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Error Analysis of Free Probability Approximations to the Density of States of Disordered Systems
Error Analysis Free Probability Approximations the Density of States Disordered Systems
2014/8/21
Theoretical studies of localization, anomalous diffusion and ergodicity breaking require solving the electronic structure of disordered systems. We use free probability to approximate the ensembleaver...
Local density of states of chiral Hall edge states in gyrotropic photonic clusters
Local density chiral Hall edge states gyrotropic photonic clusters
2015/8/7
We have constructed the Green’s tensor for two-dimensional gyrotropic photonic clusters and have calculated their optical local density of states (LDOS). For clusters that support the chiral Hall edge...
A Note on the Analyticity of Density of States
Analyticity of Density of States Mathematical Physics
2012/5/9
We consider the $d$-dimensional Anderson model, and we prove the density of states is locally analytic if the single site potential distribution is locally analytic and the disorder is large. We emplo...
Error analysis of free probability approximations to the density of states of disordered systems
Massachusetts Institute of Technology
2012/2/29
Theoretical studies of localization, anomalous diffusion and ergodicity breaking require solving the electronic structure of disordered systems. We use free probability to approximate the ensemble- av...
Efficient computation of equifrequency surfaces and density of states in photonic crystals using Dirichlet-to-Neumann maps
Efficient computation equifrequency surfaces photonic crystals Dirichlet-to-Neumann maps
2015/8/10
We present an efficient method for computing the equifrequency surfaces (EFSs) and density of states of a photonic crystal. The method is based on repeatedly solving a small nonlinear eigenvalue probl...
Uniform existence of the integrated density of states on metric Cayley graphs
random Schrodinger operator metric graph quantum graph integrated density of states
2011/7/27
Abstract: Given a finitely generated amenable group we consider ergodic random Schr\"odinger operators on a Cayley graph with random potentials and random boundary conditions. We show that the normali...
Classical and quantum behavior of the integrated density of states for a randomly perturbed lattice
Classical quantum behavior integrated density of states randomly perturbed lattice
2011/1/20
The asymptotic behavior of the integrated density of states for a randomly perturbed lattice at the infimum of the spectrum is investigated. The leading term is determined when the decay of the single...
Vacuum stability, string density of states and the Riemann zeta function
Vacuum stability string density of states Riemann zeta function
2011/3/3
We study the distribution of graded degrees of freedom in classically stable oriented closed string vacua and use the Rankin-Selberg transform to link it to the nite one-loop vacuum energy.
Lipschitz-continuity of the integrated density of states for Gaussian random potentials
Lipschitz-continuity integrated density states for Gaussian random potentials
2011/1/17
The integrated density of states of a Schr¨odinger operator with random potential given by a homogeneous Gaussian field whose covariance function is continuous, compactly supported and has positive me...
A Dispersion Relation for the Density of States With Application to the Casimir Effect
Dispersion Relation the Density of States the Casimir Effect
2010/12/27
The trace of a function of a Schrodinger operator minus the same for the Laplacian can be expressed in terms of the determinant of its scattering matrix. The naive formula for this determinant is dive...
Uniform approximation of the integrated density of states for long-range percolation Hamiltonians
the integrated density of states long-range percolation Hamiltonians
2010/11/23
In this paper we study the spectrum of long-range percolation graphs. The underlying geometry is given in terms of a finitely generated amenable group. We prove that the integrated density of states (...
Density of states in random lattices with translational invariance
Density of states random lattices with translational invariance
2010/11/22
We propose a random matrix approach to describe vibrational excitations in disordered systems.
The dynamical matrix M is taken in the form M = AAT where A is some real (not generally
symmetric) rand...
Surface density of states and topological edge states in non-centrosymmetric superconductors
Surface density of states topological edge states non-centrosymmetric superconductors
2010/11/19
We study Andreev bound state (ABS) and surface density of state (SDOS) of non-centrosymmetric
superconductor where spin-singlet d-wave pairing mixes with spin-triplet p (or f)-wave one by spinorbit c...
Density of states of a graphene in the presence of strong point defects
graphene strong point defects
2010/11/19
The density of states near zero energy in a graphene due to strong point defects with random
positions are computed. Instead of focusing on density of states directly, we analyze eigenfunctions of in...
Computational Difficulty of Computing the Density of States
Computational Computing the Density of States
2010/11/5
We study the computational difficulty of computing the ground state degeneracy and the density of states for local Hamiltonians. We show that the difficulty of both problems is exactly captured by a c...