# A kinetic regime of hydrodynamic fluctuations and long time tails for a Bjorken expansion

## Abstract

Here we develop a set of kinetic equations for hydrodynamic fluctuations which are equivalent to nonlinear hydrodynamics with noise. The hydro-kinetic equations can be coupled to existing second order hydrodynamic codes to incorporate the physics of these fluctuations, which become dominant near the critical point. We use the hydro-kinetic equations to calculate the modifications of energy momentum tensor by thermal fluctuations from the earliest moments and at late times in Bjorken expansion. The solution to the kinetic equations precisely determines the coefficient of the first fractional power (∝ τ ^{-3/2}) in the energy momentum tensor gradient expansion. Numerically, we find that the contribution to the longitudinal pressure from hydrodynamic fluctuations is comparable to the second order hydrodynamic terms for typical medium parameters used to simulate heavy ion collisions.

- Authors:

- Osaka Univ., Osaka (Japan)
- Stony Brook Univ., Stony Brook, NY (United States); Univ. Heidelberg, Heidelberg (Germany)
- Stony Brook Univ., Stony Brook, NY (United States)

- Publication Date:

- Research Org.:
- The State Univ. of New York, Stony Brook, NY (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1502379

- Grant/Contract Number:
- FG02-88ER40388

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Nuclear Physics. A

- Additional Journal Information:
- Journal Volume: 967; Journal Issue: C; Journal ID: ISSN 0375-9474

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Heavy ion collisions; Thermal fluctuations; Relativistic fluctuating hydrodynamics

### Citation Formats

```
Akamatsu, Yukinao, Mazeliauskas, Aleksas, and Teaney, Derek. A kinetic regime of hydrodynamic fluctuations and long time tails for a Bjorken expansion. United States: N. p., 2017.
Web. doi:10.1016/j.nuclphysa.2017.04.029.
```

```
Akamatsu, Yukinao, Mazeliauskas, Aleksas, & Teaney, Derek. A kinetic regime of hydrodynamic fluctuations and long time tails for a Bjorken expansion. United States. doi:10.1016/j.nuclphysa.2017.04.029.
```

```
Akamatsu, Yukinao, Mazeliauskas, Aleksas, and Teaney, Derek. Mon .
"A kinetic regime of hydrodynamic fluctuations and long time tails for a Bjorken expansion". United States. doi:10.1016/j.nuclphysa.2017.04.029. https://www.osti.gov/servlets/purl/1502379.
```

```
@article{osti_1502379,
```

title = {A kinetic regime of hydrodynamic fluctuations and long time tails for a Bjorken expansion},

author = {Akamatsu, Yukinao and Mazeliauskas, Aleksas and Teaney, Derek},

abstractNote = {Here we develop a set of kinetic equations for hydrodynamic fluctuations which are equivalent to nonlinear hydrodynamics with noise. The hydro-kinetic equations can be coupled to existing second order hydrodynamic codes to incorporate the physics of these fluctuations, which become dominant near the critical point. We use the hydro-kinetic equations to calculate the modifications of energy momentum tensor by thermal fluctuations from the earliest moments and at late times in Bjorken expansion. The solution to the kinetic equations precisely determines the coefficient of the first fractional power (∝ τ-3/2) in the energy momentum tensor gradient expansion. Numerically, we find that the contribution to the longitudinal pressure from hydrodynamic fluctuations is comparable to the second order hydrodynamic terms for typical medium parameters used to simulate heavy ion collisions.},

doi = {10.1016/j.nuclphysa.2017.04.029},

journal = {Nuclear Physics. A},

number = C,

volume = 967,

place = {United States},

year = {2017},

month = {9}

}

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