Narrow Results

Since the Wigner function (WF) is related to a Lindard-constant type linear dielectric function derived in the symmetric gauge,⁷ it is expected to show de Haas-van Alphen (dHvA) oscillations. Starting with the symmetric eigenfunctions, we derived the pure-state WF in a magnetic field, whose plots in phase space and in term of B^-1 for increasing n are consistent with the dHvA effect. Furthermore the asymptotic expansion of WF at large n show periodic oscillations with a period related to the Fermi energy. The phase space plots of WF also show that dHvA and similar oscillations could be a consequence of Nature's strategy for increasing the effective spatial range without violating the uncertainty principle. Properties of the symmetric eigenfunctions were derived. The dynamics of WF can be obtained from the solution of the time-dependent Schrödinger equation (SE). A new method to solve the SE in a magnetic field in the interaction picture based on expansion in term of symmetric eigenfunctions has been developed. The matrix element for a Gaussian potential were derived explicitly, plotted against B^-1, and showed oscillations. The total WF was shown to be a linear combination of the diagonal pure-state WF's by using the orthogonality for symmetric eigenfunctions. The no-special-point property for WF was confirmed, which is important for the construction of a numerical algorithm to solve the SE in a magnetic field.

We have addressed the central question in two-dimensional disordered systems: whether all states are localized even at infinitesimal disorder, as has been believed for over two decades but has come in question after recent experiments. We argue that the answer could still be yes since above a certain density the electrons can be treated effectively as non-interacting. Below this density, though the interactions among electrons get weaker they become more and more important as the electron density reduces. This can cause delocalization and produce a metallic phase. Some recent experimental results have been analysed to understand the nature of the newly found metallic phase at low electron-densities, and also the insulating phase at lower densities.

Localization property in the disordered few-chain DNA systems with a long-range correlation is numerically investigated. We apply the chain system with the correlated disorder in the interchain and/or intrachain hoppings to the simple model of a double strand of DNA. Numerical results for the density of states and the Lyapunov exponent of the wave function in the two- or three-chain models are given. It is found that the correlation effect enhances the localization length (the inverse least non-negative Lyapunov exponent) around the band center.

We study interlayer frictional drag between two-dimensional electron systems in the strong magnetic field limit by evaluating the weak-coupling Kubo formula for interlayer drag numerically. The key quantity in this theory is the disorder averaged "triangle function", a product of three Greens functions of electrons that represents the dc current response of electrons in one layer to charge fluctuations in a remote current-carrying layer. We find that the disorder averaged triangle functions are proportional to the momentum transfer at small and that they change sign under a ν→1-ν particle-hole transformations, vanishing for half-filled Landau levels.

We present a family of methods, analytical and numerical, which can describe behaviour in (non) equilibrium ensembles, both classical and quantum, especially in the complex systems, where the standard approaches cannot be applied. We demonstrate the creation of nontrivial (meta) stable states (patterns), localized, chaotic, entangled or decoherent, from basic localized modes in various collective models arising from the quantum hierarchy of Wigner-von Neumann-Moyal-Lindblad equations, which are the result of "wignerization" procedure of classical BBGKY hierarchy. We present the explicit description of internal quantum dynamics by means of exact analytical/numerical computations.

We consider non-interacting electrons moving on a two-dimensional square lattice in the presence of quenched correlated disorder potentials and a perpendicular magnetic field with flux density close to 1/2h/e per plaquette. In this situation, the individual sub-bands of the pure system carry σ_xy=-2e²/h per spin, similar to what has been recently observed in graphene. We find some unusual localization properties in the presence of disorder.

Recently q-breathers - time-periodic solutions which localize in the space of normal modes and maximize the energy density for some mode vector q₀ - were obtained for finite nonlinear lattices. We scale these solutions to arbitrarily large lattices in various lattice dimensions. We study the scaling consequence for previously obtained analytical estimates of the localization length of q-breathers for β-FPU and α-FPU lattices. The first finding is that the degree of localization depends only on intensive quantities and is size independent. Secondly, a critical wave vector k_m is identified, which depends on one effective nonlinearity parameter, q-breathers minimize the localization length at k₀ = k_m and completely delocalize in the limit k₀ → 0, π.

We study generic effects on the quantum dynamics of classical trapping-leaking mechanism by investigating in detail the 2δ-kicked rotors whose classical phase space is partitioned into momentum cells separated by trapping regions which slow down the motion. We focus on a range of parameters where the dynamics is generic, namely, the phase space has no stable islands. As a consequence of the trapping-leaking mechanism, we show that the classical motion is described by a process of anomalous diffusion. We investigate in detail the impact of the underlying classical anomalous diffusion on the quantum dynamics with special emphasis on the phenomenon of dynamical localization. Based on the study of the quantum density of probability, its second moment and the return probability, we identify a region of weak dynamical localization where the quantum diffusion is still anomalous but the diffusion rate is slower than in the classical case. Moreover, we examine how other relevant time scales, such as the quantum-classical breaking time and the one related to the beginning of full dynamical localization, are modified by the classical anomalous diffusion. Finally, we discuss the relevance of our results for understanding the role of classical cantori in quantum mechanics.

