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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., Comment: 8 pages, 2 figures, submitted to the Proceedings of QFEXT'05, Barcelona, Sept. 5-9, 2005

We present a simple formalism for the evaluation of the Casimir energy for two spheres and a sphere and a plane, in case of a scalar fluctuating field, valid at any separations. We compare the exact results with various approximation schemes and establish when such schemes become useful. The formalism can be easily extended to any number of spheres and/or planes in three or arbitrary dimensions, with a variety of boundary conditions or non-overlapping potentials/non-ideal reflectors., Comment: published version; 13 pages, 2 figures; add. material (in Sec.VI) and corrections (esp. in App.B)

We describe the Fermionic Casimir effect in the case of two spherical superfluid scatterers immersed in a normal Fermi system. It is shown that due to the focusing property of Andreev reflection this new Casimir-like energy is significantly enhanced when compared to the case of normal scatterers with specular reflection., Comment: 7 pages, 4 eps figures, latex (with epl.cls)

Homogeneous neutron matter at subnuclear densities becomes unstable towards the formation of inhomogeneities. Depending on the average value of the neutron density one can observe the appearance of either bubbles, rods, tubes or plates embeded in a neutron gas. We estimate the quantum corrections to the ground state energy (which could be termed either shell correction or Casimir energy) of such phases of neutron matter. The calculations are performed by evaluating the contribution of the shortest periodic orbits in the Gutzwiller trace formula for the density of states. The magnitude of the quantum corrections to the ground state energy of neutron matter are of the same order as the energy differences between various phases., Comment: 11 pages, contribution to the Nobel Symposium on Quantum Chaos Y2K, Backaskog Castle, Sweden, June 13-17, 2000

A new algorithm for determining the eigenstates of n-dimensional billiards is presented. It is based on the application of the Cauchy theorem for the determination of the null space of the boundary overlap matrix. The method is free from the limitations associated with the shape of the billiard and could be applied even for nonconvex geometries where other algorithms face difficulties. Moreover it does not suffer from the existence of eigenvalue degeneracies which is another serious shortcoming of many methods. In the paper we apply the algorithm to a few simple cases where the analytical solutions exist. Numerical solutions have been investigated for the case of annular billiard., Comment: 14 pages, 3 figures, submitted to Phys. Rev. E

The excitation of a quantum gas of 112 independent fermions in the time-dependent potential well, periodically oscillating around the spherical shape, was followed over 10 oscillation cycles. Five different oscillation frequencies are considered for each of the five types of deformations: spheroidal and Legendre polynomial ripples: P_3, P_4, P_5 and P_6. The excitation rate of the gas in the deforming hard-walled cavities substantially decreases after initial one or two cycles and the final excitation energy is a few times smaller than the wall formula predictions. Qualitatively similar results are obtained for the diffused Woods-Saxon well. The details and possible origins of this behaviour are discussed as well as the consequences for the one-body dissipation model of nuclear dynamics., Comment: REVTeX file, 13 pages, 8 postscript figures submitted to Phys. Rev. C