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arXiv quant-ph/0309076quant-ph
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圆腔内两个相互作用硬盘的量子状态方程

Two interacting hard disks within a circular cavity: towards a quantal equation of states

T. Kato, N. Nakazono, K. Nakamura

摘要:

我们研究了一个圆形腔台球内的一对相同的硬盘较小,但有限的大小被限制。每个圆盘都表现出自由运动,除了与它的伙伴和边界壁弹性反弹时。尽管它是圆对称的,但由于圆盘之间的(短程)相互作用,这个系统是不可积的,几乎是混沌的。我们将排除体积效应的波函数纳入系统。本征值和本征函数是通过调整圆盘和台球之间的相对大小来获得的。我们定义空腔的体积V和压力P,即,每个本征值对V的导数。P-V特性反映了本征值的能谱与盘尺寸的关系显示出大量的能级排斥,在每个被视为准平衡的单个激发本征态中,P-V特性显示出伴随着许多范德华峰的异常涨落。对于每一个本征态,我们计算了两个圆盘之间的平方距离的期望值,并指出了它们与压强涨落的关系。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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