The transport properties of sintered samples of NdBa_2-x La_xCu₃O_7-δ with 0 ≤ x ≤ 0.3 have been studied in the normal state by Hall effect measurements. The Hall coefficient, R_H is positive in the normal state and increases with increasing La doping concentration over the whole temperature range from the critical temperature, T_c, up to room temperature. The results for the Hall coefficient as a function of temperature and doping concentration were analyzed within the phenomenological narrow band and Anderson models. A good agreement between models and data was obtained. As in the phenomenological narrow band model, the band widths increase with increasing doping concentration. As in the Anderson model, the Hall angle is proportional to T² over the whole measured temperature range for all samples. The obtained results for both models supported the view that La doping introduces electronic disorder into the CuO₂ planes. The tendency towards localization is driven by electronic disorder. In addition to hole filling, the localization is another reason for the decreasing superconducting critical temperature in these samples.

We investigate the effects of vacancies, disorder and sublattice polarization on the electronic properties of a monolayer graphene in the quantum Hall regime. Energy spectra as a function of magnetic field and the localization properties of the states within the graphene Landau levels (LLs) are calculated through a tight-binding model. We first discuss our results considering vacancies in the lattice, where we show that vacancies introduce extra levels (or well-defined bands) between consecutive LLs. An striking consequence here is that extra Hall resistance plateaus are expected to emerge when an organized vacancy superlattice is considered. Secondly, we discuss the anomalous localization properties we have found for the lowest LL, where an increasing disorder is shown to enhance the wave functions delocalization (instead of inducing localization). This unexpected effect is shown to be directly related to the way disorder increasingly destroys the sublattice (valley) polarization of the states in the lowest LL. The reason why this anomalous disorder effect occurs only for the zero-energy LL is that, in absence of disorder, only for this level all the states are sublattice polarized, i.e., their wave functions have amplitudes in only one of the sublattices.

The results of extensive transport studies in localized regime of mesoscopic two-dimensional electron systems (2DES) with varying disorder are presented. A quick overview of previously achieved result is given. The main focus is on the observation of density dependent instabilities manifested by strong resistance oscillations induced by high perpendicular magnetic fields B_⊥. While the amplitude of the oscillations is strongly enhanced with increasing B_⊥, their position in electron density remains unaffected. The temperature dependence of resistivity shows a transition from an activated behaviour at high temperature to a saturated behaviour at low T. In the positions of resistance minima, the T dependence can even become metal-like (dρ/dT > 0). The activation energies obtained from the high T behaviour exhibit a formation of plateaux in connection with the resistance oscillations when analyzed as a function of electron density. We suggest the interplay between a strongly interacting electron phase and the background disorder as a possible explanation for our observation.

We prove that a strongly disordered two-dimensional system localizes with a localization length given analytically. We get a scaling law with a critical exponent ν = 1 in agreement with the Chayes criterion ν ≥ 1. The case we are considering is for off-diagonal disorder. The method we use is a perturbation approach holding in the limit of an infinitely large perturbation as recently devised and the Anderson model is considered with a Gaussian distribution of disorder. The localization length diverges when energy goes to zero with a scaling law in agreement to numerical and theoretical expectations.

In this paper, the localization of eigenmodes in quasi-1-D pseudo-random potential lattice electron waveguides is studied using the equivalent circuit method applied to the Schrödinger equation. It is found that the mixed deterministic and random discrete potential and limited waveguide width allow only intermediate localization of modes, and their two main types are discovered: the gap-localized and random-lattice localized modes which are stable toward variation of the waveguide's geometry. These modes can be transformed to each other by proper choosing the waveguide parameters. The discovered and studied effects and created models are interesting in the developments of spatial nano-switches of electron waves.

This research delves into the fascinating transmission characteristics of a system with variable mass, confined by a Coulomb-like potential. By utilizing an analytic approach to transmission probability, we were able to unveil the intriguing features that are observed experimentally in a specially designed two-dimensional lattice. This lattice was engineered to manipulate itinerant electrons through entanglement, resulting in variable masses as they traverse the lattice. To build our model system, we utilized the displacement operator approach to the position-dependent effective mass theory. This allowed us to investigate the effects of different configurations of leads, system geometries and lattice deformations on the transmission characteristics of the system. The resulting data showed that the model system was highly sensitive to these parameters, which led to various interesting features. First, we observed Andreev-like reflections, which occur when a particle is reflected as a hole, resulting in the transfer of both energy and charge. Another feature was reflectionless transmission, in which the transmission probability of a particle is close to unity, and almost no reflection occurs. We also observed complete localization of charge carriers, where the transmission probability is effectively zero, indicating that the charge carriers are completely confined within the lattice. Our findings demonstrate the remarkable versatility of the effective mass approach in the modeling of physical systems. By unraveling the intricate relationships between system parameters and transmission probability, we have gained new insights into the behavior of itinerant charge carriers in lattice structures. These insights may guide the design and development of novel electronic devices with enhanced performance and functionality.