Tuning Jammed Frictionless Disk Packings from Isostatic to Hyperstatic

We perform extensive computational studies of two-dimensional static bidisperse disk packings using two distinct packing-generation protocols. The first involves thermally quenching equilibrated liquid configurations to zero temperature over a range of thermal quench rates $r$ and initial packing fractions followed by compression and decompression in small steps to reach packing fractions $\phi_J$ at jamming onset. For the second, we seed the system with initial configurations that promote micro- and macrophase-separated packings followed by compression and decompression to $\phi_J$. We find that amorphous, isostatic packings exist over a finite range of packing fractions from $\phi_{\rm min} \le \phi_J \le \phi_{\rm max}$ in the large-system limit, with $\phi_{\rm max} \approx 0.853$. In agreement with previous calculations, we obtain $\phi_{\rm min} \approx 0.84$ for $r > r^*$, where $r^*$ is the rate above which $\phi_J$ is insensitive to rate. We further compare the structural and mechanical properties of isostatic versus hyperstatic packings. The structural characterizations include the contact number, bond orientational order, and mixing ratios of the large and small particles. We find that the isostatic packings are positionally and compositionally disordered, whereas bond-orientational and compositional order increase with contact number for hyperstatic packings. In addition, we calculate the static shear modulus and normal mode frequencies of the static packings to understand the extent to which the mechanical properties of amorphous, isostatic packings are different from partially ordered packings. We find that the mechanical properties of the packings change continuously as the contact number increases from isostatic to hyperstatic.Comment: 11 pages, 15 figure

Fermi-Bose mixture in mixed dimensions

One of the challenging goals in the studies of many-body physics with ultracold atoms is the creation of a topological $p_{x} + ip_{y}$ superfluid for identical fermions in two dimensions (2D). The expectations of reaching the critical temperature $T_c$ through p-wave Feshbach resonance in spin-polarized fermionic gases have soon faded away because on approaching the resonance, the system becomes unstable due to inelastic-collision processes. Here, we consider an alternative scenario in which a single-component degenerate gas of fermions in 2D is paired via phonon-mediated interactions provided by a 3D BEC background. Within the weak-coupling regime, we calculate the critical temperature $T_c$ for the fermionic pair formation, using Bethe-Salpeter formalism, and show that it is significantly boosted by higher-order diagramatic terms, such as phonon dressing and vertex corrections. We describe in detail an experimental scheme to implement our proposal, and show that the long-sought p-wave superfluid is at reach with state-of-the-art experiments.Comment: 12 pages, 6 figures, 2 tables and supplementary materia