Quasi one-dimensional particle systems have domains which are infinite
in one direction and bounded in all other directions, e.g. an infinite
cylinder. We will show that for such particle systems with Coulomb
interactions and a neutralizing background, the so-called jellium,
there is translation symmetry breaking in the Gibbs measures at any
temperature. This extends a previous result on Laughlin states in
thin, two-dimensional strips by Jansen, Lieb and Seiler (2009). The
structural argument is akin to that employed by Aizenman and Martin
(1980) for a similar statement concerning symmetry breaking at all
temperatures in strictly one-dimensional Coulomb systems. The
extension is enabled through bounds which establish tightness of
finite-volume charge fluctuations. We will also discuss an
application to quantum one-dimensional jellium which extends an old
result of Brascamp and Lieb (1975).