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The vertex arrangement of the 16-cell honeycomb is called the D 4 lattice or F 4 lattice. [2] The vertices of this lattice are the centers of the 3-spheres in the densest known packing of equal spheres in 4-space; [3] its kissing number is 24, which is also the same as the kissing number in R 4, as proved by Oleg Musin in 2003.
The Toda lattice, introduced by Morikazu Toda , is a simple model for a one-dimensional crystal in solid state physics. It is famous because it is one of the earliest examples of a non-linear completely integrable system. It is given by a chain of particles with nearest neighbor interaction, described by the Hamiltonian
When talking about solid materials, the discussion is mainly around crystals – periodic lattices. Here we will discuss a 1D lattice of positive ions. 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.
The Aubry–André model is a toy model of a one-dimensional crystal with periodically varying onsite energies. The model is employed to study both quasicrystals and the Anderson localization metal-insulator transition in disordered systems.
The Ising model is given by the usual cubic lattice graph = (,) where is an infinite cubic lattice in or a period cubic lattice in , and is the edge set of nearest neighbours (the same letter is used for the energy functional but the different usages are distinguishable based on context).
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.
A 1D optical lattice is formed by two counter-propagating laser beams of the same polarization. The beams will interfere, leading to a series of minima and maxima separated by λ / 2 {\displaystyle \lambda /2} , where λ {\displaystyle \lambda } is the wavelength of the light used to create the optical lattice.
One-dimensional lattices may be studied using density matrix renormalization group (DMRG) and related techniques such as time-evolving block decimation (TEBD). This includes calculating the ground state of the Hamiltonian for systems of thousands of particles on thousands of lattice sites, and simulating its dynamics governed by the time ...