It has been found that a model of extended electrons is more suited to describe theoretical simula- tions and experimental results obtained via scanning tunnelling microscopes, but while the dynamic properties are eas...It has been found that a model of extended electrons is more suited to describe theoretical simula- tions and experimental results obtained via scanning tunnelling microscopes, but while the dynamic properties are easily incorporated, magnetic properties, and in particular electron spin properties pose a problem due to their conceived isotropy in the absence of measurement. The spin of an electron reacts with a magnetic field and thus has the properties of a vector. However, electron spin is also isotropic, suggesting that it does not have the properties of a vector. This central conflict in the de- scription of an electron＇s spin, we believe, is the root of many of the paradoxical properties measured and postulated for quantum spin particles. Exploiting a model in which the electron spin is described consistently in real three-dimensional space - an extended electron model - we demonstrate that spin may be described by a vector and still maintain its isotropy. In this framework, we re-evaluate the Stern-Gerlach experiments, the Einstein-Podolsky-Rosen experiments, and the effect of consecutive ts and find in all cases a fairly intuitive explanation.展开更多
An extended electron model fully recovers many of the experimental results of quantum mechanics while it avoids many of the pitfalls and remains generally free of paradoxes. The formulation of the manybody electronic ...An extended electron model fully recovers many of the experimental results of quantum mechanics while it avoids many of the pitfalls and remains generally free of paradoxes. The formulation of the manybody electronic problem here resembles the Kohn Sham formulation of standard density functional theory. However, rather than referring electronic properties to a large set of single electron orbitals, the extended electron model uses only mass density and field components, leading to a substantial increase in computational efficiency. To date, the Hohenberg-Kohn theorems have not been proved for a model of this type, nor has a universal energy functional been presented. In this paper, we address these problems and show that the Hohenberg Kohn theorems do also hold for a density model of this type. We then present a proof^of^concept practical implementation of this method and show that it reproduces the accuracy of more widely used methods on a test-set of small atomic systems, thus paving the way for the development of fast, efficient and accurate codes on this basis.展开更多
The exact form of the kinetic energy functional has remained elusive in orbital-free models of density functional theory(DFT).This has been the main stumbling block for the development of a general-purpose framework o...The exact form of the kinetic energy functional has remained elusive in orbital-free models of density functional theory(DFT).This has been the main stumbling block for the development of a general-purpose framework on this basis.Here,we show that on the basis of a two-density model,which represents many-electron systems by mass density and spin density components,we can derive the exact form of such a functional.The exact functional is shown to contain previously suggested functionals to some extent,with the notable exception of the Thomas-Fermi kinetic energy functional.展开更多
文摘It has been found that a model of extended electrons is more suited to describe theoretical simula- tions and experimental results obtained via scanning tunnelling microscopes, but while the dynamic properties are easily incorporated, magnetic properties, and in particular electron spin properties pose a problem due to their conceived isotropy in the absence of measurement. The spin of an electron reacts with a magnetic field and thus has the properties of a vector. However, electron spin is also isotropic, suggesting that it does not have the properties of a vector. This central conflict in the de- scription of an electron＇s spin, we believe, is the root of many of the paradoxical properties measured and postulated for quantum spin particles. Exploiting a model in which the electron spin is described consistently in real three-dimensional space - an extended electron model - we demonstrate that spin may be described by a vector and still maintain its isotropy. In this framework, we re-evaluate the Stern-Gerlach experiments, the Einstein-Podolsky-Rosen experiments, and the effect of consecutive ts and find in all cases a fairly intuitive explanation.
文摘An extended electron model fully recovers many of the experimental results of quantum mechanics while it avoids many of the pitfalls and remains generally free of paradoxes. The formulation of the manybody electronic problem here resembles the Kohn Sham formulation of standard density functional theory. However, rather than referring electronic properties to a large set of single electron orbitals, the extended electron model uses only mass density and field components, leading to a substantial increase in computational efficiency. To date, the Hohenberg-Kohn theorems have not been proved for a model of this type, nor has a universal energy functional been presented. In this paper, we address these problems and show that the Hohenberg Kohn theorems do also hold for a density model of this type. We then present a proof^of^concept practical implementation of this method and show that it reproduces the accuracy of more widely used methods on a test-set of small atomic systems, thus paving the way for the development of fast, efficient and accurate codes on this basis.
基金EPSRC funding for the UKCP consortium(Grant No.EP/K013610/1).
文摘The exact form of the kinetic energy functional has remained elusive in orbital-free models of density functional theory(DFT).This has been the main stumbling block for the development of a general-purpose framework on this basis.Here,we show that on the basis of a two-density model,which represents many-electron systems by mass density and spin density components,we can derive the exact form of such a functional.The exact functional is shown to contain previously suggested functionals to some extent,with the notable exception of the Thomas-Fermi kinetic energy functional.
