Dean-Kawasaki fluctuating hydrodynamics for backscattering hard rods
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911725905772544 |
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| author | Powdel, Mrinal Jyoti |
| author_facet | Powdel, Mrinal Jyoti |
| contents | We study a system of backscattering hard rods in one dimension. Contrary to the usual ballistic hard rods, these hard rods flip the sign of their velocities with a rate $γ$. This leads to the decay of the odd moments of velocity while preserving the even moments: the number of conserved quantities in the system becomes half. The introduction of the flipping rate $γ$ is an integrability-breaking perturbation, and this leads to a change in the transport properties in the system. We show using a Dean-Kawasaki fluctuating hydrodynamic formulation that the unequal space-time correlation of the normal mode phase space densities attains a diffusive form at late times. Also, we show that for $t \gg 1/γ$, the two-time density-density correlation of mass densities spreads in a diffusive manner, and for $t \ll 1/γ$, the correlation spreads ballistically, for a background state given by the Boltzmann distribution. Our results present an elegant framework to study systems where integrability is broken by a stochastic noise. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_21553 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dean-Kawasaki fluctuating hydrodynamics for backscattering hard rods Powdel, Mrinal Jyoti Statistical Mechanics We study a system of backscattering hard rods in one dimension. Contrary to the usual ballistic hard rods, these hard rods flip the sign of their velocities with a rate $γ$. This leads to the decay of the odd moments of velocity while preserving the even moments: the number of conserved quantities in the system becomes half. The introduction of the flipping rate $γ$ is an integrability-breaking perturbation, and this leads to a change in the transport properties in the system. We show using a Dean-Kawasaki fluctuating hydrodynamic formulation that the unequal space-time correlation of the normal mode phase space densities attains a diffusive form at late times. Also, we show that for $t \gg 1/γ$, the two-time density-density correlation of mass densities spreads in a diffusive manner, and for $t \ll 1/γ$, the correlation spreads ballistically, for a background state given by the Boltzmann distribution. Our results present an elegant framework to study systems where integrability is broken by a stochastic noise. |
| title | Dean-Kawasaki fluctuating hydrodynamics for backscattering hard rods |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2604.21553 |