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In quantum mechanics, the particle in a one-dimensional lattice is a problem that occurs in the model of a periodic crystal lattice. The potential is caused by ions in the periodic structure of the crystal creating an electromagnetic field so electrons are subject to a regular potential inside the lattice.
In computer science, lattice problems are a class of optimization problems related to mathematical objects called lattices.The conjectured intractability of such problems is central to the construction of secure lattice-based cryptosystems: lattice problems are an example of NP-hard problems which have been shown to be average-case hard, providing a test case for the security of cryptographic ...
In a one-dimensional lattice the number of reciprocal lattice vectors that determine the bands in an energy interval is limited to two when the energy rises. In two and three dimensional lattices the number of reciprocal lattice vectors that determine the free electron bands E n ( k ) {\displaystyle E_{n}(\mathbf {k} )} increases more rapidly ...
Gold deposited on a stepped Si(553) surface has shown evidence of two simultaneous Peierls transitions. The lattice period is distorted by factors of 2 and 3, and energy gaps open for nearly 1/2-filled and 1/3–1/4 filled bands. The distortions have been studied and imaged using LEED and STM, while the energy bands were studied with ARP. [9]
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.
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 ...
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.
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.