Slow Dynamics and the Geometry of Jammed Packings
Abstract
Saddle points in the energy landscape of granular packings dominate the discrete steepest descent dynamics and ultimately determine the path that an out of mechanical equilibrium packing will follow and the resulting stable minimum that it will find. The saddle points that ultimately determine the resulting minima tend to be low-index saddle points. For models with an analytic energy landscape, such as the p-spin model, the steepest descent minimization path is affected by higher-index saddle points, which pull the system towards saddle points of decreasing index before arriving at the minima. Here, we examine the steepest descent minimization path of granular packings and compare them to the p-spin model. We show that the granular packing steepest descent minimization paths act like their smooth energy landscape counterparts and get attracted by saddle points. The index versus time curves for all models follow a shifted, stretched exponential. We further show that the shape parameter for the granular packings is unchanged when the energy landscape is modified to become analytic (Gaussian potential in a harmonic well) or non-local (Mari-Krzakala-Kurchan). The p-spin, on the other hand, has a significantly larger shape parameter. The reason is not due to the dimensionality, packing fraction, nonanalyticity, or the locality of the Hamiltonian of the models. The exact reason for the discrepancy in the shape parameter is \st{still} an unsolved mystery.
Related
- Near-surface colloidal dynamics in jammed and slipping microgel suspensions
- Conservation Laws and Slow Dynamics Determine the Universality Class of Interfaces in Active Matter
- Linear stability and viscoelastic response in weakly jammed frictional granular systems
- Slow dynamics in concrete: Effects of temperature, strength variation, and microcracking damage
- Weakly Nonlinear Analysis of Jammed Solids
BibTeX
@misc{bautista2026slow,
title = {{Slow Dynamics and the Geometry of Jammed Packings}},
author = {Eddie Bautista and Eric Corwin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11036},
eprint = {2609.11036},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11036},
}
RIS
TY - UNPB
TI - Slow Dynamics and the Geometry of Jammed Packings
AU - Eddie Bautista
AU - Eric Corwin
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11036
UR - https://arxiv.org/abs/2609.11036
AB - Saddle points in the energy landscape of granular packings dominate the discrete steepest descent dynamics and ultimately determine the path that an out of mechanical equilibrium packing will follow and the resulting stable minimum that it will find. The saddle points that ultimately determine the resulting minima tend to be low-index saddle points. For models with an analytic energy landscape, such as the p-spin model, the steepest descent minimization path is affected by higher-index saddle points, which pull the system towards saddle points of decreasing index before arriving at the minima. Here, we examine the steepest descent minimization path of granular packings and compare them to the p-spin model. We show that the granular packing steepest descent minimization paths act like their smooth energy landscape counterparts and get attracted by saddle points. The index versus time curves for all models follow a shifted, stretched exponential. We further show that the shape parameter for the granular packings is unchanged when the energy landscape is modified to become analytic (Gaussian potential in a harmonic well) or non-local (Mari-Krzakala-Kurchan). The p-spin, on the other hand, has a significantly larger shape parameter. The reason is not due to the dimensionality, packing fraction, nonanalyticity, or the locality of the Hamiltonian of the models. The exact reason for the discrepancy in the shape parameter is \st{still} an unsolved mystery.
ER -