On the range of validity of the static fluctuation approximation (SFA) in the description of a 1D trapped Bose gas

We demonstrate the instability of the static fluctuation approximation (SFA) in the description of a one-dimensional (1D) trapped hard sphere (HS) Bose gas in the strongly interacting regime. In particular, it is shown that the energy fluctuations 〈ΔE2〉 do not stabilize. It is therefore argued that SFA is not suitable for strongly interacting systems.