PT-symmetric quantum graphs

We consider PT-symmetric quantum graphs, in which the branching points provide PT-symmetric boundary
conditions for the Schrödinger equation on a graph. For such branched quantum wires, we derive
general boundary conditions, which keep the Hamiltonian as PT-symmetric with real eigenvalues and
positively defined norm of the eigenfunctions. Secular equations for finding the eigenvalues of the
quantum graph are derived. Breaking the Kirchhoff rule at the branching points in such systems is
shown. Experimental realization of PT-symmetric quantum graphs on branched optical waveguides is
discussed.

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