Jammed particulate systems are inherently nonharmonic

Normal mode analysis in the harmonic approximation underlies most of solid-state physics and applies well to both ordered and dis- ordered systems. Naturally, researches apply this analysis to jammed particulate systems, such as granular media, colloids, and foams, that interact via one-sided interactions, which are nonzero only when particles overlap. However, we find that systems with one-sided repulsive interactions possess no linear, harmonic response regime for large systems ($N\rightarrow\infty$) at finite pressures $P$, and for all $N$ near jamming onset $P\rightarrow 0$. We perform simulations on 2D frictionless bidisperse mechanically stable disk packings over a range of packing fractions $\Delta \phi = \phi-\phi_J$ above jamming onset $\phi_J$. We apply perturbations with amplitude $\delta$ to the packings along each eigen-direction from the dynamical matrix and determine whether the response of the system evolving at constant energy remains in the original eigenmode of the perturbation. For $\delta > \delta_c$, a single contact breaks and fluctuations abruptly spread to all discrete harmonic modes. As $\delta$ increases further all harmonic modes disappear into a continuous frequency band. We find that $\delta_c \sim \Delta \phi/N$, and thus jammed particulate systems are inherently nonharmonic with no linear vibrational response regime as $N\rightarrow \infty$ over the full range of $\Delta \phi$, and as $\Delta \phi \rightarrow 0$ at any $N$. This breakdown of harmonic behavior dramatically affects all aspects of system response including heat capacity, density of states, elastic moduli, and energy propagation.