Abstract

Confined quantum systems can present anomalous behaviour. In particular, thermodynamic properties such as specific heat can show special features when the system is subject to spatial confinement described, for instance, by a harmonic potential. The energy eigenvalues of this confined system can be obtained from a variational approach by using, as trial functions, the solution of a particle in a box multiplied by a gaussian. For a strong confinement regime, the energy eigenvalues converge to the same values of the particle in the box and, for a weak confinement regime, the energy eigenvalues converge to the free harmonic oscillator. This behaviour reflects in the thermodynamics properties. In the curves of specific heat as a function of temperature, for instance, it is possible to identify two regions, one when the contribution of the harmonic oscillator is dominant and the other one where the contribution of the particle in a box becomes more relevant. These results indicate a phase transition of second-order close to the Einstein temperature.

Graphic abstract

中文翻译：

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量子约束对热力学性质的影响

摘要

受限的量子系统会表现出异常行为。特别地，当系统受到例如谐波势所描述的空间限制时，诸如比热之类的热力学特性会表现出特殊的特征。该受限系统的能量本征值可以通过使用方盒中粒子的解乘以高斯作为试验函数，从变分方法中获得。对于强约束机制，能量特征值收敛到盒子中粒子的相同值；对于弱约束机制，能量特征值收敛到自由谐波振荡器。这种行为反映在热力学性质上。例如，在比热随温度变化的曲线中，可以确定两个区域，一种是谐波谐振器的贡献占主导地位，另一种是盒子中粒子的贡献变得更加相关。这些结果表明接近爱因斯坦温度的二阶相变。

图形摘要