We numerically study crossed Andreev reflection (CAR) in a topological insulator nanowire T junction where one lead is proximitized by superconductor. perform realistic simulations based on the three-dimensional (3D) Bernevig-Hughes-Zhang model and compare results with those from an effective two-dimensional (2D) surface model, whose computational cost much lower. Both approaches show that CAR ...

Let T,U and V be rings with identity and M be a unitary (T,U)-bimodule, N be a unitary (U, V )bimodule, D be a unitary (T, V )-bimodule . We characterize homomorphisms and isomorphisms of the generalized matrix ring Γ = ( T M D 0 U N 0 0 V )

We construct the crossed product A ⋊ ρ̂ of a C*-algebra A with centre Z by an endomorphism ρ , which is special in a weaker sense w.r.t. the notion introduced by Doplicher and Roberts; the notation ρ̂ denotes the tensor C*-category of powers of ρ . We assign to ρ a geometrical invariant, representing a cohomological obstruction for it to be special in the usual sense; such invariant determines ra...

An IC-plane graph is a topological graph where every edge is crossed at most once and no two crossed edges share a vertex. We show that every IC-plane graph has a visibility drawing where every vertex is of the form { , , , }, and every edge is either a horizontal or vertical segment. As a byproduct of our drawing technique, we prove that every IC-plane graph has a RAC drawing in quadratic area...

We give an algorithmic way to construct a free bimodule resolution of an algebra admitting a Gröbner base. It enables us to compute the Hochschild (co)homology of the algebra. Let A be a finitely generated algebra over a commutative ring K with a (possibly infinite) Gröbner base G on a free algebra F , that is, A is the quotient F/I(G) with the ideal I(G) of F generated by G. Given a Gröbner ba...

Let A and B be C∗-algebras. We consider a noncommutative convexity in Hilbert A -B-bimodules, called A -B-convexity, as a generalization of C∗-convexity in C∗-algebras. We show that if X is a Hilbert A -B-bimodule, then Mn(X ) is a Hilbert Mn(A )-Mn(B)-bimodule and apply it to show that the closed unit ball of every Hilbert A -B-bimodule is A -B-convex. Some properties of this kind of convexity...

We share a small connection between information theory, algebra, and topology—namely, correspondence Shannon entropy derivations of the operad topological simplices. begin with brief review operads their representations simplices real line as main example. then give general definition for derivation an in any category values abelian bimodule over operad. The result is that defines simplices, ev...