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1.
The band structures of in-plane elastic waves propagating in two-dimensional phononic crystals with one-dimensional random disorder and aperiodicity are analyzed in this paper. The localization of wave propagation is discussed by introducing the concept of the localization factor, which is calculated by the plane-wave-based transfer-matrix method. By treating the random disorder and aperiodicity as the deviation from the periodicity in a special way, three kinds of aperiodic phononic crystals that have normally distributed random disorder, Thue-Morse and Rudin-Shapiro sequence in one direction and translational symmetry in the other direction are considered and the band structures are characterized using localization factors. Besides, as a special case, we analyze the band gap properties of a periodic planar layered composite containing a periodic array of square inclusions. The transmission coefficients based on eigen-mode matching theory are also calculated and the results show the same behaviors as the localization factor does. In the case of random disorders, the localization degree of the normally distributed random disorder is larger than that of the uniformly distributed random disorder although the eigenstates are both localized no matter what types of random disorders, whereas, for the case of Thue-Morse and Rudin-Shapiro structures, the band structures of Thue-Morse sequence exhibit similarities with the quasi-periodic (Fibonacci) sequence not present in the results of the Rudin-Shapiro sequence. 相似文献
2.
E. Z. Kuchinskii N. A. Kuleeva I. A. Nekrasov M. V. Sadovskii 《Journal of Experimental and Theoretical Physics》2010,110(2):325-335
The density of states, the dynamic (optical) conductivity, and the phase diagram of the paramagnetic two-dimensional Anderson-Hubbard
model with strong correlations and disorder are analyzed within the generalized dynamical mean field theory (DMFT + Σ approximation).
Strong correlations are accounted by the DMFT, while disorder is taken into account via the appropriate generalization of
the self-consistent theory of localization. We consider the two-dimensional system with the rectangular “bare” density of
states (DOS). The DMFT effective single-impurity problem is solved by numerical renormalization group (NRG). The “correlated
metal,” Mott insulator, and correlated Anderson insulator phases are identified from the evolution of the density of states,
optical conductivity, and localization length, demonstrating both Mott-Hubbard and Anderson metal-insulator transitions in
two-dimensional systems of finite size, allowing us to construct the complete zero-temperature phase diagram of the paramagnetic
Anderson-Hubbard model. The localization length in our approximation is practically independent of the strength of Hubbard
correlations. But the divergence of the localization length in a finite-size two-dimensional system at small disorder signifies
the existence of an effective Anderson transition. 相似文献
3.
4.
A one-dimensional diagonal tight binding electronic system is analyzed with the Hamiltonian map approach to study analytically
the inverse localization length of an infinite sample. Both the uncorrelated and the dichotomic correlated random potential
sequences are considered in the evaluations of the inverse localization length. Analytical expressions for the invariant measure
or the angle density distribution are the main motivation of this work in order to derive analytical results. The well-known
uncorrelated weak disorder result of the inverse localization length is derived with a clear procedure. In addition, an analytical
expression for high disorder is obtained near the band edge. It is found that the inverse localization length goes to 1 in
this limit. Following the procedure used in the uncorrelated situation, an analytical expression for the inverse localization
length is also obtained for the dichotomic correlated sequence in the small disorder situation. 相似文献
5.
E. Orignac Y. Suzumura 《The European Physical Journal B - Condensed Matter and Complex Systems》2001,23(1):57-67
We study the interplay of Anderson localization and interaction in a two chain Hubbard ladder allowing for arbitrary ratio
of disorder strength to interchain coupling. We obtain three different types of spin gapped localized phases depending on
the strength of disorder: a pinned 4k
F Charge Density Wave (CDW) for weak disorder, a pinned 2k
F CDWπ for intermediate disorder and two independently pinned single chain 2k
F CDW for strong disorder. Confinement of electrons can be obtained as a result of strong disorder or strong attraction. We
give the full phase diagram as a function of disorder, interaction strength and interchain hopping. We also study the influence
of interchain hopping on localization length and show that localization is enhanced by a small interchain hopping but suppressed
by a large interchain hopping.
Received 6 April 2001 相似文献
6.
Mobility edges and reentrant localization in one-dimensional dimerized non-Hermitian quasiperiodic lattice 下载免费PDF全文
《中国物理 B》2021,30(9):97202-097202
The mobility edges and reentrant localization transitions are studied in one-dimensional dimerized lattice with nonHermitian either uniform or staggered quasiperiodic potentials.We find that the non-Hermitian uniform quasiperiodic disorder can induce an intermediate phase where the extended states coexist with the localized ones,which implies that the system has mobility edges.The localization transition is accompanied by the PT symmetry breaking transition.While if the non-Hermitian quasiperiodic disorder is staggered,we demonstrate the existence of multiple intermediate phases and multiple reentrant localization transitions based on the finite size scaling analysis.Interestingly,some already localized states will become extended states and can also be localized again for certain non-Hermitian parameters.The reentrant localization transitions are associated with the intermediate phases hosting mobility edges.Besides,we also find that the non-Hermiticity can break the reentrant localization transition where only one intermediate phase survives.More detailed information about the mobility edges and reentrant localization transitions are presented by analyzing the eigenenergy spectrum,inverse participation ratio,and normalized participation ratio. 相似文献
7.
