Inverse scattering problem for quantum graph vertices

Abstract

We demonstrate how the inverse scattering problem of a quantum star graph can be solved by means of diagonalization of Hermitian unitary matrix when the vertex coupling is of the scale invariant (or Fülőp-Tsutsui) form. This enables the construction of quantum graphs with desired properties in a tailor-made fashion. The procedure is illustrated on the example of quantum vertices with equal transmission probabilities.

ReVTeX, 4 pages, four figures

References in corpus (6)

• Approximation of a general singular vertex coupling in quantum graphs
• Bosonization and Scale Invariance on Quantum Wires
• Quantum graphs where back-scattering is prohibited
• Fulop-Tsutsui interactions on quantum graphs
• Tripartite connection condition for quantum graph vertex
• Hermitian unitary matrices with modular permutation symmetry

Cited by in corpus (3)

• A general approximation of quantum graph vertex couplings by scaled Schroedinger operators on thin branched manifolds
• Quantum graph vertices with permutation-symmetric scattering probabilities
• Quantum graph vertices with minimal number of passbands