Dynamic behavior and stability of two-dimensional dust clusters in power law traps

Abstract

Fundamental properties of finite two-dimensional (2D) Yukawa dust clusters, subjected to power law confining potentials, are studied using Monte Carlo simulations. We show the effects of the interplay between the Yukawa screening and the functional form of the confining potential on the structure, dynamics, and melting of few particle systems. We find numerically that one of the fundamental eigenmodes, namely, a center of mass mode, still exists for a confinement with n = 3. The stability of such clusters is discussed using the variance of the block averaged interparticle distance fluctuations (VIDF). The melting temperatures are found to depend crucially on screening length and confinement power. For the estimation of the melting temperature, the VIDF quantity is believed to be reliable only for well-packed structures, where the relative interparticle distance fluctuations (IDF) disregard the melting transition point.

On the convergence issues of the block‐average method for the melting of two‐dimensional confined systems

“…In this section, we recall Monte Carlo first‐principles results of the ground‐state configurations and the excitation spectrum of 2D clusters in traps (for an overview see Ref. ).…”

“…The dimensionless Hamiltonian of the lowest energy state of N equally charged particles in 2D power‐law traps is given by …”

“…The dimensionless Hamiltonian of the lowest energy state of N equally charged particles in 2D power-law traps is given by [7]…”

“…In finite systems, fluctuations due to the contribution of the particle vibration and particle jumps between different local minima can be quantified using the relative inter‐particle distance fluctuations (IDFs). However, it was shown that, when applied to very small systems, IDF depends crucially on the way it is computed and on the system under consideration (particle number, symmetry of the system, etc.). Furthermore, IDF can show a continuous increase over some finite temperature interval.…”

“…To circumvent the convergence problem of IDF, many investigations support the idea of introducing the variance of the block‐averaged inter‐particle distance fluctuations (VIDFs), which gives a better estimate of the melting point of 2D and 3D finite systems. Depending on the shape of the confinement potential, a variety of ground‐state configurations may be simulated.…”