Spectral properties of classical two-dimensional clusters

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 twodimensional (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 the Monte-Carlo technique which we compare with an analytical calculation where effects due to 1 anharmonicity are incorporated.

Pinning-Induced Formation of Vortex Clusters and Giant Vortices in Mesoscopic Superconducting Disks

“…Clearly, the effect of vortex confinement in single crystal-based disks is very similar to that in individual thinfilm disks [5]. Indeed, previously confinement was found to have a mitigating effect on disorder in that, despite the presence of weak pinning, vortices formed nearly perfect shell configurations [5]; similarly, well-defined shell states are observed in weak-disorder disks on single crystals [e.g., state (1,6,13) in Fig. 1a].…”

“…Analysis of different vortex configurations revealed the rules ("periodic law") of shell filling and also "magic-number" configurations corresponding to commensurability between the shells (see e.g. [6]). Importantly, regular vortex shells could only be observed in disks with sufficiently weak pinning.…”

Effect of confinement on the mode dynamics of dipole clusters

“…Most of the previous calculations for 2D systems focussed on frictionless simulations or weakly damped dust clusters were it was found that compressional modes are excited at higher frequencies than shear-like modes. 15,40,55,56 Here, damping effects lead to the blurred histograms of J c and J s and it seems as if a more complicated motion of the particles in the eld of eigenvectors is involved than that captured by eqn (9) and (10). However, from Fig.…”

“…In classical conned systems, less energy is necessary to excite angular modes compared to radial modes due to the strong radial constraints. 15,55,57 As a consequence, angular modes are less stable than radial modes and more unstable angular modes should be excited than unstable radial modes at the same energy level. We have observed for our colloidal dipole clusters that the fraction of unstable angular The sensitivity of angular modes to instabilities was previously observed for nite 2D dust clusters that interact via the screened Coulomb potential.…”

Structure and spectrum of classical two-dimensional clusters with a logarithmic interaction potential

“…Bedanov et al [1,2] studied the classical system with a finite number of particles interacting through a repulsive 1/r potential and moving in a two-dimensional plane, confined by a parabolic potential. The 1/r potential is the Coulomb potential in a three-dimensional world.…”