费米海中正常或超流粒子间的Casimir相互作用
Casimir interaction between normal or superfluid grains in the Fermi sea
摘要：
我们报告了一种新的力量，作用于空腔（字面上的空的空间区域），当他们沉浸在一个非相互作用的费米子物质场的背景。费米海中存在气泡或其他（重）粒子，例如中子星内壳中子海中的原子核或正常费米液体中的超流颗粒，从而阻碍了费米子的（量子力学）运动，从而产生了相互作用。这种效应类似于真空中金属镜之间的传统卡西米尔相互作用。然而，波动的电磁场被费米物质场所取代。我们表明，费米Casimir问题的球形腔系统可以精确地解决，因为计算可以映射到量子力学台球问题的点粒子散射的有限数量的非重叠的球体或磁盘。最后，我们将映射方法推广到其他Casimir系统，特别是Dirichlet边界条件下两球之间或球与板之间的波动标量场的情况。
英文摘要：
We report on a new force that acts on cavities (literally empty regions of space) when they are immersed in a background of non-interacting fermionic matter fields. The interaction follows from the obstructions to the (quantum mechanical) motions of the fermions caused by the presence of bubbles or other (heavy) particles in the Fermi sea, as, for example, nuclei in the neutron sea in the inner crust of a neutron star or superfluid grains in a normal Fermi liquid. The effect resembles the traditional Casimir interaction between metallic mirrors in the vacuum. However, the fluctuating electromagnetic fields are replaced by fermionic matter fields. We show that the fermionic Casimir problem for a system of spherical cavities can be solved exactly, since the calculation can be mapped onto a quantum mechanical billiard problem of a point-particle scattered off a finite number of non-overlapping spheres or disks. Finally we generalize the map method to other Casimir systems, especially to the case of a fluctuating scalar field between two spheres or a sphere and a plate under Dirichlet boundary conditions.
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