Controlling the Short-Range Order and Packing Densities of Many-Particle Systems

Questions surrounding the spatial disposition of particles in various condensed-matter systems continue to pose many theoretical challenges. This paper explores the geometric availability of amorphous many-particle configurations that conform to a given pair correlation function g(r). Such a study is required to observe the basic constraints of non-negativity for g(r) as well as for its structure factor S(k). The hard sphere case receives special attention, to help identify what qualitative features play significant roles in determining upper limits to maximum amorphous packing densities. For that purpose, a five-parameter test family of g's has been considered, which incorporates the known features of core exclusion, contact pairs, and damped oscillatory short-range order beyond contact. Numerical optimization over this five-parameter set produces a maximum-packing value for the fraction of covered volume, and about 5.8 for the mean contact number, both of which are within the range of previous experimental and simulational packing results. However, the corresponding maximum-density g(r) and S(k) display some unexpected characteristics. A byproduct of our investigation is a lower bound on the maximum density for random sphere packings in $d$ dimensions, which is sharper than a well-known lower bound for regular lattice packings for d >= 3.Comment: Appeared in Journal of Physical Chemistry B, vol. 106, 8354 (2002). Note Errata for the journal article concerning typographical errors in Eq. (11) can be found at http://cherrypit.princeton.edu/papers.html However, the current draft on Cond-Mat (posted on August 8, 2002) is correct

Static Structural Signatures of Nearly Jammed Disordered and Ordered Hard-Sphere Packings: Direct Correlation Function

Dynamical signatures are known to precede jamming in hard-particle systems, but static structural signatures have proven more elusive. The observation that compressing hard-particle packings towards jamming causes growing hyperuniformity has paved the way for the analysis of jamming as an "inverted critical point" in which the direct correlation function $c(r)$ diverges. We establish quantitative relationships between various singularities in $c(r)$ and the total correlation function $h(r)$ that provide a concrete means of identifying features that must be expressed in $c(r)$ if one hopes to reproduce details in the pair correlation function accurately. We also analyze systems of three-dimensional monodisperse hard-spheres of diameter $D$ as they approach ordered and disordered jammed configurations. For the latter, we use the Lubachevsky-Stillinger (LS) and Torquato-Jiao (TJ) packing algorithms, which both generate disordered packings, but can show perceptible structural differences. We identify a short-ranged scaling $c(r) \propto -1/r$ as $r \rightarrow 0$ and show that this, along with the developing delta function at $c(D)$, is a consequence of the growing long-rangedness in $c(r)$. Near the freezing density, we identify qualitative differences in the structure factor $S(k)$ as well as $c(r)$ between TJ- and LS-generated configurations and link them to differences in the protocols' packing dynamics. Configurations from both algorithms have structure factors that approach zero in the low-wavenumber limit as jamming is approached and are shown to exhibit a corresponding power-law decay in $c(r)$ for large $r$ as a consequence. Our work advances the notion that static signatures are exhibited by hard-particle packings as they approach jamming and underscores the utility of the direct correlation function as a means of monitoring for an incipient rigid network

Classical many-particle systems with unique disordered ground states

Classical ground states (global energy-minimizing configurations) of many-particle systems are typically unique crystalline structures, implying zero enumeration entropy of distinct patterns (aside from trivial symmetry operations). By contrast, the few previously known disordered classical ground states of many-particle systems are all high-entropy (highly degenerate) states. Here we show computationally that our recently-proposed "perfect-glass" many-particle model [Sci. Rep., 6, 36963 (2016)] possesses disordered classical ground states with a zero entropy: a highly counterintuitive situation. For all of the system sizes, parameters, and space dimensions that we have numerically investigated, the disordered ground states are unique such that they can always be superposed onto each other or their mirror image. At low energies, the density of states obtained from simulations matches those calculated from the harmonic approximation near a single ground state, further confirming ground-state uniqueness. Our discovery provides singular examples in which entropy and disorder are at odds with one another. The zero-entropy ground states provide a unique perspective on the celebrated Kauzmann-entropy crisis in which the extrapolated entropy of a supercooled liquid drops below that of the crystal. We expect that our disordered unique patterns to be of value in fields beyond glass physics, including applications in cryptography as pseudo-random functions with tunable computational complexity