# Off-equilibrium infrared structure of self-interacting scalar fields: Universal scaling, vortex-antivortex superfluid dynamics, and Bose-Einstein condensation

## Abstract

Here, we map the infrared dynamics of a relativistic single-component (N=1) interacting scalar field theory to that of nonrelativistic complex scalar fields. The Gross-Pitaevskii (GP) equation, describing the real-time dynamics of single-component ultracold Bose gases, is obtained at first nontrivial order in an expansion proportional to the powers of λΦ ^{2}/m ^{2} where λ, Φ, and m are the coupling constant, the scalar field, and the particle mass respectively. Our analytical studies are corroborated by numerical simulations of the spatial and momentum structure of overoccupied scalar fields in (2+1)-dimensions. Universal scaling of infrared modes, vortex-antivortex superfluid dynamics, and the off-equilibrium formation of a Bose-Einstein condensate are observed. Our results for the universal scaling exponents are in agreement with those extracted in the numerical simulations of the GP equation. As in these simulations, we observe coarsening phase kinetics in the Bose superfluid with strongly anomalous scaling exponents relative to that of vertex resummed kinetic theory. Our relativistic field theory framework further allows one to study more closely the coupling between superfluid and normal fluid modes, specifically the turbulent momentum and spatial structure of the coupling between a quasiparticle cascade to the infrared and an energy cascade to the ultraviolet. We outlinemore »

- Authors:

- Shandong Univ., Shandong (China)
- Univ. of Washington, Seattle, WA (United States)
- Brookhaven National Lab. (BNL), Upton, NY (United States)
- Univ. of Science and Technology of China, Anhui (China)

- Publication Date:

- Research Org.:
- Brookhaven National Laboratory (BNL), Upton, NY (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)

- OSTI Identifier:
- 1462431

- Alternate Identifier(s):
- OSTI ID: 1436897

- Report Number(s):
- BNL-207870-2018-JAAM

Journal ID: ISSN 2469-9926; PLRAAN

- Grant/Contract Number:
- SC0012704; FG02-97ER41014

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physical Review A

- Additional Journal Information:
- Journal Volume: 97; Journal Issue: 5; Journal ID: ISSN 2469-9926

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS

### Citation Formats

```
Deng, Jian, Schlichting, Soeren, Venugopalan, Raju, and Wang, Qun.
```*Off-equilibrium infrared structure of self-interacting scalar fields: Universal scaling, vortex-antivortex superfluid dynamics, and Bose-Einstein condensation*. United States: N. p., 2018.
Web. doi:10.1103/PhysRevA.97.053606.

```
Deng, Jian, Schlichting, Soeren, Venugopalan, Raju, & Wang, Qun.
```*Off-equilibrium infrared structure of self-interacting scalar fields: Universal scaling, vortex-antivortex superfluid dynamics, and Bose-Einstein condensation*. United States. doi:10.1103/PhysRevA.97.053606.

```
Deng, Jian, Schlichting, Soeren, Venugopalan, Raju, and Wang, Qun. Fri .
"Off-equilibrium infrared structure of self-interacting scalar fields: Universal scaling, vortex-antivortex superfluid dynamics, and Bose-Einstein condensation". United States.
doi:10.1103/PhysRevA.97.053606.
```

```
@article{osti_1462431,
```

title = {Off-equilibrium infrared structure of self-interacting scalar fields: Universal scaling, vortex-antivortex superfluid dynamics, and Bose-Einstein condensation},

author = {Deng, Jian and Schlichting, Soeren and Venugopalan, Raju and Wang, Qun},

abstractNote = {Here, we map the infrared dynamics of a relativistic single-component (N=1) interacting scalar field theory to that of nonrelativistic complex scalar fields. The Gross-Pitaevskii (GP) equation, describing the real-time dynamics of single-component ultracold Bose gases, is obtained at first nontrivial order in an expansion proportional to the powers of λΦ2/m2 where λ, Φ, and m are the coupling constant, the scalar field, and the particle mass respectively. Our analytical studies are corroborated by numerical simulations of the spatial and momentum structure of overoccupied scalar fields in (2+1)-dimensions. Universal scaling of infrared modes, vortex-antivortex superfluid dynamics, and the off-equilibrium formation of a Bose-Einstein condensate are observed. Our results for the universal scaling exponents are in agreement with those extracted in the numerical simulations of the GP equation. As in these simulations, we observe coarsening phase kinetics in the Bose superfluid with strongly anomalous scaling exponents relative to that of vertex resummed kinetic theory. Our relativistic field theory framework further allows one to study more closely the coupling between superfluid and normal fluid modes, specifically the turbulent momentum and spatial structure of the coupling between a quasiparticle cascade to the infrared and an energy cascade to the ultraviolet. We outline possible applications of the formalism to the dynamics of vortex-antivortex formation and to the off-equilibrium dynamics of the strongly interacting matter formed in heavy-ion collisions.},

doi = {10.1103/PhysRevA.97.053606},

journal = {Physical Review A},

number = 5,

volume = 97,

place = {United States},

year = {Fri May 11 00:00:00 EDT 2018},

month = {Fri May 11 00:00:00 EDT 2018}

}

Works referenced in this record:

##
Ordering, metastability and phase transitions in two-dimensional systems

journal, April 1973

- Kosterlitz, J M; Thouless, D J
- Journal of Physics C: Solid State Physics, Vol. 6, Issue 7, p. 1181-1203