The conductivity of the one-dimensional disordered Anderson model: a new numerical method

A new numerical method is presented, which allows for the calculation of the conductivity and the localisation properties of the eigenstates in a one-dimensional disordered system described by the Anderson Hamiltonian. The computer storage requirements of the procedure are independent of the length of the system, the maximum system length treatable being only limited by the computer time available. First results obtained for a system containing up to 108 sites indicate that the DC conductivity obeys the central limit theorem. It vanishes in the limit of zero temperature and fulfils a scaling law.