A tentative replica theory of glassy Helium 4

TL;DR

This paper introduces a quantum replica approach to estimate the glass transition in Helium 4, highlighting how quantum fluctuations influence glass formation and providing quantitative insights at high densities.

Contribution

It develops a semiclassical quantum replica method to analyze the glass transition in Helium 4, addressing quantum effects in the process.

Findings

Quantum fluctuations promote glass formation in Helium 4.

Quantitative estimates of the glass transition at high density.

Discussion of challenges in low-density, low-temperature regimes.

Abstract

We develop a quantum replica method for interacting particle systems and use it to estimate the location of the glass transition line in Helium 4. Although we do not fully succeed in taking into account all quantum effects, we make a thorough semiclassical analysis. We confirm previous suggestions that quantum fluctuations promote the formation of the glass and give a quantitative estimate of this effect at high density. Finally, we discuss the difficulties that are met when one tries to extend the calculation to the region of low densities and low temperatures, where quantum effects are strong and the semiclassical expansion breaks down.