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

Abstract

We present a numerical study of the effect of the repulsive logarithmic inter-particle interaction on the ground state configuration and the frequency spectrum of a confined classical two-dimensional cluster containing a finite number of particles. In the case of a hard wall confinement all particles form one ring situated at the boundary of the potential. For a general r n confinement potential, also inner rings can form and we find that all frequencies lie below the frequency of a particular mode, namely the breathing-like mode. An interesting situation arises for the parabolic confined system (i.e. n = 2). In this case the frequency of the breathing mode is independent of the number of particles leading to an upper bound for all frequencies. All results can be understood from Earnshaw's theorem in two dimensions. In order to check the sensitivity of these results, the spectrum of vortices in a type II superconductor which, in the limit of large penetration depths, interact through a logarithmic potential, is investigated.

A π-shaped quantum device for implementation of Bell states in solid state environment

“…The intrinsic Hamiltonian includes the confinement potential due to harmonic behavior of electrons and interaction potential due to Coulombic interaction between electrons. The Coulombic interaction has taken a logarithmic form for 2DEG [47,48].…”

Elastic modes of vortex configurations in thin disks

“…Such a state has a highly symmetric configuration, with 12 (6) tion, confined to a parabolic potential. 19,21 This may be explained by the fact that the confining potential in the present case is a mixture of parabolic confinement close to the center of the disk and some sort of deconfining potential [the term ⑀ i self in Eq. (2a); cf.…”

“…[14][15][16][17][18] The sample geometry acts as a kind of confinement potential (since the boundary determines the shielding current pattern and the appearance of "vortex images" 14 ), which makes these systems resemble charged particles confined by some potential, [19][20][21] at least for fields much smaller than H c2 . In the latter system, the normal modes were used to investigate the melting temperature and the specific heat of charged particle clusters.…”

Condensation of two-dimensional harmonically confined bosons with Bessel-type interactions

“…IV we summarize our main conclusions. We refer at this point to recent calculations on the structure and the spectrum of classical 2D clusters with a logarithmic interaction potential [16] and on ordered structures formed in rotating ultracold Bose gases [17], as introductory to a broader view of the field.…”