Anderson Localization in Dissipative Lattices

Anderson localization predicts that wave spreading in disordered lattices can come to a complete halt, providing a universal mechanism for dynamical localization. In the one-dimensional Hermitian Anderson model with uncorrelated diagonal disorder, there is a one-to-one correspondence between dynamical localization and spectral localization, that is, the exponential localization of all the Hamiltonian eigenfunctions. This correspondence can be broken when dealing with disordered dissipative lattices. When the system exchanges particles with the surrounding environment and random fluctuations of the dissipation are introduced, spectral localization is observed but without dynamical localization. Previous studies consider lattices with mixed conservative (Hamiltonian) and dissipative dynamics and are restricted to a semiclassical analysis. However, Anderson localization in purely dissipative lattices, displaying an entirely Lindbladian dynamics, remains largely unexplored. Here the purely-dissipative Anderson model in the framework of a Lindblad master equation is considered, and it is shown that, akin to the semiclassical models with conservative hopping and random dissipation, one observes dynamical delocalization in spite of strong spectral localization of the Liouvillian superoperator. This result is very distinct from delocalization observed in the Anderson model with dephasing, where dynamical delocalization arises from the delocalization of the stationary state of the Liouvillian.     

Disorder-induced localization of light near edges of nonlinear photonic lattices

We investigated the influence of edges and corners on the Anderson localization of light in disordered two-dimensional photonic lattices that are optically induced in nonlinear saturable photorefractive media. A systematic quantitative study of gradual transition from corner to bulk Anderson localization in truncated two-dimensional photonic lattices was carried out. We analyzed numerically the localization at several corners and edges of the square and triangular photonic lattices and compared them with the localization in bulk medium. We found that, for strong disorder, corners and edges effectively suppress Anderson localization, as compared to the bulk, but to a varying degree.     

Light scattering on random dielectric layers

Scattering of light by a random stack of dielectric layers represents a one-dimensional scattering problem, where the scattered field is a three-dimensional vector field. We investigate the dependence of the scattering properties (band gaps and Anderson localization) on the wavelength, strength of randomness and relative angle of the incident wave. There is a characteristic angular dependence of Anderson localization for wavelengths close to the thickness of the layers. In particular, the localization length varies non-monotonously with the angle. In contrast to Anderson localization, absorptive layers do not have this characteristic angular dependence.     

基于Mie散射理论的光子晶体安德森定域化研究

基于Mie散射理论和低浓度近似,对磷化镓光子晶体的安德森定域化进行了理论计算,并分析了影响定域化参量的各种因素。结果表明,在浓度为10%,折射率比值大于3.8,无吸收状态下,中红外区出现了安德森定域化现象,并且随粒子半径的增大,定域化区向长波段移动,且基质折射率的增大使定域化现象减弱。研究结果为该类晶体的定域化现象提供了理论参考。     

THERMALLY ACTIVATED HOPPING IN Dy1-xPrxBa2Cu3O7-δ SYSTEM

The temperature dependence of resistivity in Dy_1-xPr_xBa₂Cu₃O_7-δ system with x>0.6 was measured. The experimental results show that Pr substitution leads to the localization of mobile holes and such a localization is enhanced with increasing Pr concentration. The gradually enhancing of localization induces Anderson transitions one by one in this system, including the transition from the conduction by excitation of holes to the one by thermal activation hopping between localized states, the so called Anderson transition type-I, and the transition from nearest neighbor hopping (NNH) to variable range hopping (VRH), the Anderson transition type-II, and the Anderson transition type-lI from 3D to 2D.     

Localization of cold atoms in state-dependent optical lattices via a Rabi Pulse

We propose a novel realization of Anderson localization in nonequilibrium states of ultracold atoms in an optical lattice. A Rabi pulse transfers part of the population to a different internal state with infinite effective mass. These frozen atoms create a quantum superposition of different disorder potentials, localizing the mobile atoms. For weakly interacting mobile atoms, Anderson localization is obtained. The localization length increases with increasing disorder and decreasing interaction strength, contrary to the expectation for equilibrium localization.     

Localization Criteria for Anderson Models on Locally Finite Graphs

We prove spectral and dynamical localization for Anderson models on locally finite graphs using the fractional moment method. Our theorems extend earlier results on localization for the Anderson model on ℤ ^d . We establish geometric assumptions for the underlying graph such that localization can be proven in the case of sufficiently large disorder.     

基于Mie散射理论对砷化镓光子晶体安德森定域化研究

 基于Mie散射理论和低浓度近似,对砷化镓作为散射体光子晶体中的安德森定域化参量进行了理论计算,并分析了影响定域化现象的各种因素。结果表明:在散射体体积分数为10%,相对折射率大于3.8时,远红外区50~65 μm范围内出现严格的定域化现象;随着散射体半径的增大,定域化区向长波方向移动,且定域化参量先增大后减小。     

Quantum correlations in two-particle Anderson localization

We predict quantum correlations between noninteracting particles evolving simultaneously in a disordered medium. While the particle density follows the single-particle dynamics and exhibits Anderson localization, the two-particle correlation develops unique features that depend on the quantum statistics of the particles and their initial separation. On short time scales, the localization of one particle becomes dependent on whether or not the other particle is localized. On long time scales, the localized particles show oscillatory correlations within the localization length. These effects can be observed in Anderson localization of nonclassical light and ultracold atoms.     

