1,304 research outputs found
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 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
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
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
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
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
Electron Impact Ionization Close to the Threshold: Classical Calculations
In this paper we present Classical Trajectory Monte Carlo (CTMC) calculations
for single and multiple electron ionization of Argon atoms and ions in the
threshold region. We are able to recover the Wannier exponents a for the
power-law behavior of the cross section s versus excess energy: the exact value
of the exponent as well as the existence of its saturation for multiple
ionization appear to be related to how the total binding energy is shared
between target electrons.Comment: 9 pages. To be published in Journal of Physics
Equivalent Fixed-Points in the Effective Average Action Formalism
Starting from a modified version of Polchinski's equation, Morris'
fixed-point equation for the effective average action is derived. Since an
expression for the line of equivalent fixed-points associated with every
critical fixed-point is known in the former case, this link allows us to find,
for the first time, the analogous expression in the latter case.Comment: 30 pages; v2: 29 pages - major improvements to section 3; v3:
published in J. Phys. A - minor change
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