Exact local correlations and full counting statistics for arbitrary states of the one-dimensional interacting Bose gas

Understand

We derive exact analytic expressions for the $n$-body local correlations in the one-dimensional Bose gas with contact repulsive interactions (Lieb-Liniger model) in the thermodynamic limit.

• Our results are valid for arbitrary states of the model, including ground and thermal states, stationary states after a quantum quench, and non-equilibrium steady states arising in transport settings.
• Calculations for these states are explicitly presented and physical consequences are critically discussed.
• We also show that the $n$-body local correlations are directly related to the full counting statistics for the particle-number fluctuations in a short interval, for which we provide an explicit analytic result.