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arXiv 2012.07633cond-mat.mes-hallhep-thmath-phmath.MPquant-ph
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双环形状量子点在低温和高温下热力学性质的评注

Remarks on thermodynamic properties of a double ring-shaped quantum dot at low and high temperatures

Andrés G. Jirón Vicente, Luis B. Castro, Angel E. Obispo, Luis E. Arroyo Meza

AI总结:

本文指出Khordad等人对双环量子点中双合流Heun方程解的误导性处理,即能量不能用$n_z$标记,并用正确能谱重新计算了低高温下的配分函数、比热和熵。

摘要:

在本刊近期发表的一篇论文中,Khordad及其合作者[J Low Temp Phys (2018) 190:200]研究了在外部磁场和电场作用下GaAs双环形状量子点的热力学性质。在那项有价值的研究中,系统的能量通过求解薛定谔方程获得。径向方程被映射为合流超几何微分方程,而与$z$坐标相关的微分方程被映射为双合流Heun微分方程。本文指出,该双合流Heun方程的解存在误导性处理。研究表明,能量$E_{z}$不能用$n_{z}$标记,这一事实危及该系统的结果。我们使用正确的能谱计算配分函数,并重新计算作为低温和高温函数的比热和熵。

英文摘要:

In a recent paper published in this Journal, Khordad and collaborators [J Low Temp Phys (2018) 190:200] have studied the thermodynamics properties of a GaAs double ring-shaped quantum dot under external magnetic and electric fields. In that meritorious research the energy of system was obtained by solving the Schrödinger equation. The radial equation was mapped into a confluent hypergeometric differential equation and the differential equation associated to $z$ coordinate was mapped into a biconfluent Heun differential equation. In this paper, it is pointed out a misleading treatment on the solution of the biconfluent Heun equation. It is shown that the energy $E_{z}$ can not be labeled with $n_{z}$ and this fact jeopardizes the results of this system. We calculate the partition function with the correct energy spectrum and recalculate the specific heat and entropy as a function of low and high temperatures.

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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