Exact calculations of the thermal properties of two-electron GaAs quantum dots with inverse-square interactions
Bibliographic record
Abstract
In this study, we theoretically scrutinize the effect of the inverse-square interaction on the thermal properties of two electrons trapped in a parabolic GaAs quantum dot. The analytical energy spectrum was used to calculate the thermal properties of the system using the canonical ensemble formalism. It was found that the thermal energy increased with the increase in temperature, while it remained almost constant for sufficiently low temperatures; it was also demonstrated that the inverse-square interaction increased the thermal mean energy. Moreover, the heat capacity increased sharply within a low-temperature window and saturated to the value of 2k B in the high-temperature limit. As expected, entropy increased linearly with increasing temperature. It was also shown that both entropy and heat capacity decreased rapidly when the confinement strength increased (or the dot size decreased) in the low-temperature limit, regardless of the influence of the interaction between the electrons. We also show that the number of allowed states of the system decreased as the interaction strength increased (Z(λ = 0) > Z(λ ≠ 0)). Finally, the stability of the system was investigated through F–T curves. The three-dimensional surface for the temperature-dependent mean energy and heat capacity was also plotted. It should be noted that, for the thermal mean energy, partition function, and Helmholtz free energy, the normal physical behavior of the two-oscillator system with Fermi statistics is recovered for λ → 0. However, heat capacity and entropy show exact two-fermion oscillator system behavior. The most impressive result found in this work is that the inverse-square interaction does not affect the heat capacity and entropy at all despite its noticeable effects on the thermal mean energy. This, in turn, facilitates theoretical studies related to finding the distinctive parameters of quantum dots without going into the heavy calculations resulting from the effects of interactions.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".