Anomalous relaxation and hyperuniform fluctuations in center-of-mass conserving systems with broken time-reversal symmetry
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866917778827509760 |
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| author | Mukherjee, Anirban Tapader, Dhiraj Hazra, Animesh Pradhan, Punyabrata |
| author_facet | Mukherjee, Anirban Tapader, Dhiraj Hazra, Animesh Pradhan, Punyabrata |
| contents | We study a paradigmatic model of absorbing-phase transition - the Oslo model - on a one-dimensional ring of $L$ sites with a fixed global density $\barρ$; notably, microscopic dynamics conserve both mass and \textit{center of mass (CoM), but lacks time-reversal symmetry}. Despite having highly constrained dynamics due to CoM conservation, the system exhibits diffusive relaxation away from criticality and superdiffusive relaxation near criticality. Furthermore, the CoM conservation severely restricts particle movement, rendering the mobility to vanish exactly. Indeed the temporal growth of current fluctuation is qualitatively different from that observed in diffusive systems with a single conservation law. Away from criticality, steady-state fluctuation $\langle \mathcal{Q}_i^2(T,Δ) \rangle$ of current $\mathcal{Q}_i$ across $i$th bond up to time $T$ \textit{saturates} as $\langle \mathcal{Q}_i^2 \rangle \simeq Σ_Q^2(Δ) - {\rm const.} T^{-1/2}$; near criticality, it grows subdiffusively as $\langle \mathcal{Q}_i^2 \rangle \sim T^α$, with $0 < α< 1/2$, and eventually \textit{saturates} to $Σ_Q^2(Δ)$. The asymptotic current fluctuation $Σ_Q^2(Δ)$ is a \textit{nonmonotonic} function of $Δ$: It diverges as $Σ_Q^2(Δ) \sim Δ^2$ for $Δ\gg ρ_c$ and $Σ_Q^2(Δ) \sim Δ^{-δ}$, with $δ> 0$, for $Δ\to 0^+$. By using a mass-conservation principle, we exactly determine the exponents $δ= 2(1-1/ν_\perp)/ν_\perp$ and $α= δ/z ν_\perp$ via the correlation-length and dynamic exponents, $ν_\perp$ and $z$, respectively. Finally, we show that, in the steady state, the self-diffusion coefficient $\mathcal{D}_s(\barρ)$ of tagged particles is connected to activity by $\mathcal{D}_s(\barρ) = a(\barρ) / \barρ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_11181 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Anomalous relaxation and hyperuniform fluctuations in center-of-mass conserving systems with broken time-reversal symmetry Mukherjee, Anirban Tapader, Dhiraj Hazra, Animesh Pradhan, Punyabrata Statistical Mechanics We study a paradigmatic model of absorbing-phase transition - the Oslo model - on a one-dimensional ring of $L$ sites with a fixed global density $\barρ$; notably, microscopic dynamics conserve both mass and \textit{center of mass (CoM), but lacks time-reversal symmetry}. Despite having highly constrained dynamics due to CoM conservation, the system exhibits diffusive relaxation away from criticality and superdiffusive relaxation near criticality. Furthermore, the CoM conservation severely restricts particle movement, rendering the mobility to vanish exactly. Indeed the temporal growth of current fluctuation is qualitatively different from that observed in diffusive systems with a single conservation law. Away from criticality, steady-state fluctuation $\langle \mathcal{Q}_i^2(T,Δ) \rangle$ of current $\mathcal{Q}_i$ across $i$th bond up to time $T$ \textit{saturates} as $\langle \mathcal{Q}_i^2 \rangle \simeq Σ_Q^2(Δ) - {\rm const.} T^{-1/2}$; near criticality, it grows subdiffusively as $\langle \mathcal{Q}_i^2 \rangle \sim T^α$, with $0 < α< 1/2$, and eventually \textit{saturates} to $Σ_Q^2(Δ)$. The asymptotic current fluctuation $Σ_Q^2(Δ)$ is a \textit{nonmonotonic} function of $Δ$: It diverges as $Σ_Q^2(Δ) \sim Δ^2$ for $Δ\gg ρ_c$ and $Σ_Q^2(Δ) \sim Δ^{-δ}$, with $δ> 0$, for $Δ\to 0^+$. By using a mass-conservation principle, we exactly determine the exponents $δ= 2(1-1/ν_\perp)/ν_\perp$ and $α= δ/z ν_\perp$ via the correlation-length and dynamic exponents, $ν_\perp$ and $z$, respectively. Finally, we show that, in the steady state, the self-diffusion coefficient $\mathcal{D}_s(\barρ)$ of tagged particles is connected to activity by $\mathcal{D}_s(\barρ) = a(\barρ) / \barρ$. |
| title | Anomalous relaxation and hyperuniform fluctuations in center-of-mass conserving systems with broken time-reversal symmetry |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2312.11181 |