周期驱动恒温链中的热流 II
Heat flow in a periodically forced, thermostatted chain II
AI总结：
该研究针对右侧受周期力、左侧接触热浴的受钉扎谐振链，通过微观动力学推导扩散标度下的宏观热方程，明确了边界条件与热通量的显式计算方式。
摘要：
我们推导了受钉扎谐振链温度的宏观热方程，该链右侧受周期力作用，左侧与热浴接触。\n 体相内的微观动力学由哈密顿运动方程，加上粒子速度反转过程共同描述：每个粒子独立地以速率$\gamma$在指数分布的时间点发生速度反转，这一机制产生了有限热导率。从含$n$个粒子的链的初始概率分布出发，我们计算了由局部能量和流的期望值定义的局部温度。对空间和时间进行扩散标度后，在$n\to+\infty$的极限下，得到宏观温度分布$T(t,u)$（$t>0$，$u \in [0,1]$）满足的热方程。该方程需结合初始条件$T(0,u)$、左热库温度边界条件$T(t,0)=T_-$，以及在$u=1$处进入系统的固定热通量$J$进行求解。$J$是周期力所做的功，可对每个$n$显式计算得出。
英文摘要：
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 $n$.
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