Research Article · Preprint Physics and Astronomy
Bose gases in weakly twisted annular-sector waveguides
- Primary subject
- Physics and Astronomy
- Subject subfields
- Statistical and Nonlinear Physics · Mathematical Physics
- Paper type
- Research Article
- Manuscript stage
- Preprint
- Manuscript
- Archived
- Edition
- 2 · Permanent link
Overview
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.
Keywords Statistical and Nonlinear Physics · Mathematical Physics · mathematical research
Scope of the work
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.
Reproduction notes
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.
The manuscript
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Author 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.
A stable scholarly record
Cite this edition
Scott Schubr. (2026). Bose gases in weakly twisted annular-sector waveguides (Version 2). Luminary Research Archive. https://research.luminaryoddities.com/bose-gases-in-weakly-twisted-annular-sector-waveguides/v/2
BibTeX
@techreport{luminary_bose_gases_in_weakly_twisted_annular_sector_waveguides_v2,
title = {Bose gases in weakly twisted annular-sector waveguides},
author = {Scott Schubr},
year = {2026},
institution = {Luminary Research Archive},
type = {Research Article},
note = {Version 2},
url = {https://research.luminaryoddities.com/bose-gases-in-weakly-twisted-annular-sector-waveguides/v/2}
}Loading discussion…