We study finite two-dimensional spin lattices with definite geometry (spin billiards) demonstrating the display of collective integrable or chaotic dynamics depending on their shape.We show that such systems can be quantum simulated by ultra-cold atoms in optical lattices and discuss how to identify their dynamical features in a realistic experimental setup.Possible applications are the simulation of quantum information tasks in mesoscopic devices.
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Montangero et al. (2009) studied this question.
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