Two interacting hard disks within a circular cavity: towards a quasi-equilibrium quantal equation of states |
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| Affiliation: | 1. Christian Albrechts University, Department of Oral and Maxillofacial Surgery, UKSH- Campus Kiel, Kiel, Germany;2. Cankiri Karatekin University, Department of Periodontology, Cankiri, Turkey;1. MARE – Marine and Environmental Sciences Centre, Department of Life Sciences, University of Coimbra, Coimbra, Portugal;2. CFE – Centre for Functional Ecology, Department of Life Sciences, University of Coimbra, Coimbra, Portugal;3. LIEC – Laboratoire Interdisciplinaire des Environnements Continentaux, University of Lorraine, Metz, France;4. IUF – Institut Universitaire de France, Paris, France;1. Department of Sociology, University of Hawaiʻi at Mānoa, Honolulu, HI, U.S.A;2. Thompson School of Social Work & Public Health, University of Hawaiʻi at Mānoa Honolulu, HI, U.S.A |
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| Abstract: | Two interacting hard disks confined in a circular cavity are investigated. Each disk shows a free motion except when bouncing elastically with its partner and with the boundary wall. According to the analysis of Lyapunov exponents, this system is classically nonintegrable and almost chaotic because of the (short-range) interaction between the disks. The system can be quantized 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. The pressure P is defined as the derivative of each eigenvalue with respect to the cavity volume V. Since the energy spectra of eigenvalues versus the disk size show a multitude of level repulsions, P–V characteristics shows the anomalous pressure fluctuations accompanied by many van der Waals-like peaks in each of 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. Role of Bose and Fermi statistics is also investigated. |
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