Simulating hyperbolic space and holography in circuits

Julius-Maximilians-Universität Würzburg

In this talk, I present recent developments in circuit implementations of hyperbolic geometries and holographic models. Electrical circuit networks are a versatile platform that enables tabletop simulations of a wide variety of discrete physical models. They established themselves as a platform for the realization of topological states, but also allow for non-Hermitian physics thanks to the availability of gain/loss and active elements, as well as nonlinear systems and parametrically driven systems. In the context of non-Euclidean geometries, we make use of the relative independence of the dynamics of a circuit network from its geometrical arrangement, allowing for the implicit realization of curved spaces through the network structure alone. By this approach, circuit networks can be used to realize systems in hyperbolic lattices, a discretized form of hyperbolic space, and allow us to explore their phenomena in an experimental setup.