Casimir effect in a one-dimensional gas of free fermions
Eugene B. Kolomeisky, Joseph P. Straley, Michael Timmins
备注：
13 pages, 5 figures. A generalization to the case of an arbitrary harmonic liquid is given and discussion is improved. Version to be published in Phys. Rev. A
We compute an analog Casimir effect in a one-dimensional spinless Luttinger liquid confined to a segment in the presence of a nearly-impenetrable partition dividing the segment into two compartments. The Casimir interaction is found to be a bounded piecewise-continuous oscillatory function whose maxima are points of force discontinuity and correspond to resonant tunneling across the partition. The well-known regularization-based results are reproduced by the lower envelope of this function, which corresponds to an approximation that ignores the rather large oscillations due to particle discreteness. These macroscopic conclusions are tested and confirmed via a rigorous analysis of the Casimir effect in an exactly-solvable model of a one-dimensional non-relativistic spinless gas of free fermions, thus resolving an objection that has been raised by Volovik (2003).
Additionally we confirm the result of a recent calculation which employed an effective low-energy theory with a cutoff to find the Casimir interaction between two strong well-separated impurities placed in a Luttinger liquid.
Casimir force variability in one-dimensional QED systems
本文用$\ln\text{[Wronskian]}$围道积分方法研究了一维大质量狄拉克费米子背景下两个短程电荷源之间的Casimir力。对于具有相同（正）电荷的相同源，我们发现，在非微扰区域，它们之间的Casimir相互作用可以达到足够大的负值，同时揭示了长程力的特征，尽管非零费米子质量，这可能会显着影响这种准一维QED系统的性质。对于大的距离$s$之间的源，我们恢复，他们的相互作用首先是由一个单一的源的离散谱的结构，在依赖于它可以被调谐到给一个吸引力，排斥，或（几乎）补偿卡西米尔力与各种速率的指数下降，完全不同的标准$\exp (-2 m s)$法律。通过相同的$\ln\text{[Wronskian]}$技术，两个$δ$源的情况下也被认为是在一个自洽的方式与类似的结果的变化的卡西米尔力。在反对称源-反源系统中，Casimir力的行为与实验结果完全不同。特别是，在这种情况下，源之间不可能发生远距离相互作用。Casimir力的渐近性遵循标准的$\exp (-2 m s)$定律。此外，对于源之间的小间隔，对称和反对称情况下的卡西米尔力原来是相反的符号。
