Unusual localisation effects in quantum percolation

We present a detailed study of the quantum site percolation problem on simple cubic lattices, thereby focussing on the statistics of the local density of states and the spatial structure of the single particle wavefunctions. Using the Kernel Polynomial Method we refine previous studies of the metal-insulator transition and demonstrate the non-monotonic energy dependence of the quantum percolation threshold. Remarkably, the data indicates a ``fragmentation'' of the spectrum into extended and localised states. In addition, the observation of a chequerboard-like structure of the wavefunctions at the band centre can be interpreted as anomalous localisation.Comment: 5 pages, 7 figure

The Link between General Relativity and Shape Dynamics

We show that one can construct two equivalent gauge theories from a linking theory and give a general construction principle for linking theories which we use to construct a linking theory that proves the equivalence of General Relativity and Shape Dynamics, a theory with fixed foliation but spatial conformal invariance. This streamlines the rather complicated construction of this equivalence performed previously. We use this streamlined argument to extend the result to General Relativity with asymptotically flat boundary conditions. The improved understanding of linking theories naturally leads to the Lagrangian formulation of Shape Dynamics, which allows us to partially relate the degrees of freedom.Comment: 19 pages, LaTeX, no figure

The electronic structure of amorphous silica: A numerical study

We present a computational study of the electronic properties of amorphous SiO2. The ionic configurations used are the ones generated by an earlier molecular dynamics simulations in which the system was cooled with different cooling rates from the liquid state to a glass, thus giving access to glass-like configurations with different degrees of disorder [Phys. Rev. B 54, 15808 (1996)]. The electronic structure is described by a tight-binding Hamiltonian. We study the influence of the degree of disorder on the density of states, the localization properties, the optical absorption, the nature of defects within the mobility gap, and on the fluctuations of the Madelung potential, where the disorder manifests itself most prominently. The experimentally observed mismatch between a photoconductivity threshold of 9 eV and the onset of the optical absorption around 7 eV is interpreted by the picture of eigenstates localized by potential energy fluctuations in a mobility gap of approximately 9 eV and a density of states that exhibits valence and conduction band tails which are, even in the absence of defects, deeply located within the former band gap.Comment: 21 pages of Latex, 5 eps figure

Preferred foliation effects in Quantum General Relativity

We investigate the infrared (IR) effects of Lorentz violating terms in the gravitational sector using functional renormalization group methods similar to Reuter and collaborators. The model we consider consists of pure quantum gravity coupled to a preferred foliation, described effectively via a scalar field with non-standard dynamics. We find that vanishing Lorentz violation is a UV attractive fixed-point of this model in the local potential approximation. Since larger truncations may lead to differing results, we study as a first example effects of additional matter fields on the RG running of the Lorentz violating term and provide a general argument why they are small.Comment: 12 pages, no figures, compatible with published versio

Three-Dimensional Quantum Percolation Studied by Level Statistics

Three-dimensional quantum percolation problems are studied by analyzing energy level statistics of electrons on maximally connected percolating clusters. The quantum percolation threshold \pq, which is larger than the classical percolation threshold \pc, becomes smaller when magnetic fields are applied, i.e., \pq(B=0)>\pq(B\ne 0)>\pc. The critical exponents are found to be consistent with the recently obtained values of the Anderson model, supporting the conjecture that the quantum percolation is classified onto the same universality classes of the Anderson transition. Novel critical level statistics at the percolation threshold is also reported.Comment: to appear in the May issue of J. Phys. Soc. Jp

Electronic Structure of Dangling Bonds in Amorphous Silicon Studied via a Density-Matrix Functional Method

A structural model of hydrogenated amorphous silicon containing an isolated dangling bond is used to investigate the effects of electron interactions on the electronic level splittings, localization of charge and spin, and fluctuations in charge and spin. These properties are calculated with a recently developed density-matrix correlation-energy functional applied to a generalized Anderson Hamiltonian, consisting of tight-binding one-electron terms parametrizing hydrogenated amorphous silicon plus a local interaction term. The energy level splittings approach an asymptotic value for large values of the electron-interaction parameter U, and for physically relevant values of U are in the range 0.3-0.5 eV. The electron spin is highly localized on the central orbital of the dangling bond while the charge is spread over a larger region surrounding the dangling bond site. These results are consistent with known experimental data and previous density-functional calculations. The spin fluctuations are quite different from those obtained with unrestricted Hartree-Fock theory.Comment: 6 pages, 6 figures, 1 tabl

Properties of the Volume Operator in Loop Quantum Gravity I: Results

We analyze the spectral properties of the volume operator of Ashtekar and Lewandowski in Loop Quantum Gravity, which is the quantum analogue of the classical volume expression for regions in three dimensional Riemannian space. Our analysis considers for the first time generic graph vertices of valence greater than four. Here we find that the geometry of the underlying vertex characterizes the spectral properties of the volume operator, in particular the presence of a `volume gap' (a smallest non-zero eigenvalue in the spectrum) is found to depend on the vertex embedding. We compute the set of all non-spatially diffeomorphic non-coplanar vertex embeddings for vertices of valence 5--7, and argue that these sets can be used to label spatial diffeomorphism invariant states. We observe how gauge invariance connects vertex geometry and representation properties of the underlying gauge group in a natural way. Analytical results on the spectrum on 4-valent vertices are included, for which the presence of a volume gap is proved. This paper presents our main results; details are provided by a companion paper arXiv:0706.0382v1.Comment: 36 pages, 7 figures, LaTeX. See also companion paper arXiv:0706.0382v1. Version as published in CQG in 2008. See arXiv:1003.2348 for important remarks regarding the sigma configurations. Subsequent computations have revealed some minor errors, which do not change the qualitative results but modify some of the numbers presented her

Gauge invariant perturbations around symmetry reduced sectors of general relativity: applications to cosmology

We develop a gauge invariant canonical perturbation scheme for perturbations around symmetry reduced sectors in generally covariant theories, such as general relativity. The central objects of investigation are gauge invariant observables which encode the dynamics of the system. We apply this scheme to perturbations around a homogeneous and isotropic sector (cosmology) of general relativity. The background variables of this homogeneous and isotropic sector are treated fully dynamically which allows us to approximate the observables to arbitrary high order in a self--consistent and fully gauge invariant manner. Methods to compute these observables are given. The question of backreaction effects of inhomogeneities onto a homogeneous and isotropic background can be addressed in this framework. We illustrate the latter by considering homogeneous but anisotropic Bianchi--I cosmologies as perturbations around a homogeneous and isotropic sector.Comment: 39 pages, 1 figur

Towards new background independent representations for Loop Quantum Gravity

Recently, uniqueness theorems were constructed for the representation used in Loop Quantum Gravity. We explore the existence of alternate representations by weakening the assumptions of the so called LOST uniqueness theorem. The weakened assumptions seem physically reasonable and retain the key requirement of explicit background independence. For simplicity, we restrict attention to the case of gauge group U(1).Comment: 22 pages, minor change