Plasma living in a curved surface at some special temperature

Abstract

The simplest statistical mechanics model of a Coulomb plasma in two spatial dimensions admits an exact analytic solution at some special temperature in several (curved) surfaces. We present in a unifying perspective these solutions for the (non-quantum) plasma, made of point particles carrying an absolute charge e, in thermal equilibrium at a temperature T = e 2 /2k B , with k B Boltzmann's constant, discussing the importance of having an exact solution, the role of the curvature of the surface, and the densities of the plasma.

Monte Carlo simulations of two-component Coulomb gases applied in surface electrodes

“…We show in figure 8 the thermodynamic average of the electrical scalar potential profile for Γ = 2.32. The calculation is made using equation (15). In that figure it can be seen that the MC results are quite consistent with the analytical electrostatic approach for this low coupling situation.…”

“…It exists near the ground state configuration of the system: the particles slightly move in the vicinity of fixed locations, without showing an ordered structure. This occurs because the gap region of the SE introduces defects in the ground state configuration of the system 15 . These defects near the boundaries of finite Coulomb 2dOCP systems also emerge in disks.…”

“…given that the trial move is accepted depending on the Boltzmann factor associated to δU (m) pp when the restriction in ( 18) is fulfilled. For the particular case of the circular SE, we can use the axial symmetry to simplify the computation with equation (15). Thus, the thermodynamic average • on a given set of equilibrated configurations Ω can be computed from…”

“…The current study attempts to model the gapped SE as a 2dTCP with no mixing, or conversely two interacting 2dOCP placed in two electrodes. The 2dOCP has been widely studied [13][14][15][16][17][18][19] because it is a simple system that mimic phase transitions [20][21][22] of real systems as dusty plasmas [23]. One of the peculiarities of these systems is that they form quasi-two-dimensional solids in the strong coupling regime (Γ → ∞).…”

“…Eventually, this acceptance ratio can be increased up to 40% for Coulomb gases in the fluid phase. Here we keep the acceptance ratio in the (0.30, 0.37) interval, where the largest values are used for simulations in the weak coupling regime 15. A defect is a particle that does not belong to the Winger crystal.…”