Symmetry, Volume 8, Issue 3

We present an analytical calculation of temporal evolution of populations for optically pumped atoms under the influence of weak, circularly polarized light. The differential equations for the populations of magnetic sublevels in the excited state, d...

Atomic nuclei exhibit approximate pseudospin symmetry. We review the arguments that this symmetry is a relativistic symmetry. The condition for this symmetry is that the sum of the vector and scalar potentials in the Dirac Hamiltonian is a constant....

A direct approach to non-linear second-order ordinary differential equations admitting a superposition principle is developed by means of Vessiot-Guldberg-Lie algebras of a dimension not exceeding three. This procedure allows us to describe generic t...

After the observation of the strong near-threshold enhancement of proton-antiproton mass spectrum in $J/\psi \to \gamma p$...

It is shown that, for both compact and non-compact Lie groups, vector-coherent-state methods provide straightforward derivations of holomorphic representations on symmetric spaces. Complementary vector-coherent-state methods are introduced to derive...

In this paper, simple models for the multiverse are analyzed. Each universe is viewed as a path in a graph, and by considering very general statistical assumptions, essentially originating from Boltzmann, we can make the set of all such paths into a...

PN (point-normal) triangles are cubic Bézier triangles which meet at their edges to surface a triangular mesh, but this only achieves G⁰ continuity. We define blending regions that span the edges shared by adjacent pairs of triangular domains and ble...

The transition of molecular crystals into a polar state is modeled by a one-dimensional Ising Hamiltonian in multipole expansion and a suitable order parameter. Two symmetry breakings are necessary for the transition: the translational and the spin f...

We compare two mathematical theories that address duality between cycles and vertex-cuts of graphs in geometric settings. First, we propose a rigorous definition of a new type of graph, vector graphs. The special case of R2-vector graphs matches the...