论文标题
使用分数变化原理获得金属中电子的凹陷方程
Obtaining the Drude Equation for Electrons in Metals Using a Fractional Variational Principle
论文作者
论文摘要
为了与包含1/2阶的分数衍生物的拉格朗日人一起使用，得出了分数变分原理。通过迫使与这种类型的拉格朗日相关的动作是固定的，可以获得修改的分数Euler-Lagrange方程。事实证明，这可以重现两个基本的一维能量触及系统的运动方程：弹簧质量系统受摩擦阻尼和串联连接的RLC电路。最后，通过使用分数Euler-lagrange方程，当在电子相关能量中考虑分数动能时，回收了金属中电子的磨损关系。
A fractional variational principle was derived in order to be used with lagrangians containing fractional derivatives of order 1/2. By forcing the action associated to this type of lagrangian to be stationary, a modified fractional Euler-Lagrange equation was obtained. This was shown to reproduce the equations of motion of two basic 1-dimensional energy-dissipative systems: a spring-mass system damped by friction, and a RLC circuit connected in series. Finally, by using the fractional Euler-Lagrange equation, the Drude relationship for electrons in metals was recovered when a fractional kinetic energy was taken into consideration in the electron's associated energies.
