Remarks on thermodynamic properties of a double ring-shaped quantum dot at low and high temperatures
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
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2020
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| _version_ | 1866909138477383680 |
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| author | Vicente, Andrés G. Jirón Castro, Luis B. Obispo, Angel E. Meza, Luis E. Arroyo |
| author_facet | Vicente, Andrés G. Jirón Castro, Luis B. Obispo, Angel E. Meza, Luis E. Arroyo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_07633 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Remarks on thermodynamic properties of a double ring-shaped quantum dot at low and high temperatures Vicente, Andrés G. Jirón Castro, Luis B. Obispo, Angel E. Meza, Luis E. Arroyo Mesoscale and Nanoscale Physics High Energy Physics - Theory Mathematical Physics Quantum Physics 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. |
| title | Remarks on thermodynamic properties of a double ring-shaped quantum dot at low and high temperatures |
| topic | Mesoscale and Nanoscale Physics High Energy Physics - Theory Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2012.07633 |