Structure and spectrum of anisotropically confined two-dimensional clusters with logarithmic interaction

Abstract

We studied the structural and spectral properties of a classical system consisting of a finite number of particles, moving in two dimensions, and interacting through a repulsive logarithmic potential and held together by an anisotropic harmonic potential. Increasing the anisotropy of the confinement potential can drive the system from a two-dimensional (2D) to a one-dimensional (1D) configuration. This change occurs through a sequence of structural transitions of first and second order which are reflected in the normal mode frequencies. Our results of the ground state configurations are compared with recent experiments and we obtained a satisfactory agreement. The transition from the 1D line structure to the 2D structure occurs through a zigzag transition which is of second order. We found analytical expressions for the eigenfrequencies before the zigzag transition, which allowed us to obtain an analytical expression for the anisotropy parameter at which the zigzag transition occurs as a function of the number of particles in the system.

Exploring rigidly rotating vortex configurations and their bifurcations in atomic Bose-Einstein condensates

“…[36], which in turn was motivated by experiments (and phase transitions observed) on systems of confined charged metallic balls [37].…”

Numerical modeling of structural transitions in few-particle confined 2D systems

“…These changes play the role of phase transitions in finite-size systems. The obtained structures compare favorably to those presented in [14], however, the specific critical values of α that correspond to the transitions between the competing structures cannot be compared directly. The authors of [14] used the logarithmic interaction which is relevant to vortices in quantum fluids.…”

“…Note that this convention is different from that used in [14]. The density of particles in typical experiments is low, thus the system can be treated within a classical approach, and the kinetic energy of particles is not taken into account.…”

“…On the other hand, one may encounter reorganization of the structure (a structural transition) in response to the modification of the external conditions. Structures of 2D few-particle systems confined by an asymmetric potential were studied experimentally [8,12,13] and theoretically [14] aiming to identify the transitions from their structural and spectral properties.…”

Effect of charge fluctuation on two dimensional dust clusters in elliptical confinement

“…The inhomogeneous melting is the typical melting process for anisotropically confined clusters particularly for small systems. 7,8 One of the most general fundamental phenomena in plasma crystals is the formation of ordered dust crystals. Dust particles are microsized with interesting properties such as size distribution and charge fluctuation.…”