![]() Fractal growth of copper electrodeposits. Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields. Fractal energy spectrum of a polariton gas in a Fibonacci quasiperiodic potential. Topological photonic quasicrystals: fractal topological spectrum and protected transport. Multifractality in human heartbeat dynamics. Physics and Fractal Structures (Springer, 1996). Diffusion and Reactions in Fractals and Disordered Systems (Cambridge Univ. Our experiment allows the verification of physical laws in a quantitative manner and reveals the transport dynamics in great detail, thus opening a path to the understanding of more complex quantum phenomena governed by fractality. In addition, the critical point at which there is a transition from normal to anomalous transport depends on the fractal geometry. Contrarily to classical fractals, we observe anomalous transport governed solely by the fractal dimension. We unveil the transport properties through the photon evolution patterns, the mean square displacement and the PĆ³lya number. Here we experimentally investigate quantum transport in fractal networks by performing continuous-time quantum walks in fractal photonic lattices. Despite abundant theoretical studies, experiments in fractal networks remain elusive. In these unconventional systems, many intrinsic features might come into play, including the fractal dimension and the fractal geometry. Fractals are fascinating, not only for their aesthetic appeal but also for allowing the investigation of physical properties in non-integer dimensions.
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