An Exact Approach to the Diluted Hubbard Model

1992 ◽  
Vol 291 ◽  
Author(s):  
Chumin Wang ◽  
O. Navarro ◽  
R. Oviedo-Roa
Keyword(s):  
Dimensional Space ◽  
Tight Binding ◽  
Real Space ◽  
Many Body ◽  
Electron Pairs ◽  
Hubbard Hamiltonian ◽  
Exact Approach ◽  
Higher Dimensional ◽  
Three Body ◽  
Body Correlation

ABSTRACTA new method to solve the extended Hubbard Hamiltonian for systems with few electrons is reported. This method is based on mapping the original many-body problem onto a tight-binding one in a higher dimensional space, which can be solved exactly. For one-and two-dimensional periodic lattices, the real-space pairing problem of two electrons with parallel and anti-parallel spins is analyzed by looking at the binding energy, the coherence length and the mobility of electron pairs. Likewise, some results of the three-body correlation are also reported.

Three-Body Correlation in the Diluted Generalized Hubbard Model

1997 ◽  
Vol 491 ◽  
Author(s):  
O. Navarro ◽  
M. Avignon
Keyword(s):  
Nearest Neighbor ◽  
Dimensional Space ◽  
Linear Chain ◽  
Tight Binding ◽  
Real Space ◽  
Many Body ◽  
Higher Dimensional ◽  
Generalized Hubbard Model ◽  
Three Body ◽  
Body Correlation

ABSTRACTA real-space method has been used to solve the generalized Hubbard Hamiltonian for a system with few electrons. The method is based on mapping the correlated many-body problem onto an equivalent tight-binding one in a higher dimensional space. For a linear chain, we have obtained an exact solution of the problem of three non-parallel electrons. The three-body correlation are studied by examining the binding energy in the ground state, for different values of the hopping parameters and of the on-site (U) and nearest-neighbor (V) interactions.

Bond-Order Potentials for Molybdenum and Niobium: An Assessment of Their Quality

1998 ◽  
Vol 538 ◽  
Author(s):  
M. Mrovec ◽  
V. Vitek ◽  
D. Nguyen-Manh ◽  
D. G. Pettifor ◽  
L. G. Wang ◽  
...  
Keyword(s):  
Bond Order ◽  
Tight Binding ◽  
Direct Calculation ◽  
Real Space ◽  
Central Force ◽  
Full Potential ◽  
Extended Defects ◽  
Many Body ◽  
Deformation Path ◽  
Bond Order Potentials

AbstractThe bond-order potentials (BOP) have been constructed for Mo and Nb. These potentials are based on the real-space parametrized tight-binding method in which diagonalization of the Hamiltonian is avoided by direct calculation of the bond-order. In this scheme the energy consists of three parts: The bond part that comprises contributions of d electrons and introduces into the scheme the covalent character of bonding, the central-force many-body part that reflects the environmental dependence of sp overlap repulsion and a pair-wise contribution. The potentials were tested by calculation of energy differences between the bcc and several alternate structures and by investigating the trigonal deformation path. These calculations have been made in parallel using BOP and the full-potential linearized augmented plane-wave method. The central-force many-body Finnis-Sinclair type potentials have also been included into the study of the deformation path. This evaluation of BOP reveals that the potentials reproduce very closely the ab initio results and are, therefore, very suitable for atomistic studies of extended defects in the transition metals.

Lone Pair Interactions in Zintl Phases and Intermetallic Compounds: Influence on Electronic Properties in Stannides and Plumbides

1998 ◽  
Vol 547 ◽  
Author(s):  
Thomas F. Fässler
Keyword(s):  
Intermetallic Compounds ◽  
Chemical Bond ◽  
Tight Binding ◽  
Lone Pair ◽  
Real Space ◽  
Localized States ◽  
Zintl Phases ◽  
Electron Pairs ◽  
Lone Pairs ◽  
Lone Pair Interactions

AbstractThe phases K6Sn23Bi2, K6Sn25, NaSn5, BaSn3, BaSn5, and K5Pb24 depict the structural transition from Zintl phases with localized chemical bonds to typical intermetallic compounds which may even have superconducting properties. The question of the nature of the chemical bond in these compounds is studied with the help of quantum mechanical calculations. Tight binding band structure calculations and real space representations using the Electron Localization Function (ELF) show that free electron pairs play a crucial role for the description of the chemical bond in polar intermetallic compounds. Interactions between lone pairs have a dominant influence on the electronic structures. The coincident appearance of quasi-molecular localized states in form of lone pairs and disperse delocalized bands at the Fermi level EF is discussed with respect to a ‘chemical view’ of the superconductivity observed for BaSn3, BaSn5, and K5Pb24.

REPRESENTATION OF THE PAIRED INTERACTION POTENTIAL IN THE FORM OF MULTIDIMENSIONAL RATIONAL SERIES IN JACOBI VARIABLES FOR MANY-BODY PROBLEMS

2021 ◽  
Vol 0 (4) ◽  
pp. 9-15
Author(s):  
R.F. AKHMETYANOV ◽  
◽  
E.S. SHIKHOVTSEVA ◽  
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Many Body ◽  
Power Functions ◽  
Spatial Variables ◽  
Physical Problems ◽  
Rational Series ◽  
T Matrix ◽  
Three Body ◽  
Three Dimensional Space

Scalar power functions of the form x1 + + xN -v Î are in some cases found in physical problems and applications, especially in many-body problems with paired interactions. There are known decompositions for two vectors in three-dimensional space. In this paper, we consider analogous decompositions with any number of N arbitrary M-dimensional vectors in Euclidean space as a product of a multidimensional rational series with respect to spatial variables and hyperspheric functions on the unit sphere SM-1. Such an advantage of expansion arises in three-body problems when solving the Faddeev equation, where it is known that the main problem is the approximate choice of approximation of interaction potentials, in which the t-matrix scattering elements acquired a separable form.

