Abstract

The evolution dynamics of wave-mechanical systems are governed by the full set of their modes and their respective eigenvalues. The key task of transferring arbitrary excitation patterns between two specific planes can therefore be accomplished by an appropriate structure of the eigenvalue spectrum. Along these lines, self-imaging is particularly effective if the spectrum is equidistantly spaced, similar to that of the harmonic oscillator. In finite-size discrete systems, the so-called J_x lattice fulfils this condition and has been employed for the perfect coherent transfer of quantum and classical states alike [4,5] and present a method to design families of compact two-dimensional equivalent systems that inherit the spectral and key dynamic features of one-dimensional J_x arrays while requiring dramatically fewer distinct coupling values [6].

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