^{1}, Joseph A. Morrone

^{2}, Kunimasa Miyazaki

^{3}, B. J. Berne

^{2,a)}, David R. Reichman

^{2,a)}and Eran Rabani

^{4,a)}

### Abstract

A comprehensive microscopic dynamical theory is presented for the description of quantum fluids as they transform into glasses. The theory is based on a quantum extension of mode-coupling theory. Novel effects are predicted, such as reentrant behavior of dynamical relaxation times. These predictions are supported by path integral ring polymermolecular dynamics simulations. The simulations provide detailed insight into the factors that govern slow dynamics in glassyquantum fluids. Connection to other recent work on both quantum glasses as well as quantum optimization problems is presented.

The authors acknowledge Francesco Zamponi for useful discussions. K.M. acknowledges support from Kakenhi (Grant Nos. 21015001 and 2154016). B.J.B. acknowledges support from NSF (Grant No. CHE-0910943). D.R.R. would like to thank the NSF ( Grant No. CHE-0719089) for support. E.R. and D.R.R. thank the US-Israel Binational Science Foundation for support.

I. INTRODUCTION

II. A SELF-CONSISTENT QUANTUM MODE-COUPLING THEORY

A. Quantum mode-coupling approach

B. The vertex

C. High and low temperature limits

D. Nonergodic parameter

III. QUANTUM INTEGRAL EQUATION THEORY

IV. RING POLYMERMOLECULAR DYNAMICS

V. SIMULATIONS DETAILS

VI. RESULTS

VII. CONCLUDING REMARKS

### Key Topics

- Polymers
- 29.0
- Diffusion
- 22.0
- Quantum fluctuations
- 20.0
- Glass transitions
- 11.0
- Quantum effects
- 11.0

## Figures

Panel (a): The diffusion constant of particles of type A as a function of the quantumness, Λ*, obtained from the RPMD simulations for a quantum Kob-Anderson LJ binary mixture for two temperatures. Panel (b): Dynamic phase diagram (volume fraction versus quantumness) calculated from the QMCT for a hard-sphere fluid. Panel (c): The mean square displacement of A particles as obtained from the RPMD simulations for the classical case (left frame, Λ* = 0), the trapped regime (middle frame, Λ* = 1.125), and the regime governed by strong quantum fluctuations (right frame, Λ* = 1.1325).

Panel (a): The diffusion constant of particles of type A as a function of the quantumness, Λ*, obtained from the RPMD simulations for a quantum Kob-Anderson LJ binary mixture for two temperatures. Panel (b): Dynamic phase diagram (volume fraction versus quantumness) calculated from the QMCT for a hard-sphere fluid. Panel (c): The mean square displacement of A particles as obtained from the RPMD simulations for the classical case (left frame, Λ* = 0), the trapped regime (middle frame, Λ* = 1.125), and the regime governed by strong quantum fluctuations (right frame, Λ* = 1.1325).

The bead (upper panel) and centroid (lower panel) radial distribution functions of A particles for a classical (Λ* = 0, dashed) and trapped quantum (Λ* = 0.75, solid) regime. The bead distribution suggests less order in the trapped regime compared to a classical simulation while the centroid structure shows an increase in order.

The bead (upper panel) and centroid (lower panel) radial distribution functions of A particles for a classical (Λ* = 0, dashed) and trapped quantum (Λ* = 0.75, solid) regime. The bead distribution suggests less order in the trapped regime compared to a classical simulation while the centroid structure shows an increase in order.

Root-mean-square of the radius of gyration of A particles as a function of Λ* obtained from the RPMD simulations for a quantum Kob-Anderson LJ binary mixture for two temperatures. The radius of gyration is defined as the average distance of the replicas from the polymer center. The results are plotted for temperatures *T** = 0.7 (circles with dashed lines) and *T** = 2.0 (triangles with dotted lines).

Root-mean-square of the radius of gyration of A particles as a function of Λ* obtained from the RPMD simulations for a quantum Kob-Anderson LJ binary mixture for two temperatures. The radius of gyration is defined as the average distance of the replicas from the polymer center. The results are plotted for temperatures *T** = 0.7 (circles with dashed lines) and *T** = 2.0 (triangles with dotted lines).

A series of snapshots taken from simulations at Λ* = 1.125 (left panels) and Λ* = 1.3125 (right panels) with *T** = 0.7. For clarity the full imaginary time path (colored red) is only shown for one particle of type A with all others represented by their centroids. The centroids for the other particles of types A and B are colored green and blue, respectively. The left panels depict configurations which reside in the trapped regime where the ring polymer is essentially localized in one cavity cage whereas in the tunneling regime (right panels) it is frequently spread across two or more cavities in the liquid resulting in more facile motion.

A series of snapshots taken from simulations at Λ* = 1.125 (left panels) and Λ* = 1.3125 (right panels) with *T** = 0.7. For clarity the full imaginary time path (colored red) is only shown for one particle of type A with all others represented by their centroids. The centroids for the other particles of types A and B are colored green and blue, respectively. The left panels depict configurations which reside in the trapped regime where the ring polymer is essentially localized in one cavity cage whereas in the tunneling regime (right panels) it is frequently spread across two or more cavities in the liquid resulting in more facile motion.

The bead vector correlation (see Eq. (48)) for a trapped regime with Λ* = 0.75 (left panel) and regime where quantum fluctuations are pronounced with Λ* = 1.3125 (right panel). The solid lines represent the bead vector correlations between A particles and the dashed ones those between B particles. In both cases *T** = 0.7. In the trapped regime the ring polymer beads show a large positive correlation around *r* = σ which results in a large repulsion when the particles attempt to move past each other. In the other regime the beads align such that the correlation is largely negative which facilitates particle motion.

The bead vector correlation (see Eq. (48)) for a trapped regime with Λ* = 0.75 (left panel) and regime where quantum fluctuations are pronounced with Λ* = 1.3125 (right panel). The solid lines represent the bead vector correlations between A particles and the dashed ones those between B particles. In both cases *T** = 0.7. In the trapped regime the ring polymer beads show a large positive correlation around *r* = σ which results in a large repulsion when the particles attempt to move past each other. In the other regime the beads align such that the correlation is largely negative which facilitates particle motion.

## Tables

Parameters used in our RPMD simulations on the Andersen-Kob Lennard-Jones glass forming system.

Parameters used in our RPMD simulations on the Andersen-Kob Lennard-Jones glass forming system.

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