标题： 相对论电子气体：自然界左手材料的候选者 显示英文标题

标题： The relativistic electron gas: a candidate for nature's left-handed material

摘要： 相对论电子气体的电容率和磁导率由量子电动力学在有限温度和密度下计算，作为温度、化学位、频率和波矢的函数。 极化和磁化线性地依赖于电场和磁场，并且是零温度和零密度真空部分与温度和化学位相关的介质部分之和。 解析计算得出依赖于三个标量函数的广义表达式。 在非相对论极限下，结果重现了林德哈德公式。 在相对论情况下以及长波长极限下，我们得到：i) 对$\omega=0$，广义的极化率可减少到已知的非相对论极限；ii) 对$\omega \neq 0$，在零温及高温下的德鲁德型响应。 后者意味着可以同时具有$\epsilon$和$\mu$为负，这是超材料的特征行为。 这明确表明，相对论电子等离子体是实现负折射率系统的一种自然候选者。 此外，介质中的麦克斯韦方程给出了电子等离子体的色散关系和折射率。 目前的结果应与等离子体物理、天体物理观测、同步辐射源以及其他存在高速运动电子的环境相关。 显示英文摘要

摘要： The electric permittivities and magnetic permeabilities for a relativistic electron gas are calculated from quantum electrodynamics at finite temperature and density as functions of temperature, chemical potential, frequency, and wavevector. The polarization and the magnetization depend linearly on both electric and magnetic fields, and are the sum of a zero-temperature and zero-density vacuum part with a temperature- and chemical potential-dependent medium part. Analytic calculations lead to generalized expressions that depend on three scalar functions. In the nonrelativistic limit, results reproduce the Lindhard formula. In the relativistic case, and in the long wavelength limit, we obtain: i) for $\omega=0$, generalized susceptibilities that reduce to known nonrelativistic limits; ii) for $\omega \neq 0$, Drude-type responses at zero and at high temperatures. The latter implies that one may have both $\epsilon$ and $\mu$ simultaneously negative, a behavior characteristic of metamaterials. This unambiguously indicates that the relativistic electron plasma is one of nature's candidates for the realization of a negative index of refraction system. Moreover, Maxwell's equations in the medium yield the dispersion relation and the index of refraction of the electron plasma. Present results should be relevant for plasma physics, astrophysical observations, synchrotrons, and other environments with fast moving electrons.