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We present analytical results for the nonlocal pair correlations inone-dimensional bosonic systems with repulsive contact interactions that areuniformly valid from the classical regime of high temperatures down to weakquantum degeneracy entering the regime of ultralow temperatures. By using theinformation contained in the short-time approximations of the full many-bodypropagator, we derive results that are nonperturbative in the interactionparameter while covering a wide range of temperatures and densities. For thecase of three particles we give a simple formula for arbitrary couplings thatis exact in the dilute limit while remaining valid up to the regime where thethermal de Broglie wavelength $\lambda_T$ is of the order of the characteristiclength $L$ of the system. We then show how to use this result to findanalytical expressions for the nonlocal correlations for arbitrary but fixedparticle numbers $N$ including finite-size corrections. Neglecting the latterin the thermodynamic limit provides an expansion in the quantum degeneracyparameter $N\lambda_T/L$. We compare our analytical results with numericalBethe ansatz calculations, finding excellent agreement.

Nonlocal pair correlations in Lieb-Liniger gases: A unified nonperturbative approach from weak degeneracy to high temperatures