Optimal lattice configurations for interacting spatially extended particles

We investigate lattice energies for radially symmetric, spatially extended particles interacting via a radial potential and arranged on the sites of a two-dimensional Bravais lattice. We show the global minimality of the triangular lattice among Bravais lattices of fixed density in two cases: In the first case, the distribution of mass is sufficiently concentrated around the lattice points, and the mass concentration depends on the density we have fixed. In the second case, both interacting potential and density of the distribution of mass are described by completely monotone functions in which case the optimality holds at any fixed density.Comment: 17 pages. 1 figure. To appear in Letters in Mathematical Physic

Chiral Tensor Particles in the Early Universe - Present Status

In this work an update of the cosmological role and place of the chiral tensor particles in the Universe history is provided. We discuss an extended model with chiral tensor particles. The influence of these particles on the early Universe evolution is studied. Namely, the increase of the Universe expansion rate caused by the additional particles in this extended model is calculated, their characteristic interactions with the particles of the hot Universe plasma are studied and the corresponding times of their creation, scattering, annihilation and decay are estimated for accepted values of their masses and couplings, based on the recent experimental constraints. The period of abundant presence of these particles in the Universe evolution is determined.Comment: 7 pages, 2 figures, research article, Preprint of an article published in MPLA's, Volume No.32, Issue No. 34, 201

Generalized Falicov-Kimball Models

In this paper we extend the Falicov-Kimball model (FKM) to the case where the "quasi-particles" entering the FKM are not "ordinary" fermions. As an example we first discuss how the FKM can be generalized to the case with spin-dependent hopping. Afterwards we discuss several cases where the "quasi-particles" entering the FKM are Majorana fermions (extended Majorana-Falicov-Kimball Model (MFKM). Two examples of extended MFKM are discussed in detail: (i) a $p$-wave BCS superconductor on a bipartite lattice and (ii) a BCS-Anderson model. We also discuss the most general forms of extended MFKM, including a brief discussion on the case where the Majorana fermions represent spins, but not real fermion particles.Comment: 9 pages, 6 figure

Symmetry breaking and clustering in a vibrated granular gas with several macroscopically connected compartments

The spontaneous symmetry breaking in a vibro-fluidized low-density granular gas in three connected compartments is investigated. When the total number of particles in the system becomes large enough, particles distribute themselves unequally among the three compartments. Particles tend to concentrate in one of the compartments, the other two having the (relatively small) same average number of particles. A hydrodynamical model that accurately predicts the bifurcation diagram of the system is presented. The theory can be easily extended to the case of an arbitrary number of connected compartments