Symmetry breaking in the self-consistent Kohn-Sham equations

The Kohn-Sham (KS) equations determine, in a self-consistent way, the particle density of an interacting fermion system at thermal equilibrium. We consider a situation when the KS equations are known to have a unique solution at high temperatures and this solution is a uniform particle density. We show that, at zero temperature, there are stable solutions that are not uniform. We provide the general principles behind this phenomenon, namely the conditions when it can be observed and how to construct these non-uniform solutions. Two concrete examples are provided, including fermions on the sphere which are shown to crystallize in a structure that resembles the C$_{60}$ molecule.Comment: a few typos eliminate

Validation of Two Distributed, Autonomous Self-Organisation Algorithms for 802.11 Mesh Networks by Simulation

Two algorithms in a "self-organisation of multi-radio mesh networks" project are described and validated by simulation. As they are to be deployed over large networks the two challenges have been the scalability and stability of the solution. The basic approach is that of a distributed, light-weight, cooperative multiagent system that guarantees scalability. As the solution is distributed it is unsuitable to achieve any global optimisation goal --- in any case, we argue that global optimisation of mesh network performance in any significant sense is not feasible in real situations that are subjected to unanticipated perturbations and external intervention. Our overall goal is simply to reduce maintenance costs for such networks by removing the need for humans to tune the network settings. So stability of the algorithms is our main concern

An edge index for the Quantum Spin-Hall effect

Quantum Spin-Hall systems are topological insulators displaying dissipationless spin currents flowing at the edges of the samples. In contradistinction to the Quantum Hall systems where the charge conductance of the edge modes is quantized, the spin conductance is not and it remained an open problem to find the observable whose edge current is quantized. In this paper, we define a particular observable and the edge current corresponding to this observable. We show that this current is quantized and that the quantization is given by the index of a certain Fredholm operator. This provides a new topological invariant that is shown to take same values as the Spin-Chern number previously introduced in the literature. The result gives an effective tool for the investigation of the edge channels' structure in Quantum Spin-Hall systems. Based on a reasonable assumption, we also show that the edge conducting channels are not destroyed by a random edge.Comment: 4 pages, 3 figure

Performance Evaluation of a Self-Organising Scheme for Multi-Radio Wireless Mesh Networks

Multi-Radio Wireless Mesh Networks (MR-WMN) can substantially increase the aggregate capacity of the Wireless Mesh Networks (WMN) if the channels are assigned to the nodes in an intelligent way so that the overall interference is limited. We propose a generic self-organisation algorithm that addresses the two key challenges of scalability and stability in a WMN. The basic approach is that of a distributed, light-weight, co-operative multiagent system that guarantees scalability. The usefulness of our algorithm is exhibited by the performance evaluation results that are presented for different MR-WMN node densities and typical topologies. In addition, our work complements the Task Group 802.11s Extended Service Set (ESS) Mesh networking project work that is in progress