In this paper, the localization length that represents the distance of elastic waves propagating along the disordered periodic structures is defined as the reciprocal of the smallest positive Lyapunov exponent, i.e. the localization factor. The algorithm for determining all the Lyapunov exponents in continuous dynamic systems presented by Wolf et al. is employed to calculate those in discrete dynamic systems. Numerical results of the localization lengths of SH-wave are presented and discussed in ordered and disordered piezoelectric phononic crystals to identify the different effect degrees for the decay of electrical potential in the polymers and the randomness on the localization level. For the disordered case, disorder in the thickness of the polymers and disorder in the elastic constant of the piezoelectric ceramics are all considered. The results show that some parameters such as the incident angle of elastic wave, the randomness degree and the piezoelectricity of piezoelectric ceramics and so on have pronounced effects on the frequency-dependent localization length. 相似文献
8.
X. Xu 《Applied physics. B, Lasers and optics》2007,86(3):467-471
The photon localization in disordered two-dimensional photonic crystal is studied theoretically. It is found that the mean
transmission coefficient in the photonic band decreases exponentially as the disorder degree increases, reflecting the occurrence
of Anderson localization. The strength of photon localization can be controlled by tuning the disorder degree in the photonic
crystal. We think the variation regular of the transmission coefficient in our disordered system is equivalent to that of
the scaling theory of localization.
PACS 42.70.Qs; 41.20.Jb; 42.25.Dd 相似文献
9.
将一维随机二元固体模型应用于DNA分子链,利用传输矩阵方法来研究系统电子态的局域性质并进而讨论系统的导电性质.对一个链长为50000个碱基对的DNA序列,数值分析了局域长度和电导随碱基对的摩尔百分数、本征能量和无序度的变化关系.结果表明,系统的局域长度和电导强烈地依赖于能量,在能带中心部分局域长度大于边沿部分.无序度也在一定程度上影响着局域长度,双方成反向变化的关系.对有限长度的DNA分子链,局域长度体现出明显的对碱基对摩尔百分数的依赖关系,对正常成分比例的随机DNA序列,在所有能量范围内系统的态都是局域的,系统的电导很小,系统呈现绝缘体行为.仅当一种碱基对在序列中所占比例很小时,系统中可以发现与特定分立能量值相对应的“扩展态”存在,处在这些态下的系统有较大的电导,但这些扩展态是不稳定的,在热力学极限之下会消失.
关键词:
DNA分子链
电子局域
局域长度
电导 相似文献
10.
We investigate localization behavior of quasiparticles in
disordered multi-plane superconductors with s-wave pairing. By
introducing disorder with random site energies, the spatial
fluctuations of Bogoliubov-de Gennes pairing potential are
self-consistently determined. The size dependence of rescaled
localization length for a long bar is calculated by using the
transfer-matrix method. From the finite-size scaling analysis we
show that there exists a critical point of the disorder strength
Wc which separates the extended and localized quasiparticle
states in such quasi-two-dimensional systems. The associated
critical behavior is studied and the relationship of the results
to the number of planes is discussed. 相似文献
11.
The localization length as a function of energy and disorder of a three dimensional disordered system described by the Anderson Hamiltonian is determined. The phase diagram for localization is discussed with particular emphasis on the mechanisms which are important for localization (quantum interference and tunneling). 相似文献
12.
《中国物理快报》2016,(7)
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. 相似文献
13.
N. Laflorencie H. Rieger 《The European Physical Journal B - Condensed Matter and Complex Systems》2004,40(2):201-207
In this paper we study the localization transition induced by the disorder in random antiferromagnetic spin-
chains. The results of numerical large scale computations are presented for the XX model using its free fermions representation. The scaling behavior of the spin stiffness is investigated for various disorder strengths. The disorder dependence of the localization length is studied and a comparison between numerical results and bosonization arguments is presented. A non trivial connection between localization effects and the crossover from the pure XX fixed point to the infinite randomness fixed point is pointed out.Received: 6 February 2004, Published online: 12 August 2004PACS:
75.10.Jm Quantized spin models - 75.40.Mg Numerical simulation studies - 05.70.Jk Critical point phenomena - 75.50.Lk Spin glasses and other random magnets 相似文献
14.
