Related papers: The Diamond ensemble: a constructive set of points…
Given a standard myopic dynamic process among coalition structures, an absorbing set is a minimal collection of such structures that is never left once entered through that process. Absorbing sets are an important solution concept in…
Finite semisimple group algebras for which all the minimal ideals are easily computable dimension (ECD) are characterized and some lower bounds for the minimum Hamming distance of group codes in these algebras are offered. Examples…
We discuss a generalized quantum microcanonical ensemble. It describes isolated systems that are not necessarily in an eigenstate of the Hamilton operator. Statistical averages are obtained by a combination of a time average and a maximum…
In this review paper we introduce at first the cage nature of diamondoid molecules, the variety of their crystalline lattice structures, the nature of their structural isomers, their stereoisomers, and their other molecular specificities.…
We consider the possibility that classical dynamical systems display motion in their lowest energy state, forming a time analogue of crystalline spatial order. Challenges facing that idea are identified and overcome. We display arbitrary…
We investigate the dynamics in the logarithmic galactic potential with an analytical approach. The phase-space structure of the real system is approximated with resonant detuned normal forms constructed with the method based on the Lie…
Low-energy structures are found on the potential energy surfaces of the neutral, cationic, and anionic gold clusters Au_{5 \leq n \leq 8}^Z (Z = 0, \pm) and on the neutral potential energy surface of Au_9. These structures provide insights…
Diamond is studied by path integral molecular dynamics simulations of the atomic nuclei in combination with a tight-binding Hamiltonian to describe its electronic structure and total energy. This approach allows us to quantify the influence…
In the paper we prove that any sumset or difference set has large E_3 energy. Also, we give a full description of families of sets having critical relations between some kind of energies such as E_k, T_k and Gowers norms. In particular, we…
We classify low-energy $\alpha$-harmonic maps from a closed non-spherical Riemannian surface $\Sigma$ of constant curvature to the round sphere via their bubble scales and centres. In particular we show that as $1<\alpha\downarrow 1$ and…
A commutative ring $R$ is stable if every non-zero ideal $I$ of $R$ is projective over its ring of endomorphisms. Motivated by a paper of Bass in the 1960s, stable rings have received wide attention in the literature ever since then. Much…
We analyse the classical and quantum behaviour of a particle trapped in a diamond shaped billiard. We defined this billiard as a half stadium connected with a triangular billiard. A parameter $\xi$ which gradually change the shape of the…
The diamond norm is a norm defined over the space of quantum transformations. This norm has a natural operational interpretation: it measures how well one can distinguish between two transformations by applying them to a state of…
A sumset semigroup is a non-cancellative commutative monoid obtained from the sumset of finite non-negative integer sets. In this work, an algorithm for computing the ideals associated with some sumset semigroups is provided. Using these…
The field of quantum metrology promises measurement devices that are fundamentally superior to conventional technologies. Specifically, when quantum entanglement is harnessed the precision achieved is supposed to scale more favourably with…
Classical random matrix ensembles were originally introduced in physics to approximate quantum many-particle nuclear interactions. However, there exists a plethora of quantum systems whose dynamics is explained in terms of few-particle…
Using a global optimization approach that directly searches for the composition of greatest stability, we have been able to find the particularly stable structures for binary Lennard-Jones clusters with up to 100 atoms for a range of…
Exceptional points are universal level degeneracies induced by non-Hermiticity. Whereas past decades witnessed their new physics, the unified understanding has yet to be obtained. Here we present the complete classification of generic…
Crystals which have a uniform distribution of defects are endowed with a Lie group description which allows one to construct an associated discrete structure. These structures are in fact the discrete subgroups of the ambient Lie group. The…
Multiple pendulums are investigated numerically and analytically to clarify the nonuniformity of average kinetic energies of particles. The nonuniformity is attributed to the system having constraints and it is consistent with the…