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For a hard-core Bose gas on a one-dimensional lattice we find characteristicoscillations in the density-density correlation function. Their wavelengthdiverges as the system undergoes a continuous transition from an incommensurateto a Mott insulating phase. The associated static structure factor vanishes asthe Mott insulating phase is approached. The qualitative picture is unchangedwhen a weak confinig potential is applied to the system.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Let

Density fluctuations of a hard-core Bose gas in a one-dimensional lattice near the Mott insulating phase