# Pre-asymptotic dynamics of the infinite size Neumann (p=2 spherical) model

## TL;DR

This paper investigates the pre-asymptotic dynamics of the infinite size Neumann (p=2 spherical) model, providing detailed analysis and exploring the potential for describing the steady state using a Generalised Gibbs Ensemble.

## Contribution

It extends previous work by analyzing the pre-asymptotic behavior and discussing the steady state description in the classical disordered p=2 spherical model.

## Key findings

- Detailed characterization of pre-asymptotic dynamics
- Discussion on the applicability of Generalised Gibbs Ensemble
- Summary of asymptotic results from prior work

## Abstract

In this contribution we further study the classical disordered p=2 spherical model with Hamiltonian dynamics, or in integrable systems terms, the Neumann model, in the infinite size limit. We summarise the asymptotic results that some of us presented in a recent publication, and we deepen the analysis of the pre-asymptotic dynamics. We also discuss the possible description of the asymptotic steady state with a Generalised Gibbs Ensemble.