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Dynamical phase transitions in two-dimensional Brownian matter

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  • Silvano, Nathan O.
  • Barci, Daniel G.

Abstract

We investigate collective behavior of a system of two-dimensional interacting Brownian particles in the hydrodynamic regime. By means of the Martin–Siggia–Rose–Jenssen–de Dominicis formalism, we built up a generating functional for correlations functions. In the continuum limit, we uncover an exact symmetry under area-preserving diffeomorphism transformations that characterizes a liquid state. This symmetry leads to the conservation of local vorticity. By computing the generating functional within the saddle-point plus Gaussian fluctuations approximation, we reveal the emergence of a U(1) gauge symmetry that allows us to describe the dynamics of density fluctuations as a gauge theory. We solve the corresponding equations of motion for short as well as long ranged interactions showing up the presence of multiple dynamical regimes and associated dynamical phase transitions, even for pure repulsive interactions.

Suggested Citation

  • Silvano, Nathan O. & Barci, Daniel G., 2025. "Dynamical phase transitions in two-dimensional Brownian matter," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 665(C).
    • Handle: RePEc:eee:phsmap:v:665:y:2025:i:c:s0378437125001347
    DOI: 10.1016/j.physa.2025.130482
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    References listed on IDEAS

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    1. Bartosz A. Grzybowski & Howard A. Stone & George M. Whitesides, 2000. "Dynamic self-assembly of magnetized, millimetre-sized objects rotating at a liquid–air interface," Nature, Nature, vol. 405(6790), pages 1033-1036, June.
    2. Carmine Di Rienzo & Vincenzo Piazza & Enrico Gratton & Fabio Beltram & Francesco Cardarelli, 2014. "Probing short-range protein Brownian motion in the cytoplasm of living cells," Nature Communications, Nature, vol. 5(1), pages 1-8, December.
    3. Kawasaki, Kyozi, 1994. "Stochastic model of slow dynamics in supercooled liquids and dense colloidal suspensions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 208(1), pages 35-64.
    4. Silvano, Nathan O. & Barci, Daniel G., 2023. "The role of multiplicative noise in critical dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).
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