Thermodynamics properties of confined inverted harmonic oscillator in a quantum well
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De-hua Wang
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Tian-tian Tang
Abstract
We present a pioneering investigation into the thermodynamic properties of the one-dimensional (1-D) inverted harmonic oscillator confined within a quantum well. Utilizing the linear variational method, we compute the eigen-energy of the confined inverted harmonic oscillator (CIHO) and find good agreement with exact solutions. Our analysis unveils an intriguing phenomenon: the energy of the CIHO can exhibit both positive and negative values due to the interplay between quantum confinement and the inverted harmonic potential. This anomalous behavior directly affects the system’s quantum statistics thermodynamic properties. Our calculation reveals that, for a fixed quantum well width, the average energy, free energy, and entropy all decrease as the inverted harmonic frequency increases. However, the variation of heat capacity (C V ) with harmonic frequency is remarkably peculiar. Specifically, in the low-temperature region, C V diminishes with increasing harmonic frequency, while the opposite trend occurs at higher temperatures. We also investigate the influence of quantum confinement on the thermodynamic properties of the CIHO. Our results indicate that the thermodynamic properties of the CIHO can be effectively controlled by adjusting both the size of the quantum well and the harmonic frequency. This work can guide the future research on the thermodynamic property of the confined harmonic oscillator and may find applications in various fields, including high-energy physics, condensed state physics, statistical physics, and cold atomic physics.
Funding source: Natural Science Foundation of Shandong Province
Award Identifier / Grant number: ZR2019MA066
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11374133
Acknowledgments
We thank the referees for their good suggestions.
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Research ethics: This study was performed in line with the principles of the Declaration of De Gruyter policy.
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Informed consent: Informed consent was obtained from all individuals included in this study.
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Author contributions: De-hua Wang and Tian-tian Tang contributed equally to this work and should be regarded as cofirst authors. De-hua Wang and Tian-tian Tang: review and conceptualization, editing; Feng-zhen Wang: original draft, data curation.
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Use of Large Language Models, AI and Machine Learning Tools: We use Deepseek to check for grammatical errors and modify the format of the references.
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Conflict of interest: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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Research funding: This work was supported by the Natural Science Foundation of Shandong Province, China (grant no. ZR2019MA066), and the National Natural Science Foundation of China (grant no.11374133).
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Data availability: Data will be made available on reasonable request.
References
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