Pressures for a One-Component Plasma on a Pseudosphere

TL;DR

This paper investigates the classical two-dimensional one-component plasma on a pseudosphere, analyzing different pressure definitions, deriving relations, and providing exact solutions at a specific temperature to understand its thermodynamic behavior.

Contribution

It extends the study of plasma pressures to negatively curved surfaces and provides exact solutions and relations between pressures on a pseudosphere.

Findings

Derived relations between different pressure definitions.

Obtained exact grand canonical solutions at a special temperature.

Analyzed thermodynamic limit of the plasma system.

Abstract

The classical (i.e. non-quantum) equilibrium statistical mechanics of a two-dimensional one-component plasma (a system of charged point-particles embedded in a neutralizing background) living on a pseudosphere (an infinite surface of constant negative curvature) is considered. In the case of a flat space, it is known that, for a one-component plasma, there are several reasonable definitions of the pressure, and that some of them are not equivalent to each other. In the present paper, this problem is revisited in the case of a pseudosphere. General relations between the different pressures are given. At one special temperature, the model is exactly solvable in the grand canonical ensemble. The grand potential and the one-body density are calculated in a disk, and the thermodynamic limit is investigated. The general relations between the different pressures are checked on the solvable model.