## SciPost Submission Page

# Dynamical Instantons and Activated Processes in Mean-Field Glass Models

### by V. Ros, G. Biroli, C. Cammarota

### Submission summary

As Contributors: | Valentina Ros |

Arxiv Link: | https://arxiv.org/abs/2006.08399v2 (pdf) |

Date submitted: | 2020-07-08 02:00 |

Submitted by: | Ros, Valentina |

Submitted to: | SciPost Physics |

Discipline: | Physics |

Subject area: | Statistical and Soft Matter Physics |

Approach: | Theoretical |

### Abstract

We focus on the energy landscape of simple mean-field models of glasses and analyze activated barrier-crossing by combining the Kac-Rice method for high-dimensional Gaussian landscapes with dynamical field theory. In particular, we consider Langevin dynamics at low temperature in the energy landscape of the spherical $p$-spin model. We select as initial condition for the dynamics one of the many unstable index-1 saddles in the vicinity of a reference local minimum. We show that the associated dynamical mean-field equations admit two solutions: one corresponds to falling back to the original reference minimum, and the other to reaching a new minimum past the barrier. By varying the saddle we scan and characterize the properties of such minima reachable by activated barrier-crossing. Finally, using time-reversal transformations, we construct the two-point function dynamical instanton of the corresponding activated process.