Search results for "localization"

Spatial multifractal properties of wave packets in the Anderson model of localization.

1993

The multifractal properties of electronic wave functions in disordered samples are investigated. In a given energy range all eigenstates are determined for the same disorder configuration in the Anderson model of localization. It is shown that the singularity spectrum and the generalized dimensions change only slowly with energy, aside from statistical fluctuations. More important, the wave packet constructed by linear combination of the eigenstates shows quantitatively the same multifractal properties. Consequences for the transport properties of electronic states in disordered systems are discussed.

Fermion confinement via quantum walks in (2+1)-dimensional and (3+1)-dimensional space-time

2017

We analyze the properties of a two- and three-dimensional quantum walk that are inspired by the idea of a brane-world model put forward by Rubakov and Shaposhnikov [Phys. Lett. B 125, 136 (1983)PYLBAJ0370-269310.1016/0370-2693(83)91253-4]. In that model, particles are dynamically confined on the brane due to the interaction with a scalar field. We translated this model into an alternate quantum walk with a coin that depends on the external field, with a dependence which mimics a domain wall solution. As in the original model, fermions (in our case, the walker) become localized in one of the dimensions, not from the action of a random noise on the lattice (as in the case of Anderson localiza…

Electronic structure, localization, and spin-state transition in Cu-substitutedFeSe:Fe1−xCuxSe

2010

We report density-functional studies of the ${\text{Fe}}_{1\ensuremath{-}x}{\text{Cu}}_{x}\text{Se}$ alloy done using supercell and coherent-potential approximation methods. Magnetic behavior was investigated using the disordered local moment approach. We find that Cu occurs in a nominal ${d}^{10}$ configuration and is highly disruptive to the electronic structure of the Fe sheets. This would be consistent with a metal-insulator transition due to Anderson localization. We further find a strong crossover from a weak moment itinerant system to a local moment magnet at $x\ensuremath{\approx}0.12$. We associate this with the experimentally observed jump near this concentration. Our results are …

Spatiotemporal rotational dynamics of laser-driven molecules

2020

Molecular alignment and orientation by laser fields has attracted significant attention in recent years, mostly due to new capabilities to manipulate the molecular spatial arrangement. Molecules can now be efficiently prepared for ionization, structural imaging, orbital tomography, and more, enabling, for example, shooting of dynamic molecular movies. Furthermore, molecular alignment and orientation processes give rise to fundamental quantum and classical phenomena like quantum revivals, Anderson localization, and rotational echoes, just to mention a few. We review recent progress on the visualization, coherent control, and applications of the rich dynamics of molecular rotational wave pack…

Analytical description of the transverse Anderson localization of light

2017

Energy spectrum, persistent current and electron localization in quantum rings

2003

Energy spectra of quasi-one-dimensional quantum rings with a few electrons are studied using several different theoretical methods. Discrete Hubbard models and continuum models are shown to give similar results governed by the special features of the one-dimensionality. The energy spectrum of the many-body system can be described with a rotation-vibration spectrum of a 'Wigner molecule' of 'localized' electrons, combined with the spin-state determined from an effective antiferromagnetic Heisenberg Hamiltonian. The persistent current as a function of magnetic flux through the ring shows periodic oscillations arising from the 'rigid rotation' of the electron ring. For polarized electrons the …

Laplacian-level density functionals for the exchange-correlation energy of low-dimensional nanostructures

2010

In modeling low-dimensional electronic nanostructures, the evaluation of the electron-electron interaction is a challenging task. Here we present an accurate and practical density-functional approach to the two-dimensional many-electron problem. In particular, we show that spin-density functionals in the class of meta-generalized-gradient approximations can be greatly simplified by reducing the explicit dependence on the Kohn-Sham orbitals to the dependence on the electron spin density and its spatial derivatives. Tests on various quantum-dot systems show that the overall accuracy is well preserved, if not even improved, by the modifications.

A Monte Carlo Study of the Low-Temperature Properties of Strongly Correlated Localized Particles in Disordered Systems

1993

A computer simulation method is presented, which yields the ground state as well as the low-energy excitations for disordered systems of many interacting particles. The efficiency of the method is demonstrated by the application to the Coulomb glass, i.e. many localized electrons with long-range interaction. The obtained knowledge about the specific configurations of a large number of excited states is only the starting point for further investigations. First results are presented which shed a new light on old controversies about the behaviour of correlated electrons within the Coulomb gap regime.

Transport in topological insulators with bulk-surface coupling: Interference corrections and conductance fluctuations

2018

Motivated by the experimental difficulty to produce topological insulators (TIs) of the ${\text{Bi}}_{2}{\text{Se}}_{3}$ family with pure surface-state conduction, we study the effect that the bulk can have on the low-temperature transport properties of gated thin TI films. In particular, we focus on interference corrections, namely weak localization (WL) or weak antilocalization (WAL), and conductance fluctuations (CFs) based on an effective low-energy Hamiltonian. Utilizing diagrammatic perturbation theory, we first analyze the bulk and the surface separately and subsequently discuss WL/WAL and CFs when a tunneling-coupling is introduced. We identify the relevant soft diffusion modes of t…

The multifractal character of the electronic states in disordered two-dimensional systems

1995

The nature of electronic states in disordered two-dimensional (2D) systems is investigated. With this aim, we present our calculations of both density of states and d.c. conductivity for square lattices modelling the Anderson Hamiltonian with on-site energies randomly chosen from a box distribution of width W. For weak disorder (W), the eigenfunctions calculated by means of the Lanczos diagonalization algorithm display spatial fluctuations reflecting their (multi)fractal behaviour. For increasing disorder the observed increase of the curdling of the wavefunction reflects its stronger localization. However, as a function of energy, the eigenstates at energy mod E mod /V approximately=1.5 are…