Abstract
The dynamics of electrons in a sheet of graphene can be described as a quantum field living in a discrete space—the graphene honeycomb lattice. As this space can be curved in various ways, the system offers a fascinating tool for studying and simulating the impacts of non-trivial geometries on quantum fields living in it. Local and global deformations as well as defects of the lattice can be mapped, via a discrete differential geometry, onto curvature and torsion in the continuous analog model. This allows for physical simulation and observation of quantum evolution and scattering in curved geometry and interaction with torsion. Time-dependent lattice perturbations, such as sound waves, can be interpreted as dynamical geometry and mimic gravitational waves. The immanent quantum character of the lattice structure—composed of carbon atoms—can be used for proposing a physical simulator of quantum geometry. We discuss the main ideas constituting these analogies, the latter being the topic of our ongoing project.
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Szpak, N. (2014). A Sheet of Graphene: Quantum Field in a Discrete Curved Space. In: Bičák, J., Ledvinka, T. (eds) Relativity and Gravitation. Springer Proceedings in Physics, vol 157. Springer, Cham. https://doi.org/10.1007/978-3-319-06761-2_82
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DOI: https://doi.org/10.1007/978-3-319-06761-2_82
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