Analytic dynamics of a one-dimensional system of particles with strong interaction
type: Item
instance of: scholarly article
title: Analytic dynamics of a one-dimensional system of particles with strong interaction
zbMATH Open document ID: 1266.82041
DOI: 10.1134/S0001434612070255
published in: Mathematical Notes
publication date: 2013-02-22T00:00:00Z
review text: 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.
reviewed by: Robert I. A. Patterson
Mathematics Subject Classification ID: 82C22
Mathematics Subject Classification ID: 70F10
Mathematics Subject Classification ID: 82D35
zbMATH DE Number: 6138380
zbMATH Keywords: strong interaction
zbMATH Keywords: circuit
zbMATH Keywords: electron
zbMATH Keywords: current
zbMATH Keywords: Coulomb
author: V. A. Malyshev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6138380