Superfluid density in quasi-one-dimensional systems

The helicity modulus in a quasi-one-dimensional classical XY model is calculated with the Monte Carlo method in connection with recent experiments on liquid He in quasi-one-dimension. The helicity modulus, which is closely related to superfluid density, is strongly reduced by phase slippage. However, the effect of phase slippage is not necessarily probed in a dynamical experiment. Two methods to calculate the helicity modulus that are not affected by phase slippage are proposed: One is to use a boundary condition that prohibits phase slippage and the other is to restrict the Monte Carlo sampling to samples without phase slippage. It is then found that the helicity modulus can survive at such a high temperature as the Kosterlitz-Thouless transition temperature (in films) or the bulk transition temperature (in bars) even in the one-dimensional limit. A remarkable difference in the number of thermal vortex excitations between the cases with a film and a bar is then pointed out. The relevance of the present results to recent experiments on the superfluidity of quasi-one-dimensional He is discussed.