Localization in Semiconductor Quantum Wire Nanostructures

Localization properties of quasi-one dimensional quantum wire nanostructures are investigated using the transfer matrix-Lyapunov exponent technique. We calculate the localization length as a function of the effective mean-field mobility assuming the random disorder potential to be arising from dopant-induced short-range $\delta$-function or finite-range Gaussian impurity scattering. The localization length increases approximately linearly with the effective mobility, and is also enhanced by finite-range disorder. There is a sharp reduction in the localization length when the chemical potential crosses into the second subband.Comment: 4 pages, RevTeX 3.0, 5 figures (available upon request

Electron localisation in static and time-dependent one-dimensional model systems

Electron localization is the tendency of an electron in a many-body system to exclude other electrons from its vicinity. Using a new natural measure of localization based on the exact manyelectron wavefunction, we find that localization can vary considerably between different ground-state systems, and can also be strongly disrupted, as a function of time, when a system is driven by an applied electric field. We use our new measure to assess the well-known electron localization function (ELF), both in its approximate single-particle form (often applied within density-functional theory) and its full many-particle form. The full ELF always gives an excellent description of localization, but the approximate ELF fails in time-dependent situations, even when the exact Kohn-Sham orbitals are employed.Comment: 7 pages, 4 figure

Nonlocally-correlated disorder and delocalization in one dimension II: Localization length

In the previous paper (cond-mat/9809323), we calculated the density of staes in the random-mass Dirac fermion system. In this paper, we obtain the mean localization length of the single-fermion Greem's function by using the supersymmetric methods. It is shown that the localization length is a increasing function of the correation length of the disorders. This result is in agreement with the density of states and the numerical studies (cond-mat/9903389).Comment: Latex, 25 page

Localization-delocalization transition in one-dimensional electron systems with long-range correlated disorder

We investigate localization properties of electron eigenstates in one-dimensional (1d) systems with long-range correlated diagonal disorder. Numerical studies on the localization length $\xi$ of eigenstates demonstrate the existence of the localization-delocalization transition in 1d systems and elucidate non-trivial behavior of $\xi$ as a function of the disorder strength. The critical exponent $\nu$ for localization length is extracted for various values of parameters characterizing the disorder, revealing that every $\nu$ disobeys the Harris criterion $\nu > 2/d$.Comment: 6 pages, 6 figuers, to be published in Phys. Rev.

Magnetolocalization in disordered quantum wires

The magnetic field dependent localization in a disordered quantum wire is considered nonperturbatively. An increase of an averaged localization length with the magnetic field is found, saturating at twice its value without magnetic field. The crossover behavior is shown to be governed both in the weak and strong localization regime by the magnetic diffusion length L_B. This function is derived analytically in closed form as a function of the ratio of the mean free path l, the wire thickness W, and the magnetic length l_B for a two-dimensional wire with specular boundary conditions, as well as for a parabolic wire. The applicability of the analytical formulas to resistance measurements in the strong localization regime is discussed. A comparison with recent experimental results on magnetolocalization is included.Comment: 22 pages, RevTe

An Inverse Problem for Localization Operators

A classical result of time-frequency analysis, obtained by I. Daubechies in 1988, states that the eigenfunctions of a time-frequency localization operator with circular localization domain and Gaussian analysis window are the Hermite functions. In this contribution, a converse of Daubechies' theorem is proved. More precisely, it is shown that, for simply connected localization domains, if one of the eigenfunctions of a time-frequency localization operator with Gaussian window is a Hermite function, then its localization domain is a disc. The general problem of obtaining, from some knowledge of its eigenfunctions, information about the symbol of a time-frequency localization operator, is denoted as the inverse problem, and the problem studied by Daubechies as the direct problem of time-frequency analysis. Here, we also solve the corresponding problem for wavelet localization, providing the inverse problem analogue of the direct problem studied by Daubechies and Paul.Comment: 18 pages, 1 figur

Exact Results in Discretized Gauge Theories

We apply the localization technique to topologically twisted N=(2,2) supersymmetric gauge theory on a discretized Riemann surface (the generalized Sugino model). We exactly evaluate the partition function and the vacuum expectation value (vev) of a specific Q-closed operator. We show that both the partition function and the vev of the operator depend only on the Euler characteristic and the area of the discretized Riemann surface and are independent of the detail of the discretization. This localization technique may not only simplify numerical analysis of the supersymmetric lattice models but also connect the well-defined equivariant localization to the empirical supersymmetric localization.Comment: 26 pages, 1 figure, references added, typos correcte

A Hybrid Global Minimization Scheme for Accurate Source Localization in Sensor Networks

We consider the localization problem of multiple wideband sources in a multi-path environment by coherently taking into account the attenuation characteristics and the time delays in the reception of the signal. Our proposed method leaves the space for unavailability of an accurate signal attenuation model in the environment by considering the model as an unknown function with reasonable prior assumptions about its functional space. Such approach is capable of enhancing the localization performance compared to only utilizing the signal attenuation information or the time delays. In this paper, the localization problem is modeled as a cost function in terms of the source locations, attenuation model parameters and the multi-path parameters. To globally perform the minimization, we propose a hybrid algorithm combining the differential evolution algorithm with the Levenberg-Marquardt algorithm. Besides the proposed combination of optimization schemes, supporting the technical details such as closed forms of cost function sensitivity matrices are provided. Finally, the validity of the proposed method is examined in several localization scenarios, taking into account the noise in the environment, the multi-path phenomenon and considering the sensors not being synchronized