# Multifield stochastic particle production: beyond a maximum entropy ansatz

## Abstract

We explore non-adiabatic particle production for N {sub 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 {sub f}=1 and N {sub f}=2 cases. We also present results for the general N {sub 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 and Baumann (2015) and the underlying statistical distribution of the self and cross couplings. We provide and justify a simple tomore »

- Authors:

- Physics and Astronomy Department, Rice University, 6100 Main Street, Houston, TX 77005 (United States)

- Publication Date:

- OSTI Identifier:
- 22667697

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Cosmology and Astroparticle Physics

- Additional Journal Information:
- Journal Volume: 2017; Journal Issue: 09; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1475-7516

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AMPLITUDES; ASYMPTOTIC SOLUTIONS; COMPARATIVE EVALUATIONS; COUPLINGS; DELTA FUNCTION; DISTRIBUTION; EFFECTIVE MASS; ENTROPY; INTERACTIONS; OCCUPATION NUMBER; PARTICLE PRODUCTION; SCALAR FIELDS; SCATTERING; STOCHASTIC PROCESSES; TIME DEPENDENCE

### Citation Formats

```
Amin, Mustafa A., Garcia, Marcos A.G., Xie, Hong-Yi, and Wen, Osmond, E-mail: mustafa.a.amin@gmail.com, E-mail: marcos.garcia@rice.edu, E-mail: hxie39@wisc.edu, E-mail: ow4@rice.edu.
```*Multifield stochastic particle production: beyond a maximum entropy ansatz*. United States: N. p., 2017.
Web. doi:10.1088/1475-7516/2017/09/015.

```
Amin, Mustafa A., Garcia, Marcos A.G., Xie, Hong-Yi, & Wen, Osmond, E-mail: mustafa.a.amin@gmail.com, E-mail: marcos.garcia@rice.edu, E-mail: hxie39@wisc.edu, E-mail: ow4@rice.edu.
```*Multifield stochastic particle production: beyond a maximum entropy ansatz*. United States. doi:10.1088/1475-7516/2017/09/015.

```
Amin, Mustafa A., Garcia, Marcos A.G., Xie, Hong-Yi, and Wen, Osmond, E-mail: mustafa.a.amin@gmail.com, E-mail: marcos.garcia@rice.edu, E-mail: hxie39@wisc.edu, E-mail: ow4@rice.edu. Fri .
"Multifield stochastic particle production: beyond a maximum entropy ansatz". United States. doi:10.1088/1475-7516/2017/09/015.
```

```
@article{osti_22667697,
```

title = {Multifield stochastic particle production: beyond a maximum entropy ansatz},

author = {Amin, Mustafa A. and Garcia, Marcos A.G. and Xie, Hong-Yi and Wen, Osmond, E-mail: mustafa.a.amin@gmail.com, E-mail: marcos.garcia@rice.edu, E-mail: hxie39@wisc.edu, E-mail: ow4@rice.edu},

abstractNote = {We explore non-adiabatic particle production for N {sub 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 {sub f}=1 and N {sub f}=2 cases. We also present results for the general N {sub 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 and 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 {sub f}>> 1.},

doi = {10.1088/1475-7516/2017/09/015},

journal = {Journal of Cosmology and Astroparticle Physics},

issn = {1475-7516},

number = 09,

volume = 2017,

place = {United States},

year = {2017},

month = {9}

}