THE BOLTZMANN EQUATION IN THE THEORY OF ELECTRICAL CONDUCTION IN METALS
THE BOLTZMANN EQUATION IN THE THEORY OF ELECTRICAL CONDUCTION IN METALS
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DOI：
10.1088/0370-1328/71/4/306
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发表时间：
1958-01-01
影响因子：
--
通讯作者：
GREENWOOD, DA
中科院分区：
文献类型：
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作者：
GREENWOOD, DA
被认为是在一个不规则的静电势散射的电场中的金属中的导电电子的运动，该模型适用于由于晶格波在高温下的电阻，并在任何温度下的缺陷。在§ 2中，玻尔兹曼方程是在没有常规微扰理论的情况下重新推导出来的，避免了通常在重复的小时间间隔后对不同电子状态的相位进行平均的必要性。只要假设散射中心在晶体中随机分布就足够了。然而，该理论仍然依赖于假设h/τ<< kT，其中τ是碰撞时间，就像通常的微扰理论一样。§ 3给出了模型电导率的一般公式，不受任何假设的影响。这有助于证明朗道的一个论点，根据该论点，通常的理论是有效的，只要h/τ<< η，其中η是费米分布的截止能量。尚未对该公式进行直接评价。
The motion of conduction electrons in a metal in an electric field, scattered by an irregular static potential, is considered; this model is applicable to the resistance due to lattice waves at high temperatures, and to imperfections at any temperature. In § 2 the Boltzmann equation is re-derived without the customary perturbation theory, avoiding the usual necessity of averaging over phases of different electron states after repeated small time intervals. The assumption that the scattering centres are distributed at random in the crystal is alone sufficient. The theory is, however, still dependent on assuming that h/τ<< kT, where τ is the collision time, as is the usual perturbation theory. § 3 gives a general formula for the conductivity of the model, not subject to any assumption. This helps to justify an argument by Landau according to which the usual theory is valid provided h/τ<< η, where η is the cut-off energy of the Fermi distribution. No direct evaluation of the formula has been achieved.