| We consider two localized impurities in a one-dimensional repulsive Bose gas at zero temperature. The latter behaves as a Luttinger liquid at low energy. The zero-point quantum oscillations of the phononic field may induce interaction between the impurities when they are farther away than the healing length. Contrary to the case of a repulsive Fermi gas, this interaction can be either zero or take a universal Casimir-like form depending on the impurity strength. Tunnelling resonances across the double impurity structure slightly modifies this picture. |
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