Anderson Localization of Polar Eigenmodes in Random Planar Composites

Anderson localization of classical waves in disordered media is a fundamental physical phenomenon that has attracted attention in the past three decades. More recently, localization of polar excitations in nanostructured metal-dielectric films (also known as random planar composite) has been subject of intense studies. Potential applications of planar composites include local near-field microscopy and spectroscopy. A number of previous studies have relied on the quasistatic approximation and a direct analogy with localization of electrons in disordered solids. Here I consider the localization problem without the quasistatic approximation. I show that localization of polar excitations is characterized by algebraic rather than by exponential spatial confinement. This result is also valid in two and three dimensions. I also show that the previously used localization criterion based on the gyration radius of eigenmodes is inconsistent with both exponential and algebraic localization. An alternative criterion based on the dipole participation number is proposed. Numerical demonstration of a localization-delocalization transition is given. Finally, it is shown that, contrary to the previous belief, localized modes can be effectively coupled to running waves.Comment: 22 pages, 7 figures. Paper was revised and a more precise definition of the participation number given, data for figures recalculated accordingly. Accepted to J. Phys.: Cond. Mat

Functional control of network dynamics using designed Laplacian spectra

Complex real-world phenomena across a wide range of scales, from aviation and internet traffic to signal propagation in electronic and gene regulatory circuits, can be efficiently described through dynamic network models. In many such systems, the spectrum of the underlying graph Laplacian plays a key role in controlling the matter or information flow. Spectral graph theory has traditionally prioritized unweighted networks. Here, we introduce a complementary framework, providing a mathematically rigorous weighted graph construction that exactly realizes any desired spectrum. We illustrate the broad applicability of this approach by showing how designer spectra can be used to control the dynamics of various archetypal physical systems. Specifically, we demonstrate that a strategically placed gap induces chimera states in Kuramoto-type oscillator networks, completely suppresses pattern formation in a generic Swift-Hohenberg model, and leads to persistent localization in a discrete Gross-Pitaevskii quantum network. Our approach can be generalized to design continuous band gaps through periodic extensions of finite networks.Comment: 9 pages, 5 figure

Chiral phase transition and Anderson localization in the Instanton Liquid Model for QCD

We study the spectrum and eigenmodes of the QCD Dirac operator in a gauge background given by an Instanton Liquid Model (ILM) at temperatures around the chiral phase transition. Generically we find the Dirac eigenvectors become more localized as the temperature is increased. At the chiral phase transition, both the low lying eigenmodes and the spectrum of the QCD Dirac operator undergo a transition to localization similar to the one observed in a disordered conductor. This suggests that Anderson localization is the fundamental mechanism driving the chiral phase transition. We also find an additional temperature dependent mobility edge (separating delocalized from localized eigenstates) in the bulk of the spectrum which moves toward lower eigenvalues as the temperature is increased. In both regions, the origin and the bulk, the transition to localization exhibits features of a 3D Anderson transition including multifractal eigenstates and spectral properties that are well described by critical statistics. Similar results are obtained in both the quenched and the unquenched case though the critical temperature in the unquenched case is lower. Finally we argue that our findings are not in principle restricted to the ILM approximation and may also be found in lattice simulations.Comment: 14 pages, 13 figure

Statistics of wave interactions in nonlinear disordered systems

We study the properties of mode-mode interactions for waves propagating in nonlinear disordered one-dimensional systems. We focus on i) the localization volume of a mode which defines the number of interacting partner modes, ii) the overlap integrals which determine the interaction strength, iii) the average spacing between eigenvalues of interacting modes, which sets a scale for the nonlinearity strength, and iv) resonance probabilities of interacting modes. Our results are discussed in the light of recent studies on spreading of wave packets in disordered nonlinear systems, and are related to the quantum many body problem in a random chain.Comment: 7 pages, 7 figure

Magnetic-field-driven localization of light in a cold-atom gas

We discover a transition from extended to localized quasi-modes for light in a gas of immobile two-level atoms in a magnetic field. The transition takes place either upon increasing the number density of atoms in a strong field or upon increasing the field at a high enough density. It has many characteristic features of a disorder-driven (Anderson) transition but is strongly influenced by near-field interactions between atoms and the anisotropy of the atomic medium induced by the magnetic field.Comment: 5+8 pages, 4+8 figures, supplemental material adde

Partitioning of the molecular density matrix over atoms and bonds

A double-index atomic partitioning of the molecular first-order density matrix is proposed. Contributions diagonal in the atomic indices correspond to atomic density matrices, whereas off-diagonal contributions carry information about the bonds. The resulting matrices have good localization properties, in contrast to single-index atomic partitioning schemes of the molecular density matrix. It is shown that the electron density assigned to individual atoms, when derived from the density matrix partitioning, can be made con- sistent with well-known partitions of the electron density over AIM basins, either with sharp or with fuzzy boundaries. The method is applied to a test set of about 50 molecules, representative for various types of chemical binding. A close correlation is observed between the trace of the bond matrices and the SEDI (shared electron density index) bond index.Comment: 25 pages, 8 figures, preprin