1111.0659 (Timothy D. Andersen)

Exact solution to the 1d one component Coulomb gas at fixed energy    [PDF]

Timothy D. Andersen

The one dimensional one component plasma has applications to one dimensional particle systems with logarithmic interactions such as charges in a single channel wire or vortex filaments in a fluid convection stream. The exact integral of this plasma in the canonical ensemble with a gaussian confining potential has already been computed. In this paper, I compute the exact volume of the phase space of the plasma of N particles at fixed energy without a confining potential using a microcanonical ensemble and show that, as in the two-dimensional case, it has negative temperature states, suggesting that one dimensional turbulence can occur from vortex/electron clustering.

View original: http://arxiv.org/abs/1111.0659