CONSERVATION LAWS AND EXACT SOLUTIONS OF THE BOLTZMANN EQUATION
CONSERVATION LAWS AND EXACT SOLUTIONS OF THE BOLTZMANN EQUATION
复制标题
玻尔兹曼方程的守恒定律和精确解
DOI：
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发表时间：
1989
期刊：
影响因子：
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通讯作者：
Hua Chen
中科院分区：
文献类型：
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作者：
D. Mattis;A. Szpilka;Hua Chen
证明了具有完全弹性随机散射体的Lorentz模型的非负分布函数f满足随时间变化的Boltzmann方程（BE），并在后向散射占主导地位时精确计算。焦耳加热和欧姆定律得到恢复，尽管f没有稳态极限，这与松弛时间近似相反。（与时间无关的BE的传统近似也产生欧姆定律，但不产生焦耳热，更糟糕的是，它非物理地预测f<0。）将精确解与各种有效温度近似值进行比较，结果表明，即使在存在少量非弹性散射的情况下，精确解在很长时间内几乎保持不变。
The distribution function f which satisfies the time-dependent Boltzmann equation (BE) for a Lorentz model with perfectly elastic random scatterers is proved nonnegative, and is computed exactly when backscattering dominates. Joule heating and Ohm’s law are recovered, although f has no steady-state limit, contrary to the relaxation-time approximation. (The conventional approximation to the time-independent BE also yields Ohm’s law but not the Joule heating and, worse, it unphysically predicts f<0.) The exact solution is compared with various effective-temperature approximations, and is shown to remain very nearly unchanged over a wide range of times even in the presence of a small amount of inelastic scattering.