Fulop-Tsutsui interactions on quantum graphs

Abstract

We examine scale invariant Fulop-Tsutsui couplings in a quantum vertex of a general degree $n$. We demonstrate that essentially same scattering amplitudes as for the free coupling can be achieved for two $(n-1)$-parameter Fulop-Tsutsui subfamilies if $n$ is odd, and for three $(n-1)$-parameter Fulop-Tsutsui subfamilies if $n$ is even. We also work up an approximation scheme for a general Fulop-Tsutsui vertex, using only $n$ $\delta$ function potentials.

14 pages elsevier format, new references added

References in corpus (7)

• Approximation of a general singular vertex coupling in quantum graphs
• Bosonization and Scale Invariance on Quantum Wires
• Boundary conditions for the states with resonant tunnelling across the ${\delta }^{\prime }$-potential
• Index theorems for quantum graphs
• Irregular Dynamics in a Solvable One-Dimensional Quantum Graph
• Spectral filtering in quantum Y-junction
• Chaos in a one-dimensional integrable quantum system

Cited by in corpus (9)

• Potential-controlled filtering in quantum star graphs
• Tripartite connection condition for quantum graph vertex
• Hermitian unitary matrices with modular permutation symmetry
• Path Integral on Star Graph
• Path Integral Junctions
• Quantum graph vertices with permutation-symmetric scattering probabilities
• Inverse scattering problem for quantum graph vertices
• Quantum graph as a quantum spectral filter
• Quantum graph vertices with minimal number of passbands