Celestial Tapestry

2020 ◽  
Author(s):  
Nicholas Mee
Keyword(s):  
Mathematics Curriculum ◽  
Dimensional Space ◽  
Golden Section ◽  
Single Point ◽  
Historical Context ◽  
Computer Art ◽  
Lightning Strike ◽  
Secret Message ◽  
Axiomatic Method ◽  
Higher Dimensional

Celestial Tapestry places mathematics within a vibrant cultural and historical context, highlighting links to the visual arts and design, and broader areas of artistic creativity. Threads are woven together telling of surprising influences that have passed between the arts and mathematics. The story involves many intriguing characters: Gaston Julia, who laid the foundations for fractals and computer art while recovering in hospital after suffering serious injury in the First World War; Charles Howard, Hinton who was imprisoned for bigamy but whose books had a huge influence on twentieth-century art; Michael Scott, the Scottish necromancer who was the dedicatee of Fibonacci’s Book of Calculation, the most important medieval book of mathematics; Richard of Wallingford, the pioneer clockmaker who suffered from leprosy and who never recovered from a lightning strike on his bedchamber; Alicia Stott Boole, the Victorian housewife who amazed mathematicians with her intuition for higher-dimensional space. The book includes more than 200 colour illustrations, puzzles to engage the reader, and many remarkable tales: the secret message in Hans Holbein’s The Ambassadors; the link between Viking runes, a Milanese banking dynasty, and modern sculpture; the connection between astrology, religion, and the Apocalypse; binary numbers and the I Ching. It also explains topics on the school mathematics curriculum: algorithms; arithmetic progressions; combinations and permutations; number sequences; the axiomatic method; geometrical proof; tessellations and polyhedra, as well as many essential topics for arts and humanities students: single-point perspective; fractals; computer art; the golden section; the higher-dimensional inspiration behind modern art.

scholarly journals Aperiodic Crystals

2014 ◽  
Vol 70 (a1) ◽  
pp. C1-C1 ◽  
Author(s):  
Ted Janssen ◽  
Aloysio Janner
Keyword(s):  
Physical Properties ◽  
Dimensional Space ◽  
X Rays ◽  
New Techniques ◽  
New Family ◽  
Modulated Phases ◽  
Open Questions ◽  
Higher Dimensional ◽  
Lattice Periodicity ◽  
Aperiodic Crystals

2014 is the International Year of Crystallography. During at least fifty years after the discovery of diffraction of X-rays by crystals, it was believed that crystals have lattice periodicity, and crystals were defined by this property. Now it has become clear that there is a large class of compounds with interesting properties that should be called crystals as well, but are not lattice periodic. A method has been developed to describe and analyze these aperiodic crystals, using a higher-dimensional space. In this lecture the discovery of aperiodic crystals and the development of the formalism of the so-called superspace will be described. There are several classes of such materials. After the incommensurate modulated phases, incommensurate magnetic crystals, incommensurate composites and quasicrystals were discovered. They could all be studied using the same technique. Their main properties of these classes and the ways to characterize them will be discussed. The new family of aperiodic crystals has led also to new physical properties, to new techniques in crystallography and to interesting mathematical questions. Much has been done in the last fifty years by hundreds of crystallographers, crystal growers, physicists, chemists, mineralogists and mathematicians. Many new insights have been obtained. But there are still many questions, also of fundamental nature, to be answered. We end with a discussion of these open questions.

scholarly journals Atomic-state-dependent screening model for hot and warm dense plasmas

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Fuyang Zhou ◽  
Yizhi Qu ◽  
Junwen Gao ◽  
Yulong Ma ◽  
Yong Wu ◽  
...  
Keyword(s):  
Radiation Transport ◽  
Atomic State ◽  
Many Body ◽  
Dense Plasmas ◽  
Screening Model ◽  
State Dependent ◽  
Recombination Processes ◽  
Three Body ◽  
Many Body Interactions ◽  
Body Recombination

AbstractAn ion embedded in warm/hot dense plasmas will greatly alter its microscopic structure and dynamics, as well as the macroscopic radiation transport properties of the plasmas, due to complicated many-body interactions with surrounding particles. Accurate theoretically modeling of such kind of quantum many-body interactions is essential but very challenging. In this work, we propose an atomic-state-dependent screening model for treating the plasmas with a wide range of temperatures and densities, in which the contributions of three-body recombination processes are included. We show that the electron distributions around an ion are strongly correlated with the ionic state studied due to the contributions of three-body recombination processes. The feasibility and validation of the proposed model are demonstrated by reproducing the experimental result of the line-shift of hot-dense plasmas as well as the classical molecular dynamic simulations of moderately coupled ultra-cold neutral plasmas. Our work opens a promising way to treat the screening effect of hot and warm dense plasma, which is a bottleneck of those extensive studies in high-energy-density physics, such as atomic processes in plasma, plasma spectra and radiation transport properties, among others.

Sign in / Sign up

Export Citation Format

Share Document