Related papers: Discrete symmetries in the cluster shell model
We give a comparative description of monopole and electrically charged spherically symmetric dust thin shells. Herewith we consider two of the most interesting configurations: the hollow shell and shell, surrounding a body with opposite…
The Lie point symmetries of a coupled system of two nonlinear differential-difference equations are investigated. It is shown that in special cases the symmetry group can be infinite dimensional, in other cases up to 10 dimensional. The…
The single-particle spectrum of deformed shell-model states in nuclei, is shown to exhibit a supersymmetric pattern. The latter involves deformed pseudospin doublets and intruder levels. The underlying supersymmetry is associated with the…
Spherical harmonics form a complete orthonormal basis which allows any function on the sphere to be expanded. The nuclear shape of a given eigenstate can thus be described within Bohr's quasi-molecular model by a coordinate transformation…
We study the cluster structure of $^{12}$C and $^{13}$C in the framework of the cluster shell model. Simple relations are derived for ratios of longitudinal form factors as well as transition probabilities. It is shown that the available…
Anisotropy at the level of the inter-particle interaction provides the particles with specific instructions for the self-assembly of target structures. The ability to synthesize non-spherical colloids, together with the possibility of…
We review pedagogically non-Abelian discrete groups, which play an important role in the particle physics. We show group-theoretical aspects for many concrete groups, such as representations, their tensor products. We explain how to derive,…
While non-abelian groups are undoubtedly the cornerstone of Grand Unified Theories (GUTs), phenomenology shows that the role of abelian and discrete symmetries is equally important in model building. The latter are the appropriate tool to…
In theories of the Kaluza-Klein kind there are spins or total angular moments in higher dimensions which manifest as charges in the observable $d=(3+1)$. The charge conjugation requirement, if following the prescription in ($3+1$), would…
Many remarkably robust, rapid and spontaneous self-assembly phenomena in nature can be modeled geometrically starting from a collection of rigid bunches of spheres. This paper highlights the role of symmetry in sphere-based assembly…
Spontaneous self-assembly of hard convex polyhedra are known to form orientationally disordered crystalline phases, where particle orientations do not follow the same pattern as the positional arrangement of the crystal. A distinct type of…
We analyse the fusion, braiding and scattering properties of discrete non-abelian anyons. These occur in (2+1)-dimensional theories where a gauge group G is spontaneously broken down to some discrete subgroup H. We identify the…
More than half a century after the fundamental, spherical shell structure in nuclei has been established, theoretical predictions indicate that the shell-gaps comparable or even stronger than those at spherical shapes may exist.…
Nuclei exhibit both single-particle and collective degrees of freedom, with the latter often subdivided into vibrational and rotational motions. Experimentally identifying the relative roles of these collective modes is extremely…
We formulate a simple algorithm for computing global exact symmetries of closed discrete curves in plane. The method is based on a suitable trigonometric interpolation of vertices of the given polyline and consequent computation of the…
We study experimentally what is arguably the simplest yet non-trivial colloidal system: two-dimensional clusters of 6 spherical particles bound by depletion interactions. These clusters have multiple, degenerate ground states whose…
Many features of spin models can be interpreted in geometrical terms by means of the properties of well defined clusters of spins. In case of spontaneous symmetry breaking, the phase transition of models like the q-state Potts model, O(n),…
The $\alpha$ cluster states are discussed in a model frame of extended quantum molecular dynamics. Different alpha cluster structures are studied in details, such as $^8$Be two-$\alpha$ cluster structure, $^{12}$C triangle structure,…
Two-dimensional classical cluster of particles interacting through a screened Coulomb potential is studied. This system can be used as a model for "dusty particles" in high-frequency discharge plasma. For systems consisting of N = 2 - 40…
We complete the discrete cluster categories of type $\mathbb{A}$ as defined by Igusa and Todorov, by embedding such a discrete cluster category inside a larger one, and then taking a certain Verdier quotient. The resulting category is a…