Quantum graph vertices with permutation-symmetric scattering probabilities

Inverse scattering problem for quantum graph vertices

Scattering in PT -Symmetric Quantum Mechanics

A general formalism is worked out for the description of one-dimensional scattering in non-hermitian quantum mechanics and constraints on transmission and reflection coefficients are derived in the cases of P, T or PT invariance of the Hamiltonian. Applications to some solvable PT -symmetric potentials are shown in detail. Our main original results concern the association of reflectionless pote...

Probing scattering mechanisms with symmetric quantum cascade lasers.

A characteristic feature of quantum cascade lasers is their unipolar carrier transport. We exploit this feature and realize nominally symmetric active regions for terahertz quantum cascade lasers, which should yield equal performance with either bias polarity. However, symmetric devices exhibit a strongly bias polarity dependent performance due to growth direction asymmetries, making them an id...

Centrally Symmetric Manifolds with Few Vertices

A centrally symmetric 2d-vertex combinatorial triangulation of the product of spheres S × Sd−2−i is constructed for all pairs of non-negative integers i and d with 0 ≤ i ≤ d − 2. For the case of i = d − 2 − i, the existence of such a triangulation was conjectured by Sparla. The constructed complex admits a vertex-transitive action by a group of order 4d. The crux of this construction is a defin...

Approximations of permutation-symmetric vertex couplings in quantum graphs

We consider boundary conditions at the vertex of a star graph which make Schrödinger operators on the graph self-adjoint, in particular, the two-parameter family of such conditions invariant with respect to permutations of graph edges. It is proved that the corresponding operators can be approximated in the norm-resolvent sense by elements of another Schrödinger operator family on the same grap...