Localization In One-dimensional Systems Research Articles

Anderson localization in one-dimensional systems signified by localization tensor

A localization tensor in term of periodic position operator is recently proposed (de Aragão et al. (2019) [20]). We numerically study it in the one-dimensional Anderson model, Aubry-André-Harper model and slowly varying incommensurate potential ones, respectively. Due to its compatibility with periodic boundary conditions, we find it can properly reflect state localization properties, mobility edges and metal-insulator transitions in these famous models. In addition, it is better than the participation ratio to reflect localization properties of extended (delocalized) states. So it can be as a sensitivity index to characterize Anderson transitions.

Classical-quantum localization in one dimensional systems: The kicked rotor

This work explores the origin of dynamical localization in one-dimensional systems using the kicked rotor as an example. In particular, we propose the fractal dimension of the phase space as a robust indicator to characterize the onset of classical chaos. As a result, we find that the system crosses the stability border when the fractal dimension ≥1.81, and we obtain a functional form for the fractal dimension as a function of the kick strength. At the same time, dynamical localization is explored in the quantum realm by looking into the energy–localization relationship across the classical stability border, thus finding a correlation between the classical chaos and the presence of dynamical localization.

Signatures of Wigner localization in one-dimensional systems.

We propose a simple and efficient approach to study Wigner localization in one-dimensional systems using ab initio theory. In particular, we propose a suitable basis for the study of localization which consists of equally spaced overlapping gaussians. We illustrate our approach with full-configuration interaction which yields exact results for a given basis set. With our approach, we were able to study up to 8 electrons with full-configuration interaction. Finally, we propose the total-position spread tensor and the total electron entropy as convenient quantities to obtain signatures of Wigner localization.

Measurement-induced disturbance near Anderson localization in one-dimensional systems

We study the localization transition in several typical one-dimensional single-particle systems by means of measurement-induced disturbance (MID). The results show that the MID presents a rapid drop around the boundary between the localized state and extended ones, and the corresponding first-order derivative exhibits a behavior of divergence around the critical point for deterministic on-site potential systems (e.g. the quasi-periodic model). These characteristics can capture a phase diagram as well as the traditional method. For the non-deterministic on-site systems (e.g. the random dimer model), the states around the resonant energies possess relatively large values for MID, which means that they are extended. In addition, as the random potential ϵb exceeds the critical value, the states possessing a large MID vanish completely. These results show that MID can be useful in detecting localization transition in these typical one-dimensional systems.

Many-body Anderson localization in one-dimensional systems

We show, using quasi-exact numerical simulations, that Anderson localization in a disordered one-dimensional potential survives in the presence of attractive interaction between particles. The localization length of the particles' center of mass—computed analytically for weak disorder—is in good agreement with the quasi-exact numerical observations using the time evolving block decimation algorithm. Our approach allows for simulation of the entire experiment including the final measurement of all atom positions.

Localization of light in a random-grating array in a single-mode fiber

We investigate light propagation in randomly spaced fiber gratings in a single mode fiber, and demonstrate the localization effect. Localization of light in random media resembles that of electrons in disordered solids, resulting from a subtle wave interference formation. We measured the light transmission after each additional grating fabrication and found an exponential decay that follows the localization theory. An important feature of the random array is its similarity to ordered gratings in the transmission and reflection behavior at the long array regime. Besides the basic interest in localization in one-dimensional systems, random grating arrays have potential applications, utilizing the possibility to fabricate long structures with strong and broadband reflections.

Bragg reflection as a mechanism of light localization in one-dimensional systems

Bragg reflection as a mechanism of light localization in one-dimensional systems

Band theory of light localization in one-dimensional disordered systems.

A simple approach to the problem of light localization in one-dimensional system is presented. The role of the Bragg reflection in one-dimensional localization of light is discussed. Contrary to the existent viewpoint, we show that the origin of band gaps of regular crystals and the localization due to disorder have a common nature, that is, the Bragg reflection. We expand the concept of band structure to random systems of finite thickness L and relate the Anderson localization of light with the total band gap growth, which is observed in our computer simulation of disordered system, as L increases.

Influence of noise on chaos in nearly Hamiltonian systems.

The simultaneous influence of small damping and white noise on Hamiltonian systems with chaotic motion is studied on the model of periodically kicked rotor. In the region of parameters where damping alone turns the motion into regular, the level of noise that can restore the chaos is studied. This restoration is created by two mechanisms: by fluctuation induced transfer of the phase trajectory to domains of local instability, which can be described by the averaging of the local instability index, and by destabilization of motion within the islands of stability by fluctuation induced parametric modulation of the stability matrix, which can be described by the methods developed in the theory of Anderson localization in one-dimensional systems.

Vibration Mode Localization in One-Dimensional Systems

The method of regular perturbation is applied to study vibration mode localization in randomly disordered weakly coupled two-dimensional cantilever-spring arrays. Localization factors, which characterize the average exponential rates of decay or growth of the amplitudes of vibration, are defined in terms of the angles of orientation. First-order approximate results of the localization factor are obtained using a combined analytical-numerical approach. The localization factors are symmetric about the cantilever and the horizontal and vertical axes passing through the cantilever at which vibration is originated. For the systems under consideration, the direction in which vibration is originated corresponds to the smallest localization factor; whereas the diagonal directions correspond to the largest rate of decay or growth of the amplitudes of vibration. When plotted in the logarithmic scale, the vibration modes are of hill shape with the amplitudes of vibration decaying linearly away from the cantilever at which vibration is originated.

Vibration mode localization in one-dimensional systems

Vibration mode localization in one-dimensional systems