Fourier's law breakdown for the planar-rotor chain with long-range coupling
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911961732612096 |
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| author | Lima, Henrique Santos Tsallis, Constantino Eroglu, Deniz Tirnakli, Ugur |
| author_facet | Lima, Henrique Santos Tsallis, Constantino Eroglu, Deniz Tirnakli, Ugur |
| contents | The thermal conductivity, $κ$, of a homogeneous chain of generically-ranged interacting planar rotors, more precisely the inertial $α-XY$ model, is numerically studied with the coupling constant decaying as $r^{-α}$. The conductance ($σ\equiv κ/L$) is calculated for typical values of $α$, temperature $T$ and lattice size $L$. For large $L$, the results can be collapsed into an universal $q$-stretched exponential form, namely $L^{δ_α} σ\propto e_{q_α}^{-B_α(L^{γ_α}T)^{η_α}}$, where $e_q^z\equiv [1+ (1-q)z]^{1/(1-q)}$. The parameters $(γ_α,δ_α,B_α, η_α)$ are $α$-dependent, and $q_α$ is the index of the $q$-stretched exponential. This form is achievable due to the ratio $η_α/(q-1)$ being almost constant with respect to the lattice size $L$. Two distinct regimes are identified: for $0 \le α< 2$, the Fourier law is violated, whereas for $α\ge 2$, it is satisfied. These findings provide significant insights into heat conduction mechanisms in systems with long-range interactions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_13843 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fourier's law breakdown for the planar-rotor chain with long-range coupling Lima, Henrique Santos Tsallis, Constantino Eroglu, Deniz Tirnakli, Ugur Statistical Mechanics Classical Physics Computational Physics The thermal conductivity, $κ$, of a homogeneous chain of generically-ranged interacting planar rotors, more precisely the inertial $α-XY$ model, is numerically studied with the coupling constant decaying as $r^{-α}$. The conductance ($σ\equiv κ/L$) is calculated for typical values of $α$, temperature $T$ and lattice size $L$. For large $L$, the results can be collapsed into an universal $q$-stretched exponential form, namely $L^{δ_α} σ\propto e_{q_α}^{-B_α(L^{γ_α}T)^{η_α}}$, where $e_q^z\equiv [1+ (1-q)z]^{1/(1-q)}$. The parameters $(γ_α,δ_α,B_α, η_α)$ are $α$-dependent, and $q_α$ is the index of the $q$-stretched exponential. This form is achievable due to the ratio $η_α/(q-1)$ being almost constant with respect to the lattice size $L$. Two distinct regimes are identified: for $0 \le α< 2$, the Fourier law is violated, whereas for $α\ge 2$, it is satisfied. These findings provide significant insights into heat conduction mechanisms in systems with long-range interactions. |
| title | Fourier's law breakdown for the planar-rotor chain with long-range coupling |
| topic | Statistical Mechanics Classical Physics Computational Physics |
| url | https://arxiv.org/abs/2407.13843 |