论文标题
在定期强制的恒温链II中的热流II
Heat flow in a periodically forced, thermostatted chain II
论文作者
论文摘要
我们为固定力在其右侧的周期性力量，并与左侧的热浴接触，从而为固定力的固定链的温度得出一个宏观的热方程。 散装中的显微动力学由汉密尔顿运动方程式给出，以及在指数时为每个粒子独立发生的粒子的速度的逆转，速率$γ$。后者产生有限的热电导率。从$ N $颗粒链的初始概率分布开始，我们计算由局部能量和电流的预期值给出的局部温度。扩展空间和时间扩散地产生，在$ n \ to+\ infty $限制中，宏观温度剖面的加热方程$ t（t，u），$ $ t> 0 $，$ u \ in [0,1] $。它应在初始条件$ t（0，u）$中解决，并指定$ t（t，0）= t _- $，左热储层的温度和固定的热量$ j $，以$ u = 1 $输入系统。 $ J $是定期力量完成的工作，该工作是针对每个$ n $明确计算的。
We derive a macroscopic heat equation for the temperature of a pinned harmonic chain subject to a periodic force at its right side and in contact with a heat bath at its left side. The microscopic dynamics in the bulk is given by the Hamiltonian equation of motion plus a reversal of the velocity of a particle occurring independently for each particle at exponential times, with rate $γ$. The latter produces a finite heat conductivity. Starting with an initial probability distribution for a chain of $n$ particles we compute the local temperature given by the expected value of the local energy and current. Scaling space and time diffusively yields, in the $n\to+\infty$ limit, the heat equation for the macroscopic temperature profile $T(t,u),$ $t>0$, $u \in [0,1]$. It is to be solved for initial conditions $T(0,u)$ and specified $T(t,0)=T_-$, the temperature of the left heat reservoir and a fixed heat flux $J$, entering the system at $u=1$. $J$ is the work done by the periodic force which is computed explicitly for each $n$.
