This work considers non-crystallographic periodic nets obtained from multiple identical copies of an underlying crystallographic net by adding or flipping edges so that the result is connected. Such a ...

We discuss the limit distribution of open quantum walks on the periodic graphs, particularly on the cycles. We show that under certain hypothesis, we can benefit from the theory of the classical ...

We consider the Dirac equation on periodic networks (quantum graphs). The self-adjoint quasiperiodic boundary conditions are derived. The secular equation allowing us to find the energy spectrum of ...

Abstract: We consider discrete Schrödinger operators with periodic potentials on periodic graphs perturbed by guided potentials, which are periodic in some directions and finitely supported in other ...

Abstract: A periodic graph models various natural and artificial periodic patterns with repetitions of a given static graph, and have vast applications in crystallography, scheduling, VLSI circuits ...