Anderson localization in topologically disordered systems: The effects of band structure

1986 ◽  
Vol 85 (2) ◽  
pp. 937-948 ◽  
Author(s):  
David E. Logan ◽  
Peter G. Wolynes
Keyword(s):  
Band Structure ◽  
Disordered Systems ◽  
Anderson Localization

TOPOLOGICAL PRINCIPLES IN THE THEORY OF ANDERSON LOCALIZATION

2010 ◽  
Vol 24 (12n13) ◽  
pp. 1895-1949 ◽  
Author(s):  
A. M. M. Pruisken
Keyword(s):  
Quantum Hall Effect ◽  
Disordered Systems ◽  
Anderson Localization ◽  
Quantum Hall ◽  
Quantum Criticality ◽  
Theoretical Physics ◽  
Strong Magnetic Fields ◽  
Localization Theory ◽  
Quantum Phenomena ◽  
Interaction Phenomena

Scaling ideas in the theory of the quantum Hall effect are fundamentally based on topological principles in Anderson localization theory. These concepts have a very general significance and are not limited to replica field theory or disordered systems alone. In this chapter, we will discuss these ideas in several distinctly different physical contexts. We start with a brief overview that spans two and a half decades of experimental research on quantum criticality in strong magnetic fields. Secondly, we address the new understanding of universality that has emerged from the theory of Anderson localization and interaction phenomena. In the last part we show how the experimentally observed quantum phenomena fundamentally alter the way in which strong coupling problems in theoretical physics are perceived.

Ribbed elastic structures under a mean flow

2005 ◽  
Vol 461 (2056) ◽  
pp. 913-931
Author(s):  
Paul D Metcalfe
Keyword(s):  
Band Structure ◽  
Transfer Matrix ◽  
Anderson Localization ◽  
Stop Band ◽  
Matrix Inversion ◽  
Mean Flow ◽  
Elastic Structures ◽  
Band Matrix ◽  
Disordered Structures ◽  
Static Fluid

The problem of a ribbed membrane or plate submerged in a fluid with mean flow is studied. We first derive a method which can be used to reduce this, and similar problems to a band matrix inversion. We then find the pass and stop band structure found in the case of static fluid persists when a mean flow is introduced, and we give an explanation in terms of the eigenvalues of the transfer matrix of the system. We then study disordered structures and observe the phenomenon of Anderson localization. In some parameter régimes the addition of disorder causes significant delocalization.

Anderson localization in two-dimensional disordered systems

2003 ◽  
Vol 139 (2) ◽  
pp. 239-244 ◽  
Author(s):  
Mikael Unge ◽  
Sven Stafström
Keyword(s):  
Disordered Systems ◽  
Anderson Localization ◽  
Two Dimensional

scholarly journals Observation of Anderson localization beyond the spectrum of the disorder

2021 ◽  
Author(s):  
Alex Dikopoltsev ◽  
Sebastian Weidermann ◽  
Mark Kremer ◽  
Andrea Steinfurth ◽  
Hanan Herzig Sheinfux ◽  
...  
Keyword(s):  
Disordered Systems ◽  
Anderson Localization ◽  
Localization Length ◽  
Fundamental Wave ◽  
Disordered System ◽  
Finite Spectrum ◽  
Photonic Lattices ◽  
The Mean ◽  
Shed Light ◽  
High Wavenumbers

Abstract Anderson localization is a fundamental wave phenomenon predicting that transport in a 1D uncorrelated disordered system comes to a complete halt, experiencing no transport whatsoever. However, in reality, a disordered physical system is always correlated, because it must have a finite spectrum. Common wisdom in the field states that localization is dominant only for wavepackets whose spectral extent resides within the region of the wavenumber span of the disorder. Here, we experimentally observe that Anderson localization can occur and even be dominant for wavepackets residing entirely outside the spectral extent of the disorder. We study the evolution of waves in synthetic photonic lattices containing bandwidth-limited (correlated) disorder, and observe Anderson localization for wavepackets of high wavenumbers centered around twice the mean wavenumber of the disorder spectrum. Likewise, we predict and observe Anderson localization at low wavenumbers, also outside the spectral extent of the disorder, and find that localization there can be as strong as for first-order transitions. This feature is universal, common to all Hermitian wave systems, implying that low-wavenumber wavepackets localize with a short localization length even when the disorder is strictly at high wavenumbers. This understanding suggests that disordered media should be opaque for long-wavelengths even when the disorder is strictly at much shorter length scales. Our results shed light on fundamental aspects of physical disordered systems and offer avenues for employing spectrally-shaped disorder for controlling transport in systems containing disorder.

scholarly journals Anomalous Anderson localization behaviors in disordered pseudospin systems

2017 ◽  
Vol 114 (16) ◽  
pp. 4087-4092 ◽  
Author(s):  
A. Fang ◽  
Z. Q. Zhang ◽  
Steven G. Louie ◽  
C. T. Chan
Keyword(s):  
Disordered Systems ◽  
Anderson Localization ◽  
Random Potential ◽  
Incident Angle ◽  
Localization Length ◽  
Normal Incidence ◽  
Wave Localization ◽  
Sharp Transition ◽  
Angle Dependence ◽  
Localization Behavior

We discovered unique Anderson localization behaviors of pseudospin systems in a 1D disordered potential. For a pseudospin-1 system, due to the absence of backscattering under normal incidence and the presence of a conical band structure, the wave localization behaviors are entirely different from those of conventional disordered systems. We show that there exists a critical strength of random potential (Wc), which is equal to the incident energy (E), below which the localization length ξ decreases with the random strength W for a fixed incident angle θ. But the localization length drops abruptly to a minimum at W=Wc and rises immediately afterward. The incident angle dependence of the localization length has different asymptotic behaviors in the two regions of random strength, with ξ∝sin−4θ when W<Wc and ξ∝sin−2θ when W>Wc. The existence of a sharp transition at W=Wc is due to the emergence of evanescent waves in the systems when W>Wc. Such localization behavior is unique to pseudospin-1 systems. For pseudospin-1/2 systems, there is also a minimum localization length as randomness increases, but the transition from decreasing to increasing localization length at the minimum is smooth rather than abrupt. In both decreasing and increasing regions, the θ dependence of the localization length has the same asymptotic behavior ξ∝sin−2θ.

scholarly journals ANDERSON LOCALIZATION AND SUPERSYMMETRY

2010 ◽  
Vol 24 (12n13) ◽  
pp. 1756-1788
Author(s):  
K. B. Efetov
Keyword(s):  
Disordered Systems ◽  
Anderson Localization ◽  
Insulator Transition ◽  
Metal Insulator Transition ◽  
Metal Insulator ◽  
Level Statistics ◽  
Disordered Metals

The supersymmetry method for study of disordered systems is shortly reviewed. The discussion starts with a historical introduction followed by an explanation of the idea of using Grassmann anticommuting variables for investigating disordered metals. After that the nonlinear supermatrix σ-model is derived. Solution of several problems obtained with the help of the σ-model is presented. This includes the problem of the level statistics in small metal grains, localization in wires and films, and Anderson metal–insulator transition. Calculational schemes developed for studying these problems form the basis of subsequent applications of the supersymmetry approach.

Anderson localization in topologically disordered systems

1985 ◽  
Vol 31 (4) ◽  
pp. 2437-2450 ◽  
Author(s):  
David E. Logan ◽  
Peter G. Wolynes
Keyword(s):  
Disordered Systems ◽  
Anderson Localization
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