the notion of generalized locally bounded $i$-topological vectorspaces is introduced. some of their important properties arestudied. the relationship between this kind of spaces and thelocally bounded $i$-topological vector spaces introduced by wu andfang [boundedness and locally bounded fuzzy topological vectorspaces, fuzzy math. 5 (4) (1985) 87$-$94] is discussed. moreover, wealso use the fam...

One-dimensional topological superconductors harbor Majorana bound states at their ends. For superconducting wires of finite length L, these Majorana states combine into fermionic excitations with an energy ε(0) that is exponentially small in L. Weak disorder leaves the energy splitting exponentially small, but affects its typical value and causes large sample-to-sample fluctuations. We show tha...

Spontaneous symmetry breaking while preserving flow ability is a remarkable feature of nematic liquid crystals. When a nematic liquid crystal coexists with a solid, the surface field of the solid tends to anchor the director direction on the surface: anchoring effects. If geometrical frustration between nematic ordering and anchoring is strong enough, stable topological defects are formed. Defe...

The quantitative description of the orthopositronium anomalies (" isotope anomaly " in a gaseous neon for the " resonance conditions " and " λT-anomaly " in non-resonance conditions) is possible on the basis of a hypothesis about restoration of spontaneously broken complete rela-tivity (A.F.Andreev, 1982) of the limited space-time " volume " (" defect " of the space-time) in a final state of β ...

We derive a series of low energy theorems for correlation functions of the topological density in gluodynamics. In particular, the topological susceptibility is found exactly in terms of the gluon condensate. Using low energy theorems, we find the θ dependence of the condensates 〈GG〉, 〈GG̃〉 and of the partition function for small θ and an arbitrary number of colors. As applications of low energy...

We study the topological entropy of the magnetic flow on closed riemannian surface. We prove that if the magnetic flow has a non-hyperbolic closed orbit in some energy set T c M = E −1 (c), then there exists an exact C ∞-perturbation of the 2-form Ω such that the new magnetic flow has positive topological entropy in T c M. We also prove that if the magnetic flow has an infinite number of closed...

We study theoretical properties of robust low energy electronic excitations associated with topological insulators and superconductors. The bulk materials are described by non-interacting single particle band Hamiltonians with a finite excitation gap. Their topological phases are classifed according to symmetries and dimensions, characterized by discrete bulk invariants, and correspond to topol...

The Lieb-Schultz-Mattis theorem and its higher-dimensional generalizations by Oshikawa and Hastings require that translationally invariant 2D spin systems with a half-integer spin per unit cell must either have a continuum of low energy excitations, spontaneously break some symmetries, or exhibit topological order with anyonic excitations. We establish a connection between these constraints and...

Ag2Te is a novel topological insulator system and new candidate for plasmon resonance due to the existence of Dirac cone in low-energy region. Although optical response spectrum has been studied by theoretical experimental methods, stability Co-doped remain elusive. Here, we theoretically report unconventional UV mode its Ag2Te. Through density functional theory (DFT), identify deep within 15–4...

We study the topological entropy of the magnetic flow on closed Riemannian surface. We prove that if the magnetic flow has a non-hyperbolic closed orbit in some energy set T c M = E −1 (c), then there exists an exact C ∞-perturbation of the 2-form Ω such that the new magnetic flow has positive topological entropy in T c M. We also prove that if the magnetic flow has an infinite number of closed...