dorsal/arxiv
View SchemaTwo interacting hard disks within a circular cavity: towards a quantal equation of states
| Authors | T. Kato, N. Nakazono, K. Nakamura |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0309076 |
| URL | https://arxiv.org/abs/quant-ph/0309076 |
Abstract
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.
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"abstract": "We investigate a circular cavity billiard within which a pair of identical\nhard disks of smaller but finite size is confined. Each disk shows a free\nmotion except when bouncing elastically with its partner and with the boundary\nwall. Despite its circular symmetry, this system is nonintegrable and almost\nchaotic because of the (short-range) interaction between the disks. We quantize\nthe system by incorporating the excluded volume effect for the wavefunction.\nEigenvalues and eigenfunctions are obtained by tuning the relative size between\nthe disks and the billiard. We define the volume V of the cavity and the\npressure P, i.e., the derivative of each eigenvalue with respect to V.\nReflecting the fact that the energy spectra of eigenvalues versus the disk size\nshow a multitude of level repulsions, P-V characteristics shows the anomalous\nfluctuations accompanied by many van der Waals-like peaks in each of individual\nexcited eigenstates taken as a quasi-equilibrium. For each eigenstate, we\ncalculate the expectation values of the square distance between two disks, and\npoint out their relationship with the pressure fluctuations.",
"arxiv_id": "quant-ph/0309076",
"authors": [
"T. Kato",
"N. Nakazono",
"K. Nakamura"
],
"categories": [
"quant-ph"
],
"title": "Two interacting hard disks within a circular cavity: towards a quantal equation of states",
"url": "https://arxiv.org/abs/quant-ph/0309076"
},
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