Thermodynamic Equivalent between Noninteracting Bose and Fermi Gas in Metallic Carbon Nanotubes

Abstract

The equivalent between Bose and Fermi ideal gases is usually taken in high temperature limit only. Recently, there has been considerable interest in surprising thermodynamic ``equivalences'' between certain ideal Bose and spineless Fermi gas systems in lower temperature. In this work, we follow that idea to investigate the quasi one-dimensional system of metallic carbon nanotubes. Due to the linear dispersion law, the non-interacting Bose and Fermi gases in metallic carbon nanotubes are equivalent. This equivalence could be applied to the gas systems of exciton photon (Bose particles) and electron hole (Fermi particles) in metallic carbon nanotubes.