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A single colloidal particle trapped in an optical vortex experiences two optical forces: a gradient force confining it to motion along a finite width ring of light, and radiation pressure driving it along the perimeter of the ring. As a result, the particle rotates, at constant angular velocity with thermal fluctuations. When a second particle is introduces to the vortex trap the two particles pair due to a pseudo-potential caused by the interplay between hydrodynamic interactions and the curvature of the particles’ trajectory. We study the collective excitations of many colloidal particles driven in an optical vortex trap. We find that even though the system is overdamped, hydrodynamic interactions due to driving give rise to non-decaying excitations with characteristic dispersion relations. The collective excitations of the colloidal ring reflect fluctuations of particle pairs rather than those of single particles.

Quantum phase transitions (QPTs) are structural changes in the properties of a physical system induced by a variation of parameters in the quantum Hamiltonian. In the present talk, we examine the order and chaos and persisting symmetries, accompanying a first-order QPT in nuclei. The Hamiltonian employed describes a QPT between spherical and deformed shapes, associated with U(5) and SU(3) dynamical symmetries, respectively. A classical analysis reveals a rich but simply-divided phase space structure with a Henon-Heiles type of chaotic dynamics ascribed to the spherical minimum, coexisting with a robustly regular dynamics ascribed to the deformed minimum in the Landau potential. A quantum analysis discloses regular U(5)-like multiplets in the spherical region and regular SU(3)-like rotational bands in the deformed region, which retain their identity amidst a complicated environment of other states. A symmetry analysis shows that these regular subsets of states, are associated with partial U(5) dynamical symmetry (PDS) and SU(3) quasi-dynamical symmetry (QDS),
respectively.

Molecular anions are of fundamental importance and ubiquitous in many chemical, physical and biological environments. The chemical and physical properties of anions are very different from their neutral or cationic counterparts making them interesting species to study and characterize. While it is straightforward to assert that excited states of the anion play a crucial role in the electron accepting capabilities of the neutral molecules, electronically stable excited states of anions are thought to be scarce at best.

Following an overview of the special characteristic of molecular anions, we shall present our study of the electronically bound spectrum of the anion. Much like the neutral fullerene, the anion possesses certain unique properties which have attracted a great deal of research. One of these special properties, only recently fully uncovered, is that the anion supports a substantial number of electronically stable excited states in contrast to other molecular anions with comparable electron affinity. In this work, we clarify how the anion can support so many stable states by analyzing the radial and angular distributions of the excess electron bound to the anion. The analysis is based on ab initio calculations which are by far the most accurate on the anion to date. Surprisingly, the radial distributions are highly similar for states of very different binding energies and the analysis stresses the importance of angular correlation in binding the excess electron.

We further analyze the effect of the single excess electron on the electrons of the underlying neutral molecule. We demonstrate how this substantially modifies the actual distribution of the excess charge by shifting the underlying electron density. Finally, the effect of the perturbation of the anionic states in the presence of incarcerated atoms within the carbon shell is analyzed and discussed.