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 in the Fermi sea caused by the presence of bubbles or other (heavy) particles immersed in the latter, as, for example, nuclei in the neutron sea in the inner crust of a neutron star.This effect resembles the traditional Casimir effect, which describes the attraction between two parallel metallic mirrors in vacuum. Here, however, the fluctuating (bosonic) electromagnetic fields are replaced by fermionic matter fields. Furthermore, the Casimir energy is inferred from the geometry-dependent part of the density of states, and its sign is not fixed, but oscillates according to the relative arrangement and distances of the cavities.In fact, with the help of Krein’s trace formula, the quantum field theory calculation is mapped onto a quantum mechanical billiard problem of a point-particle scattered off a finite number of non-overlapping spheres or disks; i.e. classically hyperbolic (or even chaotic) scattering systems.This topic is relevant to the physics of neutron stars (nuclei or quark bubbles embedded in a neutron gas), to dilute Bose-Einstein-condensate bubbles inside the background of a Fermi- Dirac condensate, to buckyballs in liquid mercury and to superconducting droplets in a Fermi liquid.
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- A force from nothing onto nothing: Casimir effect between bubbles in the Fermi sea
- Springer Netherlands