Abstract We investigate the statistical properties of a two-dimensional Dirac oscillator (2D DO) in the presence of a spin–orbit coupling, breaking its supersymmetry. The Hamiltonian of the problem is shown to admit an exact Foldy-Wouthuysen transformation, which allowed us to discard negative-energy states in carrying out our study. The main thermodynamical functions: the Helmholtz free energy, the mean energy, the entropy and the specific heat, are obtained from the canonical partition function, and their behaviours are analysed. The high temperature limit of different thermodynamical functions is probed analytically by utilizing the Euler-Maclaurin formula.

中文翻译：

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具有自旋轨道耦合的二维狄拉克振荡器的统计特性

摘要 我们研究了二维狄拉克振荡器 (2D DO) 在存在自旋轨道耦合的情况下的统计特性，打破了其超对称性。问题的哈密顿量被证明承认精确的 Foldy-Wouthuysen 变换，这使我们能够在进行研究时丢弃负能量状态。主要的热力学函数：亥姆霍兹自由能、平均能量、熵和比热，是从正则分配函数中获得的，并分析了它们的行为。利用欧拉-麦克劳林公式解析地探讨了不同热力学函数的高温极限。