# [Quantum Depletion and Momentum Distribution in the Dilute Hard-Sphere Bose Gas](Quantum-Depletion-in-the-Dilute-Hard-Sphere-Bose-Gas.pdf)

**Author:** OpenAI

**Date:** October 5, 2026

## Citation

```bibtex
@misc{OAI:Quantum-Depletion-and-Momentum-Distribution-in-the-Dilute-Hard-Sphere-Bose-Gas-October-5-2026,
  author = {{OpenAI}},
  title = {{Quantum Depletion and Momentum Distribution in the Dilute Hard-Sphere Bose Gas}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Quantum-Depletion-and-Momentum-Distribution-in-the-Dilute-Hard-Sphere-Bose-Gas-October-5-2026/Quantum-Depletion-in-the-Dilute-Hard-Sphere-Bose-Gas.pdf}{OAI:Quantum-Depletion-and-Momentum-Distribution-in-the-Dilute-Hard-Sphere-Bose-Gas-October-5-2026}},
  year = {2026}
}
```