Abstract
The eigenvalue spectrum of a gain–loss one-dimensional quasiperiodic lattice was examined. An eigenvalue analysis was performed for golden-, silver-, and bronze–mean systems. The eigenvalues of these systems tended to coalesce in discrete small areas of a complex plane, and the eigenvalues exhibited a hierarchical spatial distribution on that plane. In addition, the effect of positional disorder in this system was investigated. The scaling property of the eigenvectors in the golden-mean system was clarified. Multifractal properties of the system were observed except for the outermost edge of the eigenvalue spectrum. For more advanced control of wave phenomena, clarification of physical properties of gain–loss systems in quasi-periodic systems is expected to lead to new technical applications in the future.
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