits. The coherent periodic-orbit sums within these families, and the summation over all families, are performed analytically using advanced combinatorial methods.     

Nonuniversality of anderson localization in short-range correlated disorder

We provide an analytic theory of Anderson localization on a lattice with a weak short-range correlated disordered potential. Contrary to the general belief, we demonstrate that already next-neighbor statistical correlations in the potential can give rise to strong anomalies in the localization length and the density of states, and to the complete violation of single-parameter scaling. Such anomalies originate in additional symmetries of the lattice model in the limit of weak disorder. The results of numerical simulations are in full agreement with our theory, with no adjustable parameters.     

类Opal光子晶体红外区安德森定域化理论研究

本文根据Mie散射理论和低浓度近似下,对在中红外区高折射率半导体材料AlP等做为散射体的类Opal光子晶体的安德森定域化进行了理论研究,发现在浓度为10%,折射率比值大于3.8,无吸收状态下,此类晶体将出现两个定域化区.同时为此类晶体的定域化研究提供了一个比较理想的处理方法.     

Systematic treatment of the anderson localization on the basis of the projection operator formalism

A derivation within the projection operator technique is given for the density and current response functions of a system of independent particles moving in a random potential. The essential point is the derivation of kinetic equations for the current relaxation kernel instead of for the density propagator as in a previous treatment on the basis of the projection operator formalism. In these equations the divergent contributions from the 2k _F -scattering mechanism can be systematically separated from those of diffusional scattering. Especially, both the self-consistent current relaxation theory, developed by Götze and the self-consistent treatment of Vollhardt and Wölfle are rederived from simple approximations of the kinetic equations. The outlined method represents a systematic approach to the Anderson localization. It may be applicable also to more realistic models for the Anderson localization as well as extended to the evaluation of general transport coefficients on a level far beyond the usual perturbation theories.     

Energy absorption in time-dependent unitary random matrix ensembles: Dynamic versus anderson localization

JETP Letters - We consider energy absorption in an externally driven complex system of noninteracting fermions with the chaotic underlying dynamics described by the unitary random matrices. In the...     

Schardin问题的数值研究

激波绕过三角楔(Schardin问题)时会产生激波马赫反射与绕射、 三角楔尾涡与涡串等复杂物理现象. 本文利用三阶精度加权基本无振荡(WENO)格式、 结构化矩形网格的自适应加密方法与沉浸边界法对Schardin问题进行了数值模拟. 数值结果清晰地显示了激波与三角楔相互作用, 在楔面发生马赫反射以及在楔角绕射诱导主涡的过程, 并与Schardin等的实验结果及相关数值结果完全符合. 另外, 数值结果还详细反映了先前实验与数值结果没有详细讨论的主涡滑移层上的涡串生成机理, 以及激波与涡串相互作用和产生声波的过程.     

Schardin问题的数值研究

激波绕过三角楔(Schardin问题)时会产生激波马赫反射与绕射、 三角楔尾涡与涡串等复杂物理现象. 本文利用三阶精度加权基本无振荡(WENO)格式、 结构化矩形网格的自适应加密方法与沉浸边界法对Schardin问题进行了数值模拟. 数值结果清晰地显示了激波与三角楔相互作用, 在楔面发生马赫反射以及在楔角绕射诱导主涡的过程, 并与Schardin等的实验结果及相关数值结果完全符合. 另外, 数值结果还详细反映了先前实验与数值结果没有详细讨论的主涡滑移层上的涡串生成机理, 以及激波与涡串相互作用和产生声波的     

Topology dependent quantities at the anderson transition

The boundary condition dependence of the critical behavior for the three dimensional Anderson transition is investigated. A strong dependence of the scaling function and the critical conductance distribution on the boundary conditions is found, while the critical disorder and critical exponent are found to be independent of the boundary conditions.     

Non-Fermi-liquid behavior in the periodic anderson model

We study the Mott metal-insulator transition in the periodic Anderson model with dynamical mean field theory (DMFT). Near the quantum transition, we find a non-Fermi-liquid metallic state down to a vanishing temperature scale. We identify the origin of the non-Fermi-liquid behavior as being due to magnetic scattering of the doped carriers by the localized moments. The non-Fermi-liquid state can be tuned by either doping or external magnetic field. Our results show that the coupling to spatial magnetic fluctuations (absent in DMFT) is not a prerequisite to realizing a non-Fermi-liquid scenario for heavy fermion systems.     

A diagram method for the anderson model

Summary A diagram method to treat the Anderson model has been introduced. By applying this technique to the study of chemisorption phenomena, the density of states of adatom electrons has been calculated at finite temperature. Comparison with the results obtained in the symmetric limit atT=0 is given.

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Riassunto Un metodo diagrammatico è stato introdotto per studiare il modello di Anderson. Applicando questa tecnica al problema del chemisorbimento, è stata calcolata la densità degli stati elettronici localizzati a temperatura finita. è inoltre riportato un confronto con risultati ottenuti aT=0 nel limite simmetrico.

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Резуме Вводится диаграммный метод для рассмотрения модели Андерсона. Предложенная техника применяется для исследоваия явлений хемосорбции. При конечных температурах вычисляется плотность состояний электронов адатома. Проводится сравнение с результатами, полученными в симметричном пределе приT=0.

     

Dynamic properties of the anderson model at finiteU

TheN-fold-degenerate single impurity Anderson model is studied at finiteU, using the perturbation expansion in the hybridizationV. The 1/N-expansion and the energy-dependence of the self-energies allow to set up a system of self-consistent integral equations for the self-energies, and thef-spectral function. Thef-spectral density and transport coefficients (the electrical resistivity , the Lorenz ratioL/L ₀ , the thermoelectric powerS, and the Hall-coefficientR _H ) are calculated numerically via the self-consistent integral equations. We are particularly interested in the effect of the Coulomb interaction on the dynamic properties. Thef-spectral function is calculated at small and largeU. It shows a sharp peak at the Fermilevel (the Kondo-Abrikosov-Suhl resonance) and two broad peaks around _f and _f +U. The structure at the Fermi-level is very sensitive to the Coulomb interactionU. In order to get more information about the model, we have studied the transport coefficients at differentU, which are universal functions of the temperatureT/T _K , where the Kondo-temperature sets the scale. We find that the transport coefficients show Kondo behavior aroundTT _K , and are also sensitive toU. The Hall-coefficient is negative forTT _K already within the impurity model. This competes with the usual interpretation as a coherence effect caused by the lattice.     

Band effects on conduction electron density of states for the anderson model

Summary The effects of the shape of free conduction density of states on the physical quantities for the periodic Anderson model have been investigated.     

Numerical results in the Kondo problem

A numerically solvable Kondo model is formulated. It is shown that for certain cases the limit T → 0 does not yield the correct ground state.