Leggett's bound for amorphous solids

TL;DR

This paper explores the theoretical upper bounds on superfluidity in amorphous solids using density profiles and simulations, suggesting that observed superfluid fractions in Helium 4 are due to non-equilibrium states rather than stable glasses.

Contribution

It combines theoretical bounds with simulations to analyze superfluidity in amorphous solids, providing insights into the nature of superfluid Helium 4 after rapid quenching.

Findings

Leggett's bound suggests similar superfluidity in glasses and crystals with the same Lindemann ratio.

Simulations show rapid crystallization of Helium 4 without intermediate glassy states.

Experimental superfluidity in Helium 4 likely arises from non-equilibrium conditions.

Abstract

We investigate the constraints on the superfluid fraction of an amorphous solid following from an upper bound derived by Leggett. In order to accomplish this, we use as input density profiles generated for amorphous solids in a variety of different manners including by investigating Gaussian fluctuations around classical results. These rough estimates suggest that, at least at the level of the upper bound, there is not much difference in terms of superfluidity between a glass and a crystal characterized by the same Lindemann ratio. Moreover, we perform Path Integral Monte Carlo simulations of distinguishable Helium 4 rapidly quenched from the liquid phase to very lower temperature, at the density of the freezing transition. We find that the system crystallizes very quickly, without any sign of intermediate glassiness. Overall our results suggest that the experimental observations of large superfluid fractions in Helium 4 after a rapid quench correspond to samples evolving far from equilibrium, instead of being in a stable glass phase. Other scenarios and comparisons to other results on the super-glass phase are also discussed.