For a periodic quantum circuit made of a chain with a loop at each node, translation-invariant boundary conditions force the coupling parameter δ and the loop phase difference α to be constant along the whole chain.
Linear Operator Theory in Engineering and Science ; Applied Mathe- matical Sciences, Springer-Verlag: New York,
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On $\mathbb{Z}$-invariant self-adjoint extensions of the Laplacian on quantum circuits
For a periodic quantum circuit made of a chain with a loop at each node, translation-invariant boundary conditions force the coupling parameter δ and the loop phase difference α to be constant along the whole chain.