Hermitian dynamics in a class of pseudo-Hermitian networks

We investigate a pseudo-Hermitian lattice system, which consists of a set of isomorphic pseudo-Hermitian clusters coupled together in a Hermitian manner. We show that such non-Hermitian systems can act as Hermitian systems. This is made possible by considering the dynamics of a state involving an identical eigenmode of each isomorphic cluster. It still holds when multiple eigenmodes are involved and additional restrictions on the state are imposed. This Hermitian dynamics is demonstrated for the case of an exactly solvable PT-symmetric ladder system.