First-Principle Validation of Fourier's Law: One-Dimensional Classical Inertial Heisenberg Model
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arXiv
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| Format: | Preprint |
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2023
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| author | Lima, Henrique Santos Tsallis, Constantino Nobre, Fernando D. |
| author_facet | Lima, Henrique Santos Tsallis, Constantino Nobre, Fernando D. |
| contents | The thermal conductance of a one-dimensional classical inertial Heisenberg model of linear size $L$ is computed, considering the first and last particles in thermal contact with heat baths at higher and lower temperatures, $T_{h}$ and $T_{l}$ ($T_{h}>T_{l}$), respectively. These particles at extremities of the chain are subjected to standard Langevin dynamics, whereas all remaining rotators ($i=2, \cdots , L-1$) interact by means of nearest-neighbor ferromagnetic couplings and evolve in time following their own equations of motion, being investigated numerically through molecular-dynamics numerical simulations. Fourier's law for the heat flux is verified numerically with the thermal conductivity becoming independent of the lattice size in the limit $L \to \infty$, scaling with the temperature as $κ(T) \sim T^{-2.25}$, where $T=(T_{h}+T_{l})/2$. Moreover, the thermal conductance, $σ(L,T)=κ(T)/L$, is well-fitted by a function, typical of nonextensive statistical mechanics, according to $σ(L,T)=A \exp_{q}(-B x^η)$, where $A$ and $B$ are constants, $x=L^{0.475}T$, $q=2.28 \pm 0.04$, and $η=2.88 \pm 0.04$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_07481 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | First-Principle Validation of Fourier's Law: One-Dimensional Classical Inertial Heisenberg Model Lima, Henrique Santos Tsallis, Constantino Nobre, Fernando D. Statistical Mechanics Computational Physics The thermal conductance of a one-dimensional classical inertial Heisenberg model of linear size $L$ is computed, considering the first and last particles in thermal contact with heat baths at higher and lower temperatures, $T_{h}$ and $T_{l}$ ($T_{h}>T_{l}$), respectively. These particles at extremities of the chain are subjected to standard Langevin dynamics, whereas all remaining rotators ($i=2, \cdots , L-1$) interact by means of nearest-neighbor ferromagnetic couplings and evolve in time following their own equations of motion, being investigated numerically through molecular-dynamics numerical simulations. Fourier's law for the heat flux is verified numerically with the thermal conductivity becoming independent of the lattice size in the limit $L \to \infty$, scaling with the temperature as $κ(T) \sim T^{-2.25}$, where $T=(T_{h}+T_{l})/2$. Moreover, the thermal conductance, $σ(L,T)=κ(T)/L$, is well-fitted by a function, typical of nonextensive statistical mechanics, according to $σ(L,T)=A \exp_{q}(-B x^η)$, where $A$ and $B$ are constants, $x=L^{0.475}T$, $q=2.28 \pm 0.04$, and $η=2.88 \pm 0.04$. |
| title | First-Principle Validation of Fourier's Law: One-Dimensional Classical Inertial Heisenberg Model |
| topic | Statistical Mechanics Computational Physics |
| url | https://arxiv.org/abs/2306.07481 |