Spectral properties of charged particles in a classical finite two-dimensional system

TL;DR

This paper investigates the spectral properties, normal modes, and phase transitions of finite 2D charged particle clusters confined by a quadratic potential, revealing how configurations influence stability and melting behavior.

Contribution

It introduces a comprehensive analysis of spectral and dynamical properties of finite 2D charged clusters, including energy spectra, eigenmodes, and melting transitions, using numerical optimization and diagonalization techniques.

Findings

Lowest excitations vary with cluster size: intershell rotation for small clusters, vortex pairs for large clusters.

Transition temperatures depend strongly on cluster configuration and particle distribution.

Magic number clusters exhibit enhanced stability against intershell rotation.

Abstract

We present a study of the spectral properties like the energy spectrum, the eigenmodes and density of states of a classical finite system of two-dimensional (2D) charged particles which are confined by a quadratic potential. Using the method of Newton optimization we obtain the ground state and the metastable states. For a given configuration the eigenvectors and eigenfrequencies for the normal modes are obtained using the Householder diagonalization technique for the dynamical matrix whose elements are the second derivative of the potential energy. For small clusters the lowest excitation corresponds to an intershell rotation. The energy barrier for such rotations is calculated. For large clusters the lowest excitation consists of a vortex/anti-vortex pair. The Lindeman melting criterion is used to calculate the order-disorder transition temperature for intershell rotation and intershell diffusion. The value of the transition temperature at which intershell rotation becomes possible depends very much on the configuration of the cluster, i.e. the distribution of the particles between the different shells. Magic numbers are associated to clusters which are most stable against intershell rotation. The specific heat of the cluster is also calculated using