Bose gases in weakly twisted annular-sector waveguides
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Abstract
We study an ideal Bose gas in an infinite-volume Dirichlet tube whose annular-sector cross-section rotates with speed c(1+z^2)^(p/2), as c↓0. At particle scale c^(-1/p) the critical scaled density is finite exactly when 0<p<1; above it the excess occupies the single ground mode. The critical density retains every transverse band of an explicit operator-valued symbol. For p>1, a denser particle scale c^(-2/(p+1)) instead yields positive limiting occupation fractions in every fixed mode of an anharmonic oscillator. The marginal logarithmic scale is also identified, using a uniform two-parameter harmonic comparison specific to the sector. We prove the actual fixed-mode spectral limit, an intermediate-energy count and the full fixed-time heat-trace limit, and control the singular excited Bose occupation as the spectral gap closes. All statistical statements use grand-canonical mean occupations. The power-trap criteria and free-Gibbs occupation laws are classical; the result supplies their precise geometric realization for this nonseparable confining family.
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Research details
- Subjects
- Mathematics · Physics and Astronomy · Mathematical Physics · Statistical and Nonlinear Physics
- Keywords
- Statistical and Nonlinear Physics, Mathematical Physics, mathematical research
- Manuscript date
- 2026-10-24
- Reader reuse
- No additional permission granted
Scope
Geometric spectral and Bose-occupation limits for weakly twisted annular-sector Dirichlet tubes, including natural-scale condensation, denser all-mode regimes and the logarithmic borderline.
Disclosures
AI-assisted tools supported research exploration, literature review, manuscript preparation and internal verification. The author retains responsibility for the work. Internal AI-assisted and computational checks are distinct from external human peer review.
Reproduction
10-page manuscript and 6 source-package members. Use python build.py with an installed compatible Tectonic to compile main.tex. The spectral limits and grand-canonical occupation laws have analytic proofs and require no numerical supplement.