We study the possibility of triply degenerate points (TPs) that can be stabilized in spinless crystalline systems. Based on an exhaustive search over all 230 space groups, we find TPs exist at both high-symmetry and paths, they may have either linear or quadratic dispersions. For located points, share a common minimal set symmetries, which is point group $T$. The TP protected solely by $T$ chir...

We develop a microscopic theory of the fine structure Dirac states in $(0lh)$-grown HgTe/CdHgTe quantum wells (QWs), where $l$ and $h$ are Miller indices. It is shown that bulk, interface, inversion asymmetry causes anticrossing levels even at zero in-plane wave vector lifts state degeneracy. In QWs critical thickness, two-fold degenerate cone gets split into non-degenerate Weyl cones. The spli...

We have extended our method of grouping of Feynman diagrams (GFD theory) to study the transversal and longitudinal Greens functions G ⊥ (k) and G (k) in ϕ 4 model below the critical point (T < T c) in presence of an infinitesimal external field. Our method allows a qualitative analysis not cutting the perturbation series. We have shown that the critical behavior of the Greens functions is consi...

By using the Jacobi metric of the configuration space, and assuming ergodicity, we calculate the Boltzmann entropy S of a finite-dimensional system around a non-degenerate critical point of its potential energy V . We compare S with the entropy of a quantum or thermal system with effective potential Veff . We examine conditions, up to first order in perturbation theory, under which these entrop...

We study nonlinear eigenvalue problems of the type −div(a(x)∇u) = g(λ,x,u) in RN , where a(x) is a degenerate nonnegative weight. We establish the existence of solutions and we obtain information on qualitative properties as multiplicity and location of solutions. Our approach is based on the critical point theory in Sobolev weighted spaces combined with a Caffarelli-Kohn-Nirenberg-type inequal...

We determine all critical configurations for the Area function on polygons with vertices a circle or an ellipse. For isolated points we compute their Morse index, resp index of gradient vector field. relate computation at degenerate point to eigenvalue question about combinations. In even dimensional case non-isolated singularities occur as ‘zigzag trains’.

If each critical point is degenerate, then the conclusion that M is homeomorphic to a sphere is true. This was proved by Milnor [8] (1959) and by Rosen [10] (1960). With the aid of some techniques of Dyer and Hamstrom, recent results of Kirby, Edwards, and Cernavskii on spaces of homeomorphism on manifolds, and a selection theorem of Michael it is not difficult to establish the following topolo...