Vortex Analogue of Molecules

Abstract

Kelvin’s theory of vortex atoms, in which Kelvin considered knotted strings as atoms, has been debunked and considered to be a failure. A theory of atoms as vortices is incapable of explaining stability and vibrational properties of atoms. With electrons representing ethereal vortices, the vortex atom theory tries to explain the relation between magnetic field and electrical current. In recent years, this simple Kelvin model has been shown to bear resemblance to the superstring theory. Although the vortex atom theory is considered to be scientifically incorrect (in the sense of its being unable to explain atomic properties), it may still be valid in a dynamical sense as for an example considered in this paper. With atomic potentials of logarithmic type, a dynamically stable vortex buckyball is ‘grown’ here. If stability is considered only from point of view of Huckel theory and eigenvalues of adjacency matrix, it may not be a sufficient test. It will be shown that such a vortex molecule is stable when Floquet theory of periodic orbits is used as a test of stability.