832 research outputs found
Nearsightedness of Electronic Matter
In an earlier paper, W. Kohn had qualitatively introduced the concept of
"nearsightedness" of electrons in many-atom systems. It can be viewed as
underlying such important ideas as Pauling's "chemical bond," "transferability"
and Yang's computational principle of "divide and conquer." It describes the
fact that, for fixed chemical potential, local electronic properties, like the
density , depend significantly on the effective external potential only
at nearby points. Changes of that potential, {\it no matter how large}, beyond
a distance have {\it limited} effects on local electronic
properties, which rapidly tend to zero as function of . In the
present paper, the concept is first sharpened for representative models of
uncharged fermions moving in external potentials, followed by a discussion of
the effects of electron-electron interactions and of perturbing external
charges.Comment: final for
Nearsightedness of Electronic Matter in One Dimension
The concept of nearsightedeness of electronic matter (NEM) was introduced by
W. Kohn in 1996 as the physical principal underlining Yang's electronic
structure alghoritm of divide and conquer. It describes the fact that, for
fixed chemical potential, local electronic properties at a point , like the
density , depend significantly on the external potential only at
nearby points. Changes of that potential, {\it no matter how large},
beyond a distance , have {\it limited} effects on local electronic
properties, which tend to zero as function of . This remains true
even if the changes in the external potential completely surrounds the point
. NEM can be quantitatively characterized by the nearsightedness range,
, defined as the smallest distance from ,
beyond which {\it any} change of the external potential produces a density
change, at , smaller than a given . The present paper gives a
detailed analysis of NEM for periodic metals and insulators in 1D and includes
sharp, explicit estimates of the nearsightedness range. Since NEM involves
arbitrary changes of the external potential, strong, even qualitative changes
can occur in the system, such as the discretization of energy bands or the
complete filling of the insulating gap of an insulator with continuum spectrum.
In spite of such drastic changes, we show that has only a limited
effect on the density, which can be quantified in terms of simple parameters of
the unperturbed system.Comment: 10 pages, 9 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
Unique Solutions to Hartree-Fock Equations for Closed Shell Atoms
In this paper we study the problem of uniqueness of solutions to the Hartree
and Hartree-Fock equations of atoms. We show, for example, that the
Hartree-Fock ground state of a closed shell atom is unique provided the atomic
number is sufficiently large compared to the number of electrons. More
specifically, a two-electron atom with atomic number has a unique
Hartree-Fock ground state given by two orbitals with opposite spins and
identical spatial wave functions. This statement is wrong for some , which
exhibits a phase segregation.Comment: 18 page
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