Phenomenon Of Anderson Localization Research Articles

Tunneling and revival of Anderson localization in a Bose-Einstein condensate

We provide an analytical model to fabricate an exponential localization of a Bose-Einstein condensate under a bichromatic optical lattice. Such localization is famously known as Anderson localization. The degree of localization is investigated using the participation ratio to recognize the laser parameter domain for Anderson localization. The exponential nature of the localization is proved, and we also identify the localization length. The tunneling of an Anderson-localized condensate with time is observed, and the revival phenomenon of Anderson localization is reported. Slowing down of Anderson localization is noticed for higher laser intensity. We also study the dynamical and structural stability of the condensate during Anderson localization, which suggests the preferred values of laser power and the time instance to encounter a minimal mean difference in the presence of noise.

Wave-function extreme value statistics in Anderson localization

We consider a disordered one-dimensional tight-binding model with power-law decaying hopping amplitudes to disclose wavefunction maximum distributions related to the Anderson localization phenomenon. Deeply in the regime of extended states, the wavefunction intensities follow the Porter-Thomas distribution while their maxima assume the Gumbel distribution. At the critical point, distinct scaling laws govern the regimes of small and large wavefunction intensities with a multifractal singularity spectrum. The distribution of maxima deviates from the usual Gumbel form and some characteristic finite-size scaling exponents are reported. Well within the localization regime, the wavefunction intensity distribution is shown to develop a sequence of pre-power-law, power-law, exponential and anomalous localized regimes. Their values are strongly correlated, which significantly affects the emerging extreme values distribution.

Quantum localization and electronic transport in covalently functionalized carbon nanotubes

Carbon nanotubes are of central importance for applications in nano-electronics thanks to their exceptional transport properties. They can be used as sensors, for example in biological applications, provided that they are functionalized to detect specific molecules. Due to their one-dimensional geometry the carbon nanotubes are very sensitive to the phenomenon of Anderson localization and it is therefore essential to know how the functionalization modifies their conduction properties and if they remain good conductors. Here we present a study of the quantum localization induced by functionalization in metallic single walled carbon nanotubes (SWCNT) with circumferences up to 15 nm. We consider resonant and non-resonant adsorbates that represent two types of covalently functionalized groups with strong and moderate scattering properties. The present study provides a detailed analysis of the localization behaviour and shows that the localization length can decrease down to 20–50 nm at concentrations of about 1 percent of adsorbates. On this basis we discuss the possible electronic transport mechanisms which can be either metallic like or insulating like with variable range hopping.

Anderson localization of flexural waves in disordered elastic beams

We study, both experimentally and numerically, the Anderson localization phenomenon in flexural waves of a disordered elastic beam, which consists of a beam with randomly spaced notches. We found that the effect of the disorder on the system is stronger above a crossover frequency fc than below it. For a chosen value of disorder, we show that above fc the normal-mode wave functions are localized as occurs in disordered solids, while below fc the wave functions are partially and fully extended, but their dependence on the frequency is not governed by a monotonous relationship, as occurs in other classical and quantum systems. These findings were corroborated with the calculation of the participation ratio, the localization length and a level statistics. In particular, the nearest spacing distribution is obtained and analyzed with a suitable phenomenological expression, related to the level repulsion.

Disorder-induced high-quality wavefront in an Anderson localizing optical fiber

High-quality coherent wavefronts are extremely useful in optical communications and lasers. Disorder is usually considered as a source of noise and deviation from ideal designs for generating high-quality beams in photonic devices. Here, we demonstrate that strong disorder can be exploited to obtain high-quality wavefronts thanks to the Anderson localization phenomenon. Our analysis on a transverse Anderson localizing optical fiber reveals that a considerable number of the guided modes have M2<2 values. These high-quality modes are distributed across the transverse profile of the disordered fiber and can be excited without requiring sophisticated spatial light modulations at the input facet. The results show the potential of such fibers for novel applications in fiber lasers and nonlinear devices, where a high beam quality is desirable.

Remnants of Anderson localization in prethermalization induced by white noise

We study the non-equilibrium evolution of a one-dimensional quantum Ising chain with spatially disordered, time-dependent, transverse fields characterised by white noise correlation dynamics. We establish pre-thermalization in this model, showing that the quench dynamics of the on-site transverse magnetisation first approaches a metastable state unaffected by noise fluctuations, and then relaxes exponentially fast towards an infinite temperature state as a result of the noise. We also consider energy transport in the model, starting from an inhomogeneous state with two domain walls which separate regions characterised by spins with opposite transverse magnetization. We observe at intermediate time scales a phenomenology akin to Anderson localization: energy remains localised within the two domain walls, until the Markovian noise destroys coherence and accordingly disorder-induced localization, allowing the system to relax towards the late stages of its non-equilibrium dynamics. We benchmark our results with the simpler case of a noisy quantum Ising chain without disorder, and we find that the pre-thermal plateau is a generic property of weakly noisy spin chains, while the phenomenon of pre-thermal Anderson localisation is a specific feature arising from the competition of noise and disorder in the real-time transport properties of the system.

