Related papers: Equilibrium configurations of tripolar charges
Interacting electrons in a semiconductor quantum dot at strong magnetic fields exhibit a rich set of states, including correlated quantum fluids and crystallites of various symmetries. We develop in this paper a perturbative scheme based on…
Industrial as well as natural aggregation of fine particles is believed to be associated with electrostatics. Yet like charges repel, so it is unclear how similarly treated particles aggregate. To resolve this apparent contradiction, we…
Theories of phase change and self-assembly often invoke the idea of a `quasiequilibrium', a regime in which the nonequilibrium association of building blocks results nonetheless in a structure whose properties are determined solely by an…
The question of classicality is addressed in relation with the shape of the nuclear skeleton of molecular systems. As the most natural environment, the electrons of the molecule are considered as continuously monitoring agents for the…
We apply the general principles of effective field theories to the construction of effective interactions suitable for few- and many-body calculations in a no-core shell model framework. We calculate the spectrum of systems with three and…
Bosons and fermions are defined by their exchange properties and the underlying symmetries determine the structure of the corresponding state spaces. For two particles there are two possible exchange symmetries, resulting in symmetric or…
We investigate Thomson's problem of charges on a sphere as an example of a system with complex interactions. Assuming certain symmetries we can work with a larger number of charges than before. We found that, when the number of charges is…
The aim of this paper is to develop the combinatorics of constructions associated to what we call \emph{triangular partitions}. As introduced in arXiv:2102.07931, these are the partitions whose cells are those lying below the line joining…
We construct two combinatorially equivalent line arrangements in the complex projective plane such that the fundamental groups of their complements are not isomorphic. The proof uses a new invariant of the fundamental group of the…
If constituent quarks are to emerge from QCD they must have well defined colour and be energetically favoured. After reviewing the general properties of charges in gauge theories, a method for constructing charges is presented and applied…
A field model of two-component fermions is described, the consequences of which coincide in the main with primary postulates of the standard model. Such a model can be constructed for 4 generations at the minimum. Peculiarities of the…
Simplicial arrangements are classical objects in discrete geometry. Their classification remains an open problem but there is a list conjectured to be complete at least for rank three. A further important class in the theory of hyperplane…
In modular-invariant models of flavour, hierarchical fermion mass matrices may arise solely due to the proximity of the modulus $\tau$ to a point of residual symmetry. This mechanism does not require flavon fields, and modular weights are…
Strongly coupled supersymmetric theories can give rise to composite quarks and leptons at low energy. We show that the internal structure of these particles can explain the origin of three generations and provide a qualitative understanding…
We consider an extended linear $\sigma $ model in which the fermions are quarks and are coupled to gluons. Equivalently, this is QCD extended by coupling the quarks to a colour singlet chiral multiplet of ($ \sigma, \vec \pi $) fields. This…
The ground state configurations and the \lq{}\lq{}normal\rq{}\rq{} mode spectra of a $quasi$-one-dimensional (Q1D) binary system of charged particles interacting through a screened Coulomb potential are presented. The minimum energy…
We have studied systematically the influence of particle-hole symmetric and asymmetric kinetic terms on the ordered phases that we may observe competing or coexisting in a tetragonal system. We show that there are precise patterns of…
In non-supersymmetric grand unified models a ``radiative fermion mass hierarchy" can be achieved in which the spectrum of quark and lepton masses is determined entirely by physics at the unification scale, with many relations following from…
Quarks and leptons, the fundamental building blocks of the subatomic world, manifest in three families - replicas with identical quantum numbers that differ only in their masses. After summarizing the present data, an overview is presented…
The E. Cartan's equations defining "simple" spinors (renamed "pure" by C. Chevalley) are interpreted as equations of motions for fermion multiplets in momentum spaces which, in a constructive approach based bilinearly on those spinors,…