Physics – Quantum Physics
Scientific paper
2003-09-09
Physics
Quantum Physics
14 pages, 6 figures
Scientific paper
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.
Kato Taichi
Nakamura Kazuo
Nakazono Nobutaka
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