# Multifield Stochastic Particle Production: Beyond a Maximum Entropy Ansatz

## TL;DR

This paper develops a framework for calculating particle production rates in multi-field scalar systems with stochastic interactions, extending previous maximum entropy approaches and providing analytic results validated by numerical simulations.

## Contribution

It introduces a new analytical approach for multi-field stochastic particle production, connecting it to maximum entropy assumptions and exploring deviations for different parameter regimes.

## Key findings

- Analytic formulas for particle production in 1 and 2 fields
- Agreement between analytic results and numerical simulations
- Deviations from maximum entropy ansatz when parameters differ significantly

## Abstract

We explore non-adiabatic particle production for $N_{\rm f}$ coupled scalar fields in a time-dependent background with stochastically varying effective masses, cross-couplings and intervals between interactions. Under the assumption of weak scattering per interaction, we provide a framework for calculating the typical particle production rates after a large number of interactions. After setting up the framework, for analytic tractability, we consider interactions (effective masses and cross couplings) characterized by series of Dirac-delta functions in time with amplitudes and locations drawn from different distributions. Without assuming that the fields are statistically equivalent, we present closed form results (up to quadratures) for the asymptotic particle production rates for the $N_{\rm f}=1$ and $N_{\rm f}=2$ cases. We also present results for the general $N_{\rm f} >2$ case, but with more restrictive assumptions. We find agreement between our analytic results and direct numerical calculations of the total occupation number of the produced particles, with departures that can be explained in terms of violation of our assumptions. We elucidate the precise connection between the maximum entropy ansatz (MEA) used in Amin & Baumann (2015) and the underlying statistical distribution of the self and cross couplings. We provide and justify a simple to use (MEA-inspired) expression for the particle production rate, which agrees with our more detailed treatment when the parameters characterizing the effective mass and cross-couplings between fields are all comparable to each other. However, deviations are seen when some parameters differ significantly from others. We show that such deviations become negligible for a broad range of parameters when $N_{\rm f}\gg 1$.