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arXiv · 1111.0659

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

Timothy D. Andersen
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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.

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Timothy D. Andersen. 2011-11-02. Exact solution to the 1d one component Coulomb gas at fixed energy. https://arxiv.org/abs/1111.0659

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