Bogoliubov depletion law for hard-sphere Bose gases
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For exact pure and mixed ground states of a three-dimensional hard-sphere Bose gas, determine the nonzero-momentum occupation law in the thermodynamic limit at fixed density, followed by the dilute limit. The target is the scaled Bogoliubov profile and depletion 8/(3√π)√(ρa³)+o(√(ρa³)), uniformly over thermodynamic accumulation values.
Why it matters and what counts as progress
Why it matters: It connects the microscopic momentum distribution of exact interacting ground states with the Bogoliubov depletion prediction, beyond results about energy alone.
What counts as progress: Derive the momentum profile and depletion coefficient for exact ground states with the thermodynamic limit taken before the dilute limit; control the error uniformly over accumulation values.
How the problem developed
- 1947 · Theory [1]
Nikolay Bogoliubov Introduced the approximation that predicts the leading condensate depletion in a dilute interacting Bose gas.
- 5 Oct 2026 · Reported theorem [2]
OpenAI The manuscript reports the leading depletion coefficient and scaled momentum distribution for ground states of the dilute hard-sphere Bose gas.
AI contribution
Quantum Depletion and Momentum Distribution in the Dilute Hard-Sphere Bose Gas
For exact pure and mixed ground states of a three-dimensional hard-sphere Bose gas, the nonzero-momentum occupation measure approaches the scaled Bogoliubov profile: first take the thermodynamic limit at fixed density, then the dilute limit. Its mass gives depletion 8/(3√π)√(ρa³)+o(√(ρa³)), uniformly over thermodynamic accumulation values.
Sources
- Bogoliubov, On the theory of superfluidity
- OpenAI, Quantum Depletion and Momentum Distribution in the Dilute Hard-Sphere Bose Gas
- Quantum Depletion and Momentum Distribution in the Dilute Hard-Sphere Bose Gas
- OpenAI Math, release and verification notes
- OpenAI Math, manuscript contents
- OpenAI Math, formalization scope for family 267
Website timeline
Publication dates and editorial changes.