We study numerically how conservation laws affect the optical conductivitysigma(w) of a slightly doped one-dimensional Mott insulator. We investigate aregime where the average distance between charge excitations is large comparedto their thermal de Broglie wave length and a classical description ispossible. Due to conservation laws, the dc-conductivity is infinite and theDrude weight D is finite even at finite temperatures. Our numerical resultstest and confirm exact theoretical predictions for D both for integrable andnon-integrable models. Small deviations from integrability induce slowlydecaying modes and, consequently, low-frequency peaks in sigma(w) which can bedescribed by a memory matrix approach.
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