# Duration of Classicality of an inhomogeneous quantum field with repulsive contact self-interactions

## TL;DR

This paper compares quantum and classical evolutions of a highly degenerate quantum field with repulsive contact interactions, showing quantum modes grow exponentially while classical fields remain stable, and calculates when classical approximation fails.

## Contribution

It demonstrates the divergence between quantum and classical dynamics in inhomogeneous fields with self-interactions and quantifies the duration of classicality.

## Key findings

- Quantum modes grow exponentially under certain conditions.
- Classical approximation remains stable where quantum fields do not.
- The paper estimates the time scale for classical description validity.

## Abstract

Quantum fields with large degeneracy are often approximated as classical fields. Here, we show how quantum and classical evolution of a highly degenerate quantum field with repulsive contact self-interactions differ from each other. Initially, the field is taken to be homogeneous except for a small plane wave perturbations in only one mode. In quantum field theory, modes satisfying both momentum and energy conservation of the quasi-particles, grow exponentially with time. However, in the classical field approximation, the system is stable. We calculate the time scale after which the classical field description becomes invalid.