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.

External Ventricular Drain Infection

2007 ◽  
Vol 107 (1) ◽  
pp. 248 ◽  
Author(s):  
George K. C. Wong ◽  
Wayne W. S. Poon
Keyword(s):  
Major Trauma ◽  
Independent Predictor ◽  
External Ventricular Drain ◽  
Significant Risk ◽  
Significant Risk Factor ◽  
External Ventricular Drainage ◽  
Infection Rates ◽  
The Mean ◽  
The Relationship ◽  
Shed Light

Object The authors explored the relationship among the duration of external ventricular drainage, revision of external ventricular drains (EVDs), and cerebrospinal fluid (CSF) infection to shed light on the practice of electively revising these drains. Methods In a retrospective study of 199 patients with 269 EVDs in the intensive care unit at a major trauma center in Australasia, the authors found 21 CSF infections. Acinetobacter accounted for 10 (48%) of these infections. Whereas the duration of drainage was not an independent predictor of infection, multiple insertions of EVDs was a significant risk factor. Second and third EVDs in previously uninfected patients were more likely to become infected than first EVDs. An EVD infection was initially identified a mean of 5.5 ±0.7 days postinsertion (standard error of the mean); these data—that is, the number of days—were normally distributed. Conclusions This pattern of infection is best explained by EVD-associated CSF infections being acquired by the introduction of bacteria on insertion of the drain rather than by subsequent retrograde colonization. Elective EVD revision would be expected to increase infection rates in light of these results, and thus the practice has been abandoned by the authors' institution.

scholarly journals A STUDY OF DISORDERED SYSTEMS WITH GAIN: STOCHASTIC AMPLIFICATION

2000 ◽  
Vol 14 (16) ◽  
pp. 1669-1681 ◽  
Author(s):  
SANDEEP K. JOSHI ◽  
A. M. JAYANNAVAR
Keyword(s):  
Reflection Coefficient ◽  
Disordered Systems ◽  
Random Phase Approximation ◽  
Random Medium ◽  
Random Phase ◽  
Localization Length ◽  
Critical Length ◽  
Sample Length ◽  
Coherent Amplification ◽  
Transmission And Reflection

A study of statistics of transmission and reflection from a random medium with stochastic amplification as opposed to coherent amplification is presented. It is found that the transmission coefficient t, for sample length L less than the critical length L c grows exponentially with L. In the limit L→∞ transmission decays exponentially as < ln t>=-L/ξ where ξ is the localization length. In this limit reflection coefficient r saturates to a fixed value which shows a monotonic increase as a function of strength of amplification α. The stationary distribution of super-reflection coefficient agrees well with the analytical results obtained within the random phase approximation (RPA). Our model also exhibits the well known duality between absorption and amplification. We emphasize the major differences between coherent amplification and stochastic amplification where-ever appropriate.

scholarly journals Stochastic Estimation and Non-Linear Wall-Pressure Sources in a Separating/Reattaching Flow

2002 ◽  
Author(s):  
A. Naguib ◽  
L. Hudy ◽  
W. M. Humphreys
Keyword(s):  
Flow Field ◽  
Surface Pressure ◽  
Wall Pressure ◽  
Stochastic Estimation ◽  
Piv Measurements ◽  
Non Linear ◽  
The Mean ◽  
The Individual ◽  
Plate Geometry ◽  
Shed Light

Simultaneous wall-pressure and PIV measurements are used to study the conditional flow field associated with surface-pressure generation in a separating/reattaching flow established over a fence-with-splitter-plate geometry. The conditional flow field is captured using linear and quadratic stochastic estimation based on the occurrence of positive and negative pressure events in the vicinity of the mean reattachment location. The results shed light on the dominant flow structures associated with significant wall-pressure generation. Furthermore, analysis based on the individual terms in the stochastic estimation expansion shows that both the linear and non-linear flow sources of the coherent (conditional) velocity field are equally important contributors to the generation of the conditional surface pressure.

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.

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