Lattice In Three-dimensional Space Research Articles

Chiral dynamics in soft triaxial nuclei

The chirality in soft triaxial nuclei is investigated for the first time with the time-dependent and tilted axis cranking covariant density functional theories on a three-dimensional space lattice in a microscopic and self-consistent way. Taking the puzzling chiral nucleus 106Ag as an example, the experimental energies of the observed nearly degenerate bands are well reproduced without any free parameters beyond the well-defined density functional. A novel chiral mode in soft triaxial nuclei is newly revealed from the microscopic dynamics of the total angular momentum. This opens a new research area for the study of chirality, particularly in relation to soft nuclear shapes.

Dynamics of rotation in chiral nuclei

The dynamics of chiral nuclei is investigated for the first time with the time-dependent and tilted axis cranking covariant density functional theories on a three-dimensional space lattice in a microscopic and self-consistent way. The experimental energies of the two pairs of the chiral doublet bands in $^{135}$Nd are well reproduced without any adjustable parameters beyond the well-defined density functional. A novel mechanism, i.e., chiral precession, is revealed from the microscopic dynamics of the total angular momentum in the body-fixed frame, whose harmonicity is associated with a transition from the planar into aplanar rotations with the increasing spin. This provides a fully microscopic and dynamical view to understand the chiral excitations in nuclei.

Internal sums in full-potential multiple-scattering theory.

Full-potential multiple-scattering theory for electrons can be derived from the variational principle of Kohn and Rostoker. The resulting equations differ from the standard Korringa-Kohn-Rostoker (KKR) formalism by a matrix multiplication, which introduces an intermediate sum that should in principle be carried out to completion. This implies that the usual site-diagonal square matrices S and C of KKR theory must be represented as rectangular matrices. In the limit of completeness of this internal sum, the resulting product of matrices can be represented in closed form as a Wronskian integral extended over the common interfaces of adjacent space-filling cells, as used in the variational cellular method (VCM), based on the variational principle of Schlosser and Marcus. The standard KKR method can be extended in two ways, either by direct use of rectangular matrices, or by using the VCM surface integral as a closure correction in the energy-linearized atomic-cell orbital method. Test calculations on an empty-lattice model (fcc three-dimensional space lattice) demonstrate the viability of these extensions.

Euclidean gauge fields in four dimensions from stochastic differential equations

Using a stochastic differential equation for field configurations in a three-dimensional space lattice, one proves existence of a euclidean theory for non-abelian gauge fields on the lattice. The theory is also shown to possess a scaling limit for the mass gap at weak coupling. The construction is extended in a less rigorous manner to a theory with fermions and gauge fields.

Stochastic models for lattice gauge theories

Stochastic equations are derived which describe the (Euclidean) time evolution of lattice field configurations, with and without fermions, on a three-dimensional space lattice. It is indicated how the drifts and transition functions may be obtained as asymptotic solutions of a differential equation or from a ground state ansatz. For non-Abelian gauge fields (without fermions) a ground state is constructed which is an exact eigenstate of a Hamiltonian with the same (naive) continuum limit as the Kogut-Susskind Hamiltonian. It is described how Euclidean correlations (like the Wilson loop) are obtained from the stochastic equations and how mass gaps may be obtained from the technique of exit times.

Negative hopping photoconductivity in lattice models

In the present paper a consistent theory of absolute negative photoconductivity discovered recently in concentrated ruby crystals is proposed for the model where two-level centres form a periodic lattice in three-dimensional space. An explicit expression for the current is obtained by the density matrix method and its frequency dependence is analysed. The conditions for realisation of the effect are considered depending on the degree of compensation of the dielectric. Some peculiarities of the effect are analysed on the basis of an exactly solved one-dimensional model at an arbitrarily long excited electron lifetime.

Numerical predictions from a stochastic model for SU(2) lattice gauge fields

The (euclidean) dynamics of SU(2) lattice gauge fields is described by the time evolution of a three-dimensional space lattice ruled by a stochastic differential equation. In the framework of this model the string tension is obtained by the time correlation of two string operators and the mass gap by the technique of exit times of the stochastic process from a bounded domain. The results are consistent with a scaling behaviour above 1/ g 2 ≅ 1.6.

Three-dimensional analytical periodic solutions of the Laplace equation

A method is proposed, by which three-dimensional periodic analytical solutions of the Laplace equation can be found. The solutions obtained describe the electrostatic potential in a three-dimensional space lattice of point charges with a certain symmetry.

Covering space by spheres

Let Λ be a lattice in three-dimensional space with the property that the spheres of radius 1 centred at the points of Λ cover the whole of space. In other words, every point of space is at a distance not more than 1 from some point of Λ. It was proved by Bambah that thenequality occurring if and only if Λ is a body-centred cubic lattice with the side of the cube equal to 4/√5. Another way of stating the result is to say that the least density of covering of three-dimensional space by equal spheres, subject to the condition that the centres of the spheres form a lattice, is . Another proof of Bambah's result was given recently by Barnes. Both proofs depend on the theory of reduction of ternary quadratic forms.