Exact local correlations and full counting statistics for arbitrary states of the one-dimensional interacting Bose gas. (arXiv:1802.02115v1 [cond-mat.quant-gas])

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.

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