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The Bose-Hubbard model gives an approximate description of the physics of interacting bosons on a lattice. It is closely related to the Hubbard model which originated in solid state physics as an approximate description of the motion of electrons between the atoms of a crystalline solid. However, the Hubbard model applies to fermionic particles such as electrons, rather than bosons. The Bose-Hubbard model can be used to study systems such as bosonic atoms on an optical lattice.
The physics of this model is given by the Bose-Hubbard Hamiltonian:
Additional recommended knowledge
Here is summed over all lattice sites, and is summed over all neighboring sites. and are bosonic creation and annihilation operators. gives the number of particles on site . is the hopping matrix element, is the on site repulsion, and is the chemical potential.
|This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Bose-Hubbard_model". A list of authors is available in Wikipedia.|