Anderson Localization Enhanced Spin Selective Transport of Electrons in DNA

Recent experiments revealed the unusual strong spin effects with high spin selective transmission of electrons in double-stranded DNA. We propose a new mechanism that the strong spin effects could be understood in terms of the combination of the ehiral structure, spin-orbit coupling, and especially spin-dependent Anderson localization. The presence of chiral structure and spin-orbit coupling of DNA induce weak Fermi energy splitting between two spin polarization states. The intrinsic Anderson localization in generic DNA molecules may result in remarkable enhancement of the spin selective transport. In particular, these two spin states with energy splitting have different localization lengths. Spin up/down channel may have shorter/longer localization length so that relatively less/more spin up/down electrons may tunnel through the system. In addition, the strong length dependence of spin selectivity observed in experiments can be naturally understood. Anderson localization enhanced spin selectivity effect may provide a deeper understanding of spin-selective processes in molecular spintronics and biological systems.     

Anderson Localization in the Induced Disorder System

We propose a coherently prepared three-level atomic medium that can provide a flexible disordered scheme for realizing the Anderson localization.Different disorder levels can be attained by modulating the intensity ratio between the two control beams.Due to the real-time tunability,the localization of the signal beam is observable and controllable.The influences of the induced disorder level,atomic density and the initial waist radius of the signal beam on the Anderson localization in the medium are also discussed.     

T c of disordered superconductors near the Anderson transition

According to the Anderson theorem, the critical temperature T _c of a disordered superconductor is determined by the average density of states and does not change at the localization threshold. This statement is valid under assumption of a self-averaging order parameter, which can be violated in the strong localization region. Stimulating by statements on the essential increase of T _c near the Anderson transition, we carried out the systematic investigation of possible violations of self-averaging. Strong deviations from the Anderson theorem are possible due to resonances at the quasi-discrete levels, resulting in localization of the order parameter at the atomic scale. This effect is determined by the properties of individual impurities and has no direct relation to the Anderson transition. In particular, we do not see any reasons to say on “fractal superconductivity” near the localization threshold.     

Self-consistent theory of localization for the Anderson model

The self-consistent theory of electron localization in a random system in the form proposed by Vollhardt and Wölfle is generalized for the analysis of localization in the Anderson model. We derive the general equations appropriate for the system with rather general form of the electronic spectrum. Explicit calculations are restricted to the lattices of cubic symmetry and use the effective mass approximation to obtain the final results. Anderson's critical ratio for the localization of all the electronic states in the tight-binding band is evaluated and found to be in surprisingly good agreement with the results of numerical analysis of localization in the Anderson model.     

Observation of the gradual transition from one-dimensional to two-dimensional Anderson localization

We study the gradual transition from one-dimensional (1D) to two-dimensional (2D) Anderson localization upon transformation of the dimensionality of disordered waveguide arrays. An effective transition from a 1D to a 2D system is achieved by increasing the number of rows forming the arrays. We observe that, for a given disorder level, Anderson localization becomes weaker with increasing numbers of rows-hence the effective dimension.     

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.     

Correlated electrons in the presence of disorder

Several new aspects of the subtle interplay between electronic correlations and disorder are reviewed. First, the dynamical mean-field theory (DMFT) together with the geometrically averaged (“typical”) local density of states is employed to compute the ground state phase diagram of the Anderson-Hubbard model at half-filling. This non-perturbative approach is sensitive to Anderson localization on the one-particle level and hence can detect correlated metallic, Mott insulating and Anderson insulating phases and can also describe the competition between Anderson localization and antiferromagnetism. Second, we investigate the effect of binary alloy disorder on ferromagnetism in materials with f-electrons described by the periodic Anderson model. A drastic enhancement of the Curie temperature T_c caused by an increase of the local f-moments in the presence of disordered conduction electrons is discovered and explained.     

Some mathematical aspects of Anderson localization: boundary effect,multimodality, and bifurcation

Anderson localization is a famous wave phenomenon that describes the absence of diffusion of waves in a disordered medium. Here we generalize the landscape theory of Anderson localization to general elliptic operators and complex boundary conditions using a probabilistic approach, and further investigate some mathematical aspects of Anderson localization that are rarely discussed before. First, we observe that under the Neumann boundary condition, the low energy quantum states are localized on the boundary of the domain with high probability. We provide a detailed explanation of this phenomenon using the concept of extended subregions and obtain an analytical expression of this probability in the one-dimensional case. Second, we find that the quantum states may be localized in multiple different subregions with high probability in the one-dimensional case and we derive an explicit expression of this probability for various boundary conditions. Finally, we examine a bifurcation phenomenon of the localization subregion as the strength of disorder varies. The critical threshold of bifurcation is analytically computed based on a toy model and the dependence of the critical threshold on model parameters is analyzed.     

Anderson localization in nonlocal nonlinear media

We theoretically and numerically investigate the effect of focusing and defocusing nonlinearities on Anderson localization in highly nonlocal media. A perturbative approach is developed to solve the nonlocal nonlinear Schr?dinger equation in the presence of a random potential, showing that nonlocality stabilizes Anderson states.     

Dynamics of Anderson localization in open 3D media

We develop a self-consistent theoretical approach to the dynamics of Anderson localization in open three-dimensional (3D) disordered media. The approach allows us to study time-dependent transmission and reflection, and the distribution of decay rates of quasimodes of 3D disordered slabs near the Anderson mobility edge.     

Anderson Localization in a Two-Dimensional Electron–Hole System

JETP Letters - Anderson localization is discovered in a highly disordered two-dimensional electron–hole system in a HgTe quantum well. The behavior of this localization is fundamentally...