Disorder engineering: From structural coloration to acoustic filters

We study Anderson localization of waves in a one dimensional disordered meta-material of bilayers comprising of thin fixed length scatterers placed randomly along a homogenous medium. As an interplay between order and disorder, we identify a new regime of strong disorder where the localization length becomes independent of the amount of disorder but depends on the frequency of the wave excitation and on the properties of the fixed length scatterer. As an example of a naturally occurring nearly one dimensional disordered bilayer, we calculate the wavelength dependent reflection spectrum for Koi fish using the experimentally measured parameters, and find that the main mechanisms for the emergence of their silver structural coloration can be explained through the phenomenon of Anderson localization of light in the regime of strong disorder discussed above. Finally, we show that by tuning the thickness of the fixed length scatterer, the above design principles could be used to engineer disordered meta-materials which selectively allows harmonics of a fundamental frequency to be transmitted in an effect which is similar to the insertion of a half wave cavity in a quarter wavelength stack. However, in contrast to the Lorentzian resonant peak of a half-wave cavity, we find that our disordered layer has a Gaussian lineshape whose width becomes narrower as the number of disordered layers is increased.

Multiple spatially localized dynamical states in friction-excited oscillator chains

Friction-induced vibrations are known to affect many engineering applications. Here, we study a chain of friction-excited oscillators with nearest neighbor elastic coupling. The excitation is provided by a moving belt which moves at a certain velocity vd while friction is modelled with an exponentially decaying friction law. It is shown that in a certain range of driving velocities, multiple stable spatially localized solutions exist whose dynamical behavior (i.e. regular or irregular) depends on the number of oscillators involved in the vibration. The classical non-repeatability of friction-induced vibration problems can be interpreted in light of those multiple stable dynamical states. These states are found within a “snaking-like” bifurcation pattern. Contrary to the classical Anderson localization phenomenon, here the underlying linear system is perfectly homogeneous and localization is solely triggered by the friction nonlinearity.

Disorder in tilted Weyl semimetals from a renormalization group perspective

Isolated Weyl cones in a disordered environment do not show the phenomenon of Anderson localization due to the abscence of backscattering processes. However, besides the conventional three dimensional diffusive metal, an additional semimetallic phase can form. In this paper we study the effect of tilt on the physics of disorder in isolated Weyl cones. Our main finding is that while the semimetallic phase remains a stable phase, tilt decreases the size of the semimetallic region. Conversely, disorder increases the effective tilt of the quasiparticle excitations.

Localisation of Rayleigh–Bloch waves and damping of resonant loads on arrays of vertical cylinders

Linear potential-flow theory is used to study loads imposed on finite line arrays of rigid, bottom-mounted, surface-piercing, vertical cylinders by surface water waves. Perturbations in the cylinder locations are shown to damp the resonant loads experienced by the unperturbed array. A relationship is established between the damping and the phenomenon of Anderson localisation. Specifically, the Rayleigh–Bloch waves responsible for the resonant loads are shown to attenuate along the array when perturbations are introduced, resulting in localisation when the attenuation rate is sufficiently large with respect to the array length. Further, an efficient solution method for line arrays is introduced that captures the Rayleigh–Bloch wave modes supported by unperturbed arrays from the scattering characteristics of an individual cylinder.

Experimental Observation of Dynamical Localization in Laser-Kicked Molecular Rotors.

The periodically kicked rotor is a paradigm system for studying quantum effects on classically chaotic dynamics. The wave function of the quantum rotor localizes in angular momentum space, similarly to Anderson localization of the electronic wave function in disordered solids. Here, we observe dynamical localization in a system of true quantum rotors by subjecting nitrogen molecules to periodic sequences of femtosecond pulses. Exponential distribution of the molecular angular momentum-the hallmark of dynamical localization-is measured directly by means of coherent Raman scattering. We demonstrate the suppressed rotational energy growth with the number of laser kicks and study the dependence of the localization length on the kick strength. Because of its quantum coherent nature, both timing and amplitude noise are shown to destroy the localization and revive the diffusive growth of energy.

A Bloch decomposition-based stochastic Galerkin method for quantum dynamics with a random external potential

In this paper, we consider the numerical solution of the one-dimensional Schr\"odinger equation with a periodic lattice potential and a random external potential. This is an important model in solid state physics where the randomness is involved to describe some complicated phenomena that are not exactly known. Here we generalize the Bloch decomposition-based time-splitting pseudospectral method to the stochastic setting using the generalize polynomial chaos with a Galerkin procedure so that the main effects of dispersion and periodic potential are still computed together. We prove that our method is unconditionally stable and numerical examples show that it has other nice properties and is more efficient than the traditional method. Finally, we give some numerical evidence for the well-known phenomenon of Anderson localization.

