A Random Necklace Model

Abstract

We consider a Laplace operator on a random graph consisting of infinitely many loops joined symmetrically by intervals of unit length. The arc lengths of the loops are considered to be independent, identically distributed random variables. The integrated density of states of this Laplace operator is shown to have discontinuities provided that the distribution of arc lengths of the loops has a nontrivial pure point part. Some numerical illustrations are also presented.

5 figures

References in corpus (5)

• Kirchhoff's Rule for Quantum Wires
• The Generalized Star Product and the Factorization of Scattering Matrices on Graphs
• Quantum wires with magnetic fluxes
• Scattering Theory Approach to Random Schroedinger Operators in One Dimension
• Global Bounds for the Lyapunov Exponent and the Integrated Density of States of Random Schrödinger Operators in One Dimension

Cited by in corpus (13)

• Quantum Graphs: Applications to Quantum Chaos and Universal Spectral Statistics
• Absolutely Continuous Spectra of Quantum Tree Graphs with Weak Disorder
• Spectral Analysis of Percolation Hamiltonians
• The edge switch transformation in microwave networks
• Continuity of the integrated density of states on random length metric graphs
• Continuity properties of the integrated density of states on manifolds
• Localization on quantum graphs with random edge lengths
• Localization on quantum graphs with random vertex couplings
• Anderson Localization for radial tree-like random quantum graphs
• Uniform existence of the integrated density of states for combinatorial and metric graphs over Z^d
• Optimal Wegner estimates for random Schroedinger operators on metric graphs
• Families of isospectral and isoscattering quantum graphs
• Slowing down and reflection of waves in truncated periodic media