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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...
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...
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 (...
The Integrated Density of States for the Wilson Dirac Operator
Integrated Density of States Wilson Dirac Operator
2010/12/3
It is shown that gauge field-dependent fermion Dirac operators from lattice QCD form an ergodic operator family in the probabilistic sense, provided the gauge field is an ergodic random field. As a co...
The Integrated Density of States for an Interacting Multiparticle Homogeneous Model and Applications to the Anderson Model
Multiparticle Homogeneous Model interacting quantum particles
2009/9/4
For a system of n interacting particles moving in the background of a “homogeneous” potential, we show that if the single particle Hamiltonian admits a density of states, so does the interacting n-par...