Quantum Mechanics of Two Hard Disks within a Circle Billiard

概要

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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 bouncing elastically with its partner and with the boundary wall. Despite its circular symmetry, this system is nonintegrable and chaotic because of the (short-range) interaction between the disks. We quantize the system by incorporating the excluded volume effect for the wave function. Eigenvalues and eigenfunctions are obtained by tuning the relative size between the disks and the billiard. We define the effective volume V for the area where two disks can move freely and the pressure P, the derivative of each eigenvalue with respect to V. Reflecting the fact that the enegy 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 eigenfunction, we obtain the single particle density and two-particle correlation function, pointing out their relationship with the pressure fluctuations. Preliminary result on the feature of the corresponding classical dynamics is also given.
理論物理学刊行会の論文
2003-09-30