Title




Electronic states in ordered and disordered quantum networks: with applications to graphene and to boron nanotubes


Author






Abstract




The idea behind the original quantum network (QN) model is simple enough. One joins each atom to its nearest neighbours, and then treats electrons (though quantum mechanically of course) as though they flowed through onedimensional wires as in an electrical circuit obeying Kirchhoffs Laws at every node. Here we will begin with two periodic systems: namely a single graphene layer, which has recently been produced experimentally, and a twodimensional sheet of boron atoms. This will be followed by a discussion of B nanotubes, using the simplest QN model, supplemented by comparison of these results with very recent work of other authors using density functional theory. Then the disordered quantum network (DQN) model will be treated in some detail. First of all, the main, physically motivated, steps by which Dancz, Edwards and March passed from the DQN model to the Boltzmann equation will be set out. They will then be related to substantial progress made on the mathematical solution of the DQN model by a number of authors; again a substantial part of this work invoking the Boltzmann equation. 


Language




English


Source (journal)




Journal of mathematical chemistry.  Basel


Publication




Basel
:
2009


ISSN




02599791


DOI




10.1007/S1091000894771


Volume/pages




46
:2
(2009)
, p. 532549


ISI




000266926000015


Full text (Publisher's DOI)





