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Koke, Christian; Noh, Changsuk; Angelakis, Dimitris G. (2020): Dirac equation on a square waveguide lattice with site-dependent coupling strengths and the gravitational Aharonov-Bohm effect. In: Physical Review A, Vol. 102, No. 1, 013514
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The main objective of this work is to present a theoretical proposal for an implementation of the (2 + 1)dimensional Dirac equation in classical gravitational and electromagnetic backgrounds, in a two-dimensional waveguide array. For this, a framework for achieving site-dependent effective coupling constants in two-dimensional waveguide arrays is developed. Implementability of the Dirac equation under the proposed scheme puts minor demands on gauge and spacetime backgrounds;however, a wide array of physical spacetimes, such as all vacuum and static solutions, prove to be implementable. As an interesting and instructive example, we discuss a tabletop realization of the gravitational Aharonov-Bohm effect: After devising a thought experiment in which signatures of the gravitational Aharonov-Bohm effect could be detected, we briefly discuss how the analog of such a setting can in principle be implemented using the proposed waveguide setup.