  We investigate a circular cavity billiard within which a pair of identical
hard disks of smaller but finite size is confined. Each disk shows a free
motion except when bouncing elastically with its partner and with the boundary
wall. Despite its circular symmetry, this system is nonintegrable and almost
chaotic because of the (short-range) interaction between the disks. We quantize
the system by incorporating the excluded volume effect for the wavefunction.
Eigenvalues and eigenfunctions are obtained by tuning the relative size between
the disks and the billiard. We define the volume V of the cavity and the
pressure P, i.e., the derivative of each eigenvalue with respect to V.
Reflecting the fact that the energy spectra of eigenvalues versus the disk size
show a multitude of level repulsions, P-V characteristics shows the anomalous
fluctuations accompanied by many van der Waals-like peaks in each of individual
excited eigenstates taken as a quasi-equilibrium. For each eigenstate, we
calculate the expectation values of the square distance between two disks, and
point out their relationship with the pressure fluctuations.
