# Temperature dependence of the transition packing fraction of thermal jamming in a harmonic soft sphere system

## TL;DR

This paper proposes that the glass transition packing fraction in soft harmonic spheres decreases with temperature due to energy barrier crossings, combining effective packing fraction shifts and barrier crossing effects to explain simulation data.

## Contribution

It introduces a novel perspective that barrier crossings cause a temperature-dependent decrease in the glass transition packing fraction, extending previous models.

## Key findings

- Barrier crossings lead to a decrease in the glass transition packing fraction with temperature.
- Simulation data can be explained by combining effective packing fraction increase and barrier crossing effects.
- The proposed model aligns with observed discrepancies in soft sphere dynamics.

## Abstract

The glassy dynamics of soft harmonic spheres is often mapped onto the dynamics of hard spheres by considering an effective diameter for the soft particles and therefore an effective packing fraction. While in this approach the thermal fluctuations within valleys of the energy landscape are covered, the crossing of energy barriers from one valley into another usually is neglected. Here we argue - motivated by studies of the glass transition based on explorations of the energy landscape - that the crossing of energy barriers can be attributed by an effective decrease of the glass transition packing fraction with increasing temperature T according to T^{0.2}. Furthermore, we reanalyzing data of soft sphere simulations. Since fitting scaling laws to simulation data always allows for some arbitrariness, we cannot prove based on the simulation data that our idea of a shift of the glass transition packing fraction due to barrier crossings is the only possible way to explain the discrepancies that have been observed previously. However, we show that a possible explanation of the simulation data is given by our approach to characterize the dynamics of soft spheres by both, the previously-considered temperature-dependent effective packing fraction due to the increase of the mean overlap between neighboring particles with stronger thermal fluctuations and the newly introduced increase of the glass transition packing with an increasing probability of barrier crossings.