Non monotonic influence of Hubbard interaction on the Anderson localization of two-electron wavepackets

We show that the Hubbard-like interaction between two electrons moving in a random one-dimensional potential landscape has a non monotonic influence on the Anderson localization phenomenon. Within a tight-binding approach, we follow the time-evolution of initially localized two-electron wavepackets and compute the participation number of all two-particle eigenstates. We evidence that the coupling between bounded and unbounded two-particle states leads to an overall weakening of Anderson localization of the predominant unbounded states. However, such coupling becomes ineffective in the regime of large interaction strengths on which the energy bands corresponding to these two classes of eigenstates become quite detached. We unveil that these two competing effects are at the origin of the non monotonic influence of the inter-particle interaction on Anderson localization.

Anderson Localization Phenomenon in One-Dimensional Elastic Systems

The phenomenon of the Anderson localization of waves in elastic systems is studied. We analyze this phenomenon in two di erent sets of systems: disordered linear chains of harmonic oscillators and disordered rods which oscillate with torsional waves. The rst set is analyzed numerically whereas the second one is studied both experimentally and theoretically. In particular, we discuss the localization properties of the waves as a function of the frequency. In doing that we have used the inverse participation ratio, which is related to the localization length. We nd that the normal modes localize exponentially according to the Anderson theory. In the elastic systems, the localization length decreases with frequency. This behavior is in contrast with what happens in analogous quantum mechanical systems, for which the localization length grows with energy. This di erence is explained by means of the properties of the re ection coe cient of a single scatterer in each case.

Anderson localization in laser-kicked molecules

The paper explores the prospects of observing the phenomenon of dynamical Anderson localization via nonresonant Raman-type rotational excitation of molecules by periodic trains of short laser pulses. We define conditions for such an experiment and show that current femtosecond technology used for nonadiabatic laser alignment of linear molecules is sufficient for this task. Several observables which can serve as indicators for Anderson localization are suggested for measurement, and the influence of experimental limitations imposed by the laser intensity noise, finite pulse duration, limited number of pulses in a train, and thermal effects is analyzed.

Interface localization of light in disordered photonic lattices

The Anderson localization of light at the interface separating square and hexagonal photonic lattices is demonstrated numerically. The influence of varying lattice intensities and disorder level on the transverse localization of light is discussed. Both suppression and enhancement of light localization in the presence of the interface, depending on the difference in the lattice intensity in both regions, and the position of the excited lattice site are demonstrated. Such localization is compared to the cases with no interfaces. Also, it is analysed how the presence of a phase-slip defect modifies the phenomenon of Anderson localization of light at the interface.

Anderson localization in finite disordered vibrating rods

We study, both experimentally and numerically, the Anderson localization phenomenon in torsional waves of a disordered elastic rod, which consists of a cylinder with randomly spaced notches. We find that the normal-mode wave amplitudes are exponentially localized as occurs in disordered solids. The localization length, measured using these wave amplitudes, decreases as a function of frequency. The normal-mode spectrum is also measured as well as computed, so its level statistics can be analyzed. From the spectrum, the nearest-neighbor spacing distribution can be obtained. This distribution can be described by a phenomenological expression that depends on a parameter α, related to the level repulsion, which is also a function of the frequency. Therefore, the localization length can be expressed in terms of the parameter α. There exists a range in which the localization length grows linearly with α. However, at low values of this parameter the linear dependence does not hold.

Image transport quality can be improved in disordered waveguides

We show that the quality of image transport can be improved in disordered waveguides compared with periodic waveguides such as coherent fiber optic bundles that are commonly used for imaging applications. The improvement is due to the transverse Anderson localization phenomenon that creates localized transport channels with finite radii through the disordered imaging waveguide.

Breakdown of Anderson localization of interacting quantum bright solitons in a disorder potential

The center of mass of a bright soliton in a Bose-Einstein condensate may reveal Anderson localization in the presence of a weak disorder potential. We analyze the effects of interactions between two bright solitons on the Anderson localization phenomenon. Perturbation calculus shows that even very weak interactions modify localization properties of the system eigenstates. For stronger interactions (i.e., when the solitons are close to each other), the localization is totally broken. It implies that in order to experimentally observe the Anderson localization effects, a single bright soliton has to be prepared and excitation of soliton trains must be avoided.

Towards a new proof of Anderson localization

The wave function of a non-relativistic particle in a periodic potential admits oscillatory solutions, the Bloch waves. In the presence of a random noise contribution to the potential the wave function is localized. We outline a new proof of this Anderson localization phenomenon in one spatial dimension, extending the classical result to the case of a periodic background potential. The proof makes use of techniques previously developed to study the effects of noise on reheating in inflationary cosmology, employing methods of random matrix theory.