Phases of the excitonic condensate in two-layer graphene

Two graphene monolayers that are oppositely charged and placed close to each other are considered. Taking into account valley and spin degeneracy of electrons we analyze the symmetry of the excitonic insulator states in such a system and build a phase diagram that takes into account the effect of the symmetry breaking due to the external in-plane magnetic field and the carrier density imbalance between the layers.Comment: 12 pages, 6 figures, 1 tabl

Maximal Abelian Subgroups of the Isometry and Conformal Groups of Euclidean and Minkowski Spaces

The maximal Abelian subalgebras of the Euclidean e(p,0) and pseudoeuclidean e(p,1)Lie algebras are classified into conjugacy classes under the action of the corresponding Lie groups E(p,0) and E(p,1), and also under the conformal groups O(p+1,1) and O(p+1,2), respectively. The results are presented in terms of decomposition theorems. For e(p,0) orthogonally indecomposable MASAs exist only for p=1 and p=2. For e(p,1), on the other hand, orthogonally indecomposable MASAs exist for all values of p. The results are used to construct new coordinate systems in which wave equations and Hamilton-Jacobi equations allow the separation of variables.Comment: 31 pages, Latex (+ latexsym

Chronotaxic systems with separable amplitude and phase dynamics

Until recently, deterministic non-autonomous oscillatory systems with stable amplitudes and time-varying frequencies were not recognised as such and have often been mistreated as stochastic. These systems, named chronotaxic, were introduced in \emph{Phys. Rev. Lett.} \textbf{111}, 024101 (2013). In contrast to conventional limit cycle models of self-sustained oscillators, these systems posses a time-dependent point attractor or steady state. This allows oscillations with time-varying frequencies to resist perturbations, a phenomenon which is ubiquitous in living systems. In this work a detailed theory of chronotaxic systems is presented, specifically in the case of separable amplitude and phase dynamics. The theory is extended by the introduction of chronotaxic amplitude dynamics. The wide applicability of chronotaxic systems to a range of fields from biological and condensed matter systems to robotics and control theory is discussed