Nonclassical rotational inertia fraction in a one-dimensional model of a supersolid

We study the rotational inertia of a model of supersolid in the frame of the mean field Gross-Pitaevskii theory in one space dimension. We discuss the ground state of the model and the existence of a nonclassical inertia under rotation that models an annular geometry. An explicit formula for the nonclassical rotational inertia (NCRI) is deduced. It depends on the density profile of the ground state, in full agreement with former theories. We compare the NCRI computed through this theory with direct numerical simulations of rotating one-dimensional systems.