Continuum theory for two-dimensional complex plasma clusters

Abstract

We develop a theoretical approach to obtain a new differential equation together with a new boundary condition for the density profile of twodimensional clusters and apply it to the complex plasma case. In addition, we use the local-density approximation for the interaction energy and consider finite size effects. In this case, our differential equation and the previously used reduce to the same. By using the new boundary condition, a scale invariance appears and the obtained scale function can be used in many systems beyond complex plasmas. The obtained equations are confronted with molecular dynamics simulations. We find that the dependence of the system's size and the density profile with the number of particles, N , agrees very well with the results obtained from simulations. The theory has a surprisingly good accuracy for small systems (8 < N < 500). Moreover, we find by simulations that, for a given external potential, the final configuration from an experiment or simulation can provide us, at most, with two possible values for each interaction parameter, the charge and the screening length.

Formation and stability of conformal spirals in confined 2D crystals

“…All these configurations are concentric and, with the exception of sample R = 64r 0 , their quasi-conformal region are completely free of defects. If the crystal is conformal in this region, QQCR is expected to be very close to zero, whereas if the topology is that predicted by continuum limit theory [equation (11)], one expects QQCR 0.6, since Q(R * ) = 5.4. For all radii studied, the topological charge is indeed zero in the quasi-conformal region at T = 0.…”

“…particle-particle interactions, and the symmetry of the confining potential, which is typically circular. The resulting configurations often feature ring-like structures and curved crystalline lines, observed for many different kinds of particle-particle and confining potentials [7][8][9][10][11][12][13][14][15][16][17]48].…”