Ole Halfpap 《Annalen der Physik》2001,10(8):623-706
A new numerical method is introduced that enables a reliable study of disorder‐induced localization of interacting particles. It is based on a quantum mechanical time evolution calculation combined with a finite size scaling analysis. The time evolution of up to four particles in one dimension is studied and localization lengths are defined via the long‐time saturation values of the mean radius, the inverse participation ratio and the center of mass extension. A systematic study of finite size effects using the finite size scaling method is performed in order to extract the localization lengths in the limit of an infinite system size. For a single particle, the well‐known scaling of the localization length λ1 with disorder strength W is observed, λ1 ∝ W—2. For two particles, an interaction‐induced delocalization is found, confirming previous results obtained by numerically calculating matrix elements of the two‐particle Green's function: in the limit of small disorder, the localization length increases with decreasing disorder as λ2 ∝ W—4 and can be much larger than <$>\mitlambda λ1. For three and four particles, delocalization is even stronger. Based on analytical arguments, an upper bound for the n‐particle localization length λn is derived and shown to be in agreement with the numerical data, λn ∝ λ1. Although the localization length increases superexponentially with particle number and can become arbitrarily large for small disorder, it does not diverge for finite λ1 and n. Hence, no extendedstates exist in one dimension, at least for spinless fermions. 相似文献
15.
《Waves in Random and Complex Media》2013,23(3):261-279
In this paper, the wave propagation and localization in randomly disordered periodic multi-span beams on elastic foundations are studied. For two kinds of beams, i.e. the multi-span beams on elastic foundations with periodic flexible and simple supports, the transfer matrices between two consecutive sub-spans are obtained by means of the continuity conditions. The algorithm for determining all the Lyapunov exponents in continuous dynamic systems presented by Wolf et al. is employed to calculate those in discrete dynamic systems. The localization factor characterizing the average exponential rates of growth or decay of wave amplitudes along the disordered beams is defined as the smallest positive Lyapunov exponent of the discrete dynamical system. The localization length that represents the distance of elastic waves propagating along the disordered periodic structures is defined as the reciprocal of the smallest positive Lyapunov exponent, i.e. the localization factor. For the two kinds of disordered periodic beams on elastic foundations, the numerical results of the localization factors are presented and analysed by comparing them with the results of the beams without elastic foundations to illustrate the effects of the elastic foundations on the wave propagation and localization. The effects of the disorder of span-length and the dimensionless torsional and linear spring stiffness on the localization factors are discussed. Moreover, the localization lengths are also calculated and discussed for certain structural parameters in disordered periodic structures. It can be observed from the results that ordered periodic multi-span beams have the characteristics of the frequency passbands and stopbands and the localization of elastic waves can occur in disordered periodic systems: the localization degree of elastic waves is strengthened with the increase of the coefficient of variation of the span-length. The influences of the elastic foundations on the wave propagation and localization are more complicated. Generally speaking, in lower-frequency regions the elastic foundations have pronounced effects on the spectral structures, but in higher-frequency regions the effects are negligible. The localization degree increases as the torsional spring stiffness increases. The linear spring has few effects on the spectral structures in higher-frequency regions, but in lower-frequency regions it has prominent effects. The larger the disorder degree, the shorter the non-dimensional localization length. 相似文献
16.
Y.-X. Wang S.-J. Xiong 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,67(1):63-69
We investigate localization behavior of electron states in bilayer graphene formed with the Bernal stacking in the presence
of various types of disorder (site-energy, in-plane hopping and inter-plane hopping) by the use of the transfer matrix method.
It is found that all the states are localized at various kinds of disorder (site-energy, in-plane hopping and inter-plane
hopping) except that in the case of inter-plane-hopping disorder the states at the zero energy are critical. The implications
of the results are discussed. 相似文献
17.
To describe electron localization in substitutionally random alloysA
c
B
1–c
the coherent potential approximation (CPA) is incorporated into the self-consistent theory of Anderson localization in the form developed by Vollhardt and Wölfle. Modifications of the localization theory arise from the tight-binding model with bimodal diagonal disorder of arbitrary strength. The mean-free path, correlation and localization lengths, and the zero-temperature conductivity are calculated at dimensionalityd=3. The metal-insulator transition is studied numerically for a CPA-induced band structure under semielliptical model assumptions. 相似文献
18.
We investigate several models of a one-dimensional chain
coupling with surrounding atoms to elucidate disorder-induced
delocalization in quantum wires, a peculiar behaviour against
common wisdom. We show that the localization length is enhanced by
disorder of side sites in the case of strong disorder, but in the
case of weak disorder there is a plateau in this dependence. The
above behaviour is the conjunct influence of the coupling to the
surrounding atoms and the antiresonant effect. We also discuss
different effects and their physical origin of different types of
disorder in such systems. The numerical results show that
coupling with the surrounding atoms can induce either the
localization or delocalization effect depending on the values of
parameters. 相似文献
19.
20.
L. Ge 《Annalen der Physik》2017,529(8)
Using one‐dimensional tight‐binding lattices and an analytical expression based on the Green's matrix, we show that anomalous minimum of the localization length near an isolated flat band, previously found for evanescent waves in a defect‐free photonic crystal waveguide, is a generic feature and exists in the Anderson regime as well, i.e., in the presence of disorder. Our finding reveals a scaling behavior of the localization length in terms of the disorder strength, as well as a summation rule of the inverse localization length in terms of the density of states in different bands. Most interestingly, the latter indicates the possibility of having two localization minima inside a band gap, if this band gap is formed by two flat bands such as in a double‐sided Lieb lattice. 相似文献