44 research outputs found
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