具有自洽随机库的谐波晶体的傅里叶定律
Fourier's Law for a Harmonic Crystal with Self-consistent Stochastic Reservoirs
摘要：
我们考虑一个d维谐波晶体在每个站点与随机Langevin型热浴接触。“外部”左、右热浴的温度分别为规定值T_L和T_R，而“内部”热浴的温度是自洽选择的，使得在它们与处于稳定状态的系统之间没有平均能量通量。我们证明了这一要求唯一固定的温度和自洽系统有一个唯一的稳定状态。对于无限大系统，这种状态是局部热平衡状态。相应的热流满足傅立叶定律，具有有限的正导热系数，也可以使用Green-Kubo公式计算。对于谐波链（d=1），电导率与Bolsterli，Rich和Visscher在1970年首次研究该模型时得到的表达式一致。在另一个极限d>>1时，定常无限体积导热系数表现为1/（l_d*d），其中l_d是与中间储层的耦合。我们还分析了具有非均匀分布的热浴耦合的效果。这些结果得到严格证明，通过控制的热力学极限的相关性的行为。
英文摘要：
We consider a d-dimensional harmonic crystal in contact with a stochastic Langevin type heat bath at each site. The temperatures of the "exterior" left and right heat baths are at specified values T_L and T_R, respectively, while the temperatures of the "interior" baths are chosen self-consistently so that there is no average flux of energy between them and the system in the steady state. We prove that this requirement uniquely fixes the temperatures and the self consistent system has a unique steady state. For the infinite system this state is one of local thermal equilibrium. The corresponding heat current satisfies Fourier's law with a finite positive thermal conductivity which can also be computed using the Green-Kubo formula. For the harmonic chain (d=1) the conductivity agrees with the expression obtained by Bolsterli, Rich and Visscher in 1970 who first studied this model. In the other limit, d>>1, the stationary infinite volume heat conductivity behaves as 1/(l_d*d) where l_d is the coupling to the intermediate reservoirs. We also analyze the effect of having a non-uniform distribution of the heat bath couplings. These results are proven rigorously by controlling the behavior of the correlations in the thermodynamic limit.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
