Emergent Hydrodynamics in an Exclusion Process with Long-Range Interactions

Abstract

We study the symmetric Dyson exclusion process (SDEP)--a lattice gas with exclusion and long-range, Coulomb–type interactions that emerge both as the maximal-activity limit of the symmetric exclusion process and as a discrete version of Dyson's Brownian motion on the unitary group. Exploiting an exact ground-state (Doob) transform, we map the stochastic generator of the SDEP onto the spin-1/2 XX quantum chain, which in turn admits a free-fermion representation. At macroscopic scales we conjecture that the SDEP displays ballistic (Eulerian) scaling with a conservation law featuring a current that is a genuinely non-local functional of the density. This non-local one-component description is equivalent to a local two-components “complex Hopf’’ system for finite particle density. Closed evolution formulas allow us to solve the melting of single- and double-block initial states, producing limit shapes and arctic curves that agree with large-scale Monte-Carlo simulations. The model thus offers a tractable example of emergent non-local hydrodynamics driven by long-range interactions.

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BibTeX RIS

BibTeX

@article{zahra2026emergent,
  title = {{Emergent Hydrodynamics in an Exclusion Process with Long-Range Interactions}},
  author = {Ali Zahra and J. Dubail and Gunther M. Schütz},
  journal = {SciPost Physics},
  year = {2026},
  month = sep,
  doi = {10.21468/scipostphys.20.5.141},
  url = {https://hal.science/hal-05267122v2},
  note = {CC BY 4.0},
}

RIS

TY  - JOUR
TI  - Emergent Hydrodynamics in an Exclusion Process with Long-Range Interactions
AU  - Ali Zahra
AU  - J. Dubail
AU  - Gunther M. Schütz
PY  - 2026
DA  - 2026/09/28
JO  - SciPost Physics
DO  - 10.21468/scipostphys.20.5.141
UR  - https://hal.science/hal-05267122v2
AB  - We study the symmetric Dyson exclusion process (SDEP)--a lattice gas with exclusion and long-range, Coulomb–type interactions that emerge both as the maximal-activity limit of the symmetric exclusion process and as a discrete version of Dyson's Brownian motion on the unitary group. Exploiting an exact ground-state (Doob) transform, we map the stochastic generator of the SDEP onto the spin-1/2 XX quantum chain, which in turn admits a free-fermion representation. At macroscopic scales we conjecture that the SDEP displays ballistic (Eulerian) scaling with a conservation law featuring a current that is a genuinely non-local functional of the density. This non-local one-component description is equivalent to a local two-components “complex Hopf’’ system for finite particle density. Closed evolution formulas allow us to solve the melting of single- and double-block initial states, producing limit shapes and arctic curves that agree with large-scale Monte-Carlo simulations. The model thus offers a tractable example of emergent non-local hydrodynamics driven by long-range interactions.
SN  - 2542-4653
ER  -

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