Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.07283 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914769510858752 |
|---|---|
| author | Silvano, Nathan O. Barci, Daniel G. |
| author_facet | Silvano, Nathan O. Barci, Daniel G. |
| contents | We investigate a two-dimensional system of interacting Active Brownian Particles. Using the Martin-Siggia-Rose-Janssen-de Dominicis formalism, we built up the generating functional for correlation functions. We study in detail the hydrodynamic regime with a constant density stationary state. Our findings reveal that, within a small density fluctuations regime, an emergent $U(1)$ gauge symmetry arises, originated from the conservation of fluid vorticity. Consequently, the interaction between the orientational order parameter and density fluctuations can be cast into a gauge theory, where the concept of ``electric charge density" aligns with the local vorticity of the original fluid. We study in detail the case of a microscopic local two-body interaction. We show that, upon integrating out the gauge fields, the stationary states of the rotational degrees of freedom satisfy a non-local Frank free energy for a nematic fluid. We give explicit expressions for the splay and bend elastic constants as a function of the Péclet number (${\rm Pe}$) and the diffusion interaction constant ($k_d$). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_07283 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Emergent Gauge Symmetry in Active Brownian Matter Silvano, Nathan O. Barci, Daniel G. Statistical Mechanics We investigate a two-dimensional system of interacting Active Brownian Particles. Using the Martin-Siggia-Rose-Janssen-de Dominicis formalism, we built up the generating functional for correlation functions. We study in detail the hydrodynamic regime with a constant density stationary state. Our findings reveal that, within a small density fluctuations regime, an emergent $U(1)$ gauge symmetry arises, originated from the conservation of fluid vorticity. Consequently, the interaction between the orientational order parameter and density fluctuations can be cast into a gauge theory, where the concept of ``electric charge density" aligns with the local vorticity of the original fluid. We study in detail the case of a microscopic local two-body interaction. We show that, upon integrating out the gauge fields, the stationary states of the rotational degrees of freedom satisfy a non-local Frank free energy for a nematic fluid. We give explicit expressions for the splay and bend elastic constants as a function of the Péclet number (${\rm Pe}$) and the diffusion interaction constant ($k_d$). |
| title | Emergent Gauge Symmetry in Active Brownian Matter |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2312.07283 |