Analytic dynamics of a one-dimensional system of particles with strong interaction (Q1938651)

The paper is concerned with bounds on the time taken to establish a steady current in an electric circuit as the number of electrons, \(N\), becomes infinite. In particular the power series for the initial transient solution for electron velocities is shown to have a radius of convergence with a lower bound that is \(\mathcal{O}\left(N^{-\frac{5}{6}}\right)\). It is conjectured that there is an \(\mathcal{O}\left(N^{-\frac{1}{2}}\right)\) upper bound, but ``this has not been proved yet''. The analysis is carried out by deriving series representations of the electron velocities and several associated recurrence relations. The resulting manipulations are extensive, but are broken up nicely into smaller steps and appear possible to follow with patience.