Impact of jamming criticality on low-temperature anomalies in structural glasses

Glass transition of quantum hard spheres in high dimensions

We study the equilibrium thermodynamics of quantum hard spheres in the infinite-dimensional limit, determining the boundary between liquid and glass phases in the temperature-density plane by means of the Franz-Parisi potential. We find that as the temperature decreases from high values, the effective radius of the spheres is enhanced by a multiple of the thermal de Broglie wavelength, thus increasing the effective filling fraction and decreasing the critical density for the glass phase. Numerical calculations show that the critical density continues to decrease monotonically as the temperature decreases further, suggesting that the system will form a glass at sufficiently low temperatures for any density. The methods used in this paper can be extended to more general potentials, and also to other transitions such as the Kauzman/Replica Symmetry Breaking (RSB) transition, the Gardner transition, and potentially even jamming.

Depletion of two-level systems in highly stable glasses with different molecular ordering

Recent findings of structural glasses with extremely high kinetic and thermodynamic stability have attracted much attention. The question has been raised as to whether the well-known, low-temperature “glassy anomalies” (attributed to the presence of two-level systems [TLS] and the “boson peak”) persist or not in these ultrastable glasses of much lower configurational entropy. To resolve previous contradictory results, we study a particular type of ultrastable glass, TPD, which can be prepared by physical vapor deposition in a highly-stable state with different degrees of layering and molecular orientation, and also as a conventional glass and in crystalline state. After a thorough characterization of the different samples prepared, we have measured their specific heat down to 0.4 K. Whereas the conventional glass exhibits the typical glassy behaviour and the crystal the expected Debye cubic dependence at very low temperatures, a strong depletion of the TLS contribution is found in both kinds of ultrastable glass, regardless of their layering and molecular ordering.

Hard-sphere jamming through the lens of linear optimization

The jamming transition is ubiquitous. It is present in granular matter, foams, colloids, structural glasses, and many other systems. Yet, it defines a critical point whose properties still need to be fully understood. Recently, a major breakthrough came about when the replica formalism was extended to build a mean-field theory that provides an exact description of the jamming transition of spherical particles in the infinite-dimensional limit. While such theory explains the jamming critical behavior of both soft and hard spheres, investigating the transition in finite-dimensional systems poses very difficult and different problems, in particular from the numerical point of view. Soft particles are modeled by continuous potentials; thus, their jamming point can be reached through efficient energy minimization algorithms. In contrast, the latter methods are inapplicable to hard-sphere (HS) systems since the interaction energy among the particles is always zero by construction. To overcome these difficulties, here we recast the jamming of hard spheres as a constrained optimization problem and introduce the CALiPPSO algorithm, capable of readily producing jammed HS packings without including any effective potential. This algorithm brings a HS configuration of arbitrary dimensions to its jamming point by solving a chain of linear optimization problems. We show that there is a strict correspondence between the force balance conditions of jammed packings and the properties of the optimal solutions of CALiPPSO, whence we prove analytically that our packings are always isostatic and in mechanical equilibrium. Furthermore, using extensive numerical simulations, we show that our algorithm is able to probe the complex structure of the free-energy landscape, finding qualitative agreement with mean-field predictions. We also characterize the algorithmic complexity of CALiPPSO and provide an open-source implementation of it.

Frequency-dependent specific heat in quantum supercooled liquids: A mode-coupling study

Frequency-dependence of specific heat in supercooled hard sphere liquid is computed using quantum mode-coupling theory (QMCT). Mode-coupling equations are solved using a recently proposed perturbative method that allows us to study relaxation in the moderate quantum regime where quantum effects assist liquid to glass transition. Zwanzig's formulation is used to compute the frequency-dependent specific heat in the supercooled state using dynamical information from QMCT. Specific heat shows strong variation as the quantumness of the liquid is changed, which becomes more significant as density is increased. It is found that, near the transition point, different dynamical modes contribute to specific heat in classical and quantum liquids.

Emergent solidity of amorphous materials as a consequence of mechanical self-organisation

Amorphous solids have peculiar properties distinct from crystals. One of the most fundamental mysteries is the emergence of solidity in such nonequilibrium, disordered state without the protection by long-range translational order. A jammed system at zero temperature, although marginally stable, has solidity stemming from the space-spanning force network, which gives rise to the long-range stress correlation. Here, we show that such nonlocal correlation already appears at the nonequilibrium glass transition upon cooling. This is surprising since we also find that the system suffers from giant anharmonic fluctuations originated from the fractal-like potential energy landscape. We reveal that it is the percolation of the force-bearing network that allows long-range stress transmission even under such circumstance. Thus, the emergent solidity of amorphous materials is a consequence of nontrivial self-organisation of the disordered mechanical architecture. Our findings point to the significance of understanding amorphous solids and nonequilibrium glass transition from a mechanical perspective.

Zero-gravity thermal convection in granular gases

Previous experimental and theoretical evidence has shown that convective flow may appear in granular fluids if subjected to a thermal gradient and gravity (Rayleigh-Bénard-type convection). In contrast to this, we present here evidence of gravity-free thermal convection in a granular gas, with no presence of external thermal gradients either. Convection is here maintained steady by internal gradients due to dissipation and thermal sources at the same temperature. The granular gas is composed by identical disks and is enclosed in a rectangular region. Our results are obtained by means of an event-driven algorithm for inelastic hard disks.

Depletion of Two-Level Systems in Ultrastable Computer-Generated Glasses

Amorphous solids exhibit quasiuniversal low temperature anomalies whose origin has been ascribed to localized tunneling defects. Using an advanced Monte Carlo procedure, we create in silico glasses spanning from hyperquenched to ultrastable glasses. Using a multidimensional path-finding protocol, we locate tunneling defects with energy splittings smaller than k_{B}T_{Q}, with T_{Q} the temperature below which quantum effects are relevant (T_{Q}≈1  K in most experiments). We find that as the stability of a glass increases, its energy landscape as well as the manner in which it is probed tend to deplete the density of tunneling defects, as observed in recent experiments. We explore the real-space nature of tunneling defects, and find that they are mostly localized to a few atoms, but are occasionally dramatically delocalized.

Vibrational density of states and specific heat in glasses from random matrix theory

The low-temperature properties of glasses present important differences with respect to crystalline matter. In particular, models such as the Debye model of solids, which assume the existence of an underlying regular lattice, predict that the specific heat of solids varies with the cube of temperature at low temperatures. Since the 1970s at least, it is a well-established experimental fact that the specific heat of glasses is instead just linear in T at T∼1 K and presents a pronounced peak when normalized by T^{3}, known as the boson peak. Here we present an approach which suggests that the vibrational and thermal properties of amorphous solids are affected by the random-matrix part of the vibrational spectrum. The model is also able to reproduce, for the first time, the experimentally observed inverse proportionality between the boson peak in the specific heat and the shear modulus.