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

TL;DR

This paper derives the exact phase space volume for a 1D Coulomb gas at fixed energy, revealing negative temperature states and implications for turbulence in vortex or charge systems.

Contribution

It provides the first exact microcanonical phase space volume calculation for the 1D Coulomb gas without confining potential, highlighting negative temperature phenomena.

Findings

Existence of negative temperature states in 1D Coulomb gas

Exact phase space volume computed at fixed energy

Implications for vortex and charge clustering in 1D systems

Abstract

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.