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Phonon Casimir effect is the long-range interaction between impurities incondensed matter systems, mediated by vacuum fluctuations of the phonon field.For pairs of impurities, this interaction has been shown to follow aquasi-power law at zero-temperature and evolve into an exponentially decayingform as the temperature is increased. This work introduces an approach to dealwith systems of more than two impurities, both at zero and finite temperatures.

Many-impurity phonon Casimir effect in atomic chains