Search results
Results from the WOW.Com Content Network
Assuming the spacing between two ions is a, the potential in the lattice will look something like this: The mathematical representation of the potential is a periodic function with a period a. According to Bloch's theorem, [1] the wavefunction solution of the Schrödinger equation when the potential is periodic, can be written as:
Transfer-matrix methods have been critical for many exact solutions of problems in statistical mechanics, including the Zimm–Bragg and Lifson–Roig models of the helix-coil transition, transfer matrix models for protein-DNA binding, as well as the famous exact solution of the two-dimensional Ising model by Lars Onsager.
A three-dimensional lattice filled with two molecules A and B, here shown as black and white spheres. Lattices such as this are used - for example - in the Flory–Huggins solution theory In mathematical physics , a lattice model is a mathematical model of a physical system that is defined on a lattice , as opposed to a continuum , such as the ...
This models a one-dimensional lattice of fixed particles with spin 1/2. A simple version (the antiferromagnetic XXX model) was solved, that is, the spectrum of the Hamiltonian of the Heisenberg model was determined, by Hans Bethe using the Bethe ansatz . [ 2 ]
In physics, the Bethe ansatz is an ansatz for finding the exact wavefunctions of certain quantum many-body models, most commonly for one-dimensional lattice models.It was first used by Hans Bethe in 1931 to find the exact eigenvalues and eigenvectors of the one-dimensional antiferromagnetic isotropic (XXX) Heisenberg model.
However, to date, no three-dimensional (3D) problem has had a solution that is both complete and exact. [4] Over the last ten years, Aranovich and Donohue have developed lattice density functional theory (LDFT) based on a generalization of the Ono-Kondo equations to three-dimensions, and used the theory to model a variety of physical phenomena.
A lattice in the sense of a 3-dimensional array of regularly spaced points coinciding with e.g. the atom or molecule positions in a crystal, or more generally, the orbit of a group action under translational symmetry, is a translation of the translation lattice: a coset, which need not contain the origin, and therefore need not be a lattice in ...
In condensed matter physics, the Su–Schrieffer–Heeger (SSH) model or SSH chain is a one-dimensional lattice model that presents topological features. [1] It was devised by Wu-Pei Su, John Robert Schrieffer, and Alan J. Heeger in 1979, to describe the increase of electrical conductivity of polyacetylene polymer chain when doped, based on the existence of solitonic defects.