The conduction current for an ion channel, in a quantum model, is derived. For some particular ion concentrations, the channel is a quasi 1D or a 1D system. We assumed that the ion channel is 1D and we calculated the density of states and the current. If the number of different vacant states is much larger than the number of ions, the ensemble is described by Maxwell-Boltzmann statistics. When the number of states is of same order of magnitude as the number of particles, the ensemble is degenerate and must be described with the quantum statistics. The effect of a barrier on the ions is presented in the last section.
Mariana Latu, Mariana Latu,
"Nanostructure of ion channels", Proc. SPIE 7297, Advanced Topics in Optoelectronics, Microelectronics, and Nanotechnologies IV, 72971Q (7 January 2009); doi: 10.1117/12.823673; https://doi.org/10.1117/12.823673