Universal correlations of trapped one-dimensional impenetrable bosons

We calculate the asymptotic behaviour of the one-body density matrix of one-dimensional impenetrable bosons in finite size geometries. Our approach is based on a modification of the replica method from the theory of disordered systems. We obtain explicit expressions for oscillating terms, similar to fermionic Friedel oscillations. These terms are universal and originate from the strong short-range correlations between bosons in one dimension.