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This study explores the possibility and presents a methodology to synthesizea classical mechanical analogue to the quantum mechanical 1D Kitaev model.While being fundamentally different, we will identify significant conceptualsimilarities between the two models that culminate in the occurrence, in theclassical analogue system, of topologically non-trivial bound states that areakin to Majorana zero modes. By reformulating the Hamiltonian of the classicalsystem in a form reminiscent of second quantization, we show that a 1Dstaggered classical mechanical chain can exhibit dynamic characteristicsanalogous to the Kitaev's 1D superconducting model, as well as itscharacteristic bound states. The non-trivial topological nature of the boundstates is further confirmed by the topological band structure analysis and bythe topological invariant. While the non-Abelian nature of these states remainsan open question, these results allow envisioning the possibility to achievetopological braiding in classical mechanical systems.

Classical analogue to the Kitaev model and Majorana-like topological bound states