A Tentative Replica Theory of Glassy Helium 4

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.

Efficiency of quantum vs. classical annealing in nonconvex learning problems

“…The physical interpretation of these results is that quantum fluctuations lower the energy of a cluster proportionally to its size or, in other words, that quantum fluctuations allow the system to lower its kinetic energy by delocalizing; see refs. 25 , 26 , and 39 for related results. Along the process of reduction of the transverse field, we do not observe any phase transition which could induce a critical slowing down of the QA process, and we expect SQA and QA to behave similarly ( 11 , 36 ).…”

“…The large deviation analysis that has unveiled the existence of the rare dense regions has led to several novel algorithms, including a Monte Carlo scheme defined over an appropriate objective function ( 20 ) that bears close similarities with a quantum Monte Carlo (QMC) technique based on the Suzuki–Trotter transformation ( 5 ). Motivated by this analytical mapping and by the geometrical structure of the dense and degenerate ground states which is expected to favor zero-temperature kinetic processes ( 25 , 26 ), we have conducted a full analytical and numerical statistical physics study of the QA problem, reaching the conclusion that in the quantum limit, the QMC process, i.e., simulated QA (SQA), can equilibrate efficiently, while the classical SA gets stuck in high-energy metastable states. These results generalize to multilayered networks.…”

Static and dynamic structure factor in solid 4 He: Absence of a glassy phase

“…The signal is almost entirely due to inelastic scattering. This makes the detection of the conjectured amorphous phase [1] impossible in a total scattering experiment. It also suggests that estimates of an amorphous fraction based on the magnitude of diffuse scattering can be misleading.…”

“…However, to the best of our knowledge, this fact has not been verified experimentally. A metastable glass phase has been recently predicted [1], albeit at higher temperatures and pressures.…”