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.

Exponential Ramp in the Quadratic Sachdev-Ye-Kitaev Model.

A long period of linear growth in the spectral form factor provides a universal diagnostic of quantum chaos at intermediate times. By contrast, the behavior of the spectral form factor in disordered integrable many-body models is not well understood. Here we study the two-body Sachdev-Ye-Kitaev model and show that the spectral form factor features an exponential ramp, in sharp contrast to the linear ramp in chaotic models. We find a novel mechanism for this exponential ramp in terms of a high-dimensional manifold of saddle points in the path integral formulation of the spectral form factor. This manifold arises because the theory enjoys a large symmetry group. With finite nonintegrable interaction strength, these delicate symmetries reduce to a relative time translation, causing the exponential ramp to give way to a linear ramp.

Application of a three-dimensional (3D) particle tracking method to microfluidic particle focusing.

In this paper, a defocusing-based three-dimensional (3D) particle tracking method is presented and demonstrated for microfluidic particle focusing applications. Previous work in particle focusing has verified particle position in two dimensions (2D) using micro-streak velocimetry, or confocal and stereoscopic setups for 3D tracking. The results obtained from the methodology presented are compared with the theoretical and previously observed trends, and it is shown that the defocusing technique provides a simple and precise tool for determining the 3D locations of cell-sized particles in microscale flows (Re ≤ 100). Although similar methods exist for micro-particle image velocimetry (µ-PIV) applications, this is the first implementation of this technique for particle focusing applications.