Session L53: Invited Session: Advances in Glassy Systems Across Many Scales

Thermodynamic glass transitions in three dimensional glasses

The physics associated to the glass transition controls the dramatic evolution of transport coefficients in systems as diverse as dense liquids, polymers, colloids, but also granular particles and active matter. The experimental liquid-glass transition in equilibrium fluids is characterized by several phenomenological crossovers, but glasses can form without crossing any sharp singularity. I will present multiple evidences suggesting that the glass formation process is underlied by equilibrium phase transitions. Combining numerical tools developed to study ordinary phase transitions to recent theoretical analytical progress I will demonstrate that studies of the glass transition have entered a new phase, where the relevant order parameter, thermodynamic fluctuations and phase transformations can be directly analysed in finite dimensional model glasses.   

Exact computation of the critical exponents of the jamming transition

The jamming transition marks the emergence of rigidity in a system of amorphous and athermal grains. It is characterized by a divergent correlation length of the force-force correlation and non-trivial critical exponents that are independent of spatial dimension, suggesting that a mean field theory can correctly predict their values. I will discuss a mean field approach to the problem based on the exact solution of the hard sphere model in infinite dimension. An unexpected analogy with the Sherrington-Kirkpatrick spin glass model emerges in the solution: as in the SK model, the glassy states turn out to be marginally stable, and are described by a Parisi equation. Marginal stability has a deep impact on the critical properties of the jamming transition and allows one to obtain analytic predictions for the critical exponents. The predictions are consistent with a recently developed scaling theory of the jamming transition, and with numerical simulations. Finally, I will briefly discuss some possible extensions of this approach to other open issues in the theory of glasses.   

Revealing the critical behavior of jamming: high precision simulations of large,exactly isostatic packings

Recently, an exact first-principle theory of jamming criticality in infinite dimensions has emerged. However, it is an understatement to say that $d=\infty$ is very far from the physically relevant dimensions of $d=2$ and 3. In this work we probe how meaningful these infinite-dimensional predictions are in low dimensions by examining the scaling of the weak contact forces at jamming. We use a combination of 1) newly developed GPU techniques implementing quad-precision simulations and 2) an algorithm to calculate extremely accurate interparticle forces for isostatic packings to probe the behavior of systems of very-many particles in dimensions $d=2-6$. We find that the weak forces arise from two populations, one associated with localized excitations and the other with extended excitations. We find that the fraction of localized excitations decreases with increasing dimension. Surprisingly, the infinite-dimensional predictions hold \textit{exactly} all the way down to $d=2$ for the extended excitations.   

Seeking Quantum Speedup Through Spin Glasses: Evidence of Tunneling?

Quantum annealing machines use a non-mainstream method known as adiabatic quantum annealing to perform optimization tasks. Very recently, tests performed by different research teams on the D-Wave Two quantum annealer using spin glasses as a benchmark have shown that, although the machine indeed appears to tap into quantum effects, it shows no speedup over traditional computing architectures. We present results that suggest that the benchmark instances used are too simple to detect quantum speedup and based on insights from spin-glass physics outline strategies to develop hard instance classes. With our choice of benchmark strategy, we show that the D-Wave Two quantum annealer does not outperform current computer technologies, mainly due to noise and calibration errors of the device. However, our results do indicate that quantum tunneling might be present.\\[4pt] Work done in collaboration with F. Hamze (D-Wave Systems, Inc.), Zheng Zhu (Texas A\&M University) and Andrew J. Ochoa (Texas A\&M University). H.G.K. acknowledges support from the NSF (Grant No. DMR-1151387).