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Research Article · Preprint Physics and Astronomy

Bose gases in weakly twisted annular-sector waveguides

Scott Schubr

Luminary Oddities LLC

  • Physics and Astronomy
  • Statistical and Nonlinear Physics
  • Mathematical Physics
Primary subject
Physics and Astronomy
Paper type
Research Article
Manuscript stage
Preprint
Manuscript
Archived
Edition
1 · Permanent link
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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 decreases to zero. At particle scale c^(-1/p), critical scaled density is finite exactly for 0 < p < 1, with the excess in the single ground mode. An operator-valued symbol retains every transverse band. For p > 1, the denser scale c^(-2/(p+1)) produces positive limiting occupation fractions in every fixed mode of an anharmonic oscillator. The marginal logarithmic scale is identified by a sector-specific uniform harmonic comparison. Actual fixed-mode spectral limits, intermediate-energy counts, full fixed-time heat traces and singular excited occupations are controlled. All statistical conclusions concern grand-canonical mean occupations; classical power-trap and free-Gibbs laws are credited.

Keywords Statistical and Nonlinear Physics · Mathematical Physics · mathematical research

Scope of the work

Dirichlet physical annular-sector tube with beta_c=c(1+z²)^(p/2): actual fixed-mode oscillator limit/gap, uniform low-energy count and full-band fixed-time heat trace. Grand-canonical natural particle scale c^(-1/p) has finite critical density exactlyp<1; p=1 logarithmic scale has criticalrho=a/(2pi beta) and reviewed mean/chemical laws; p>1 denser c^(-2/(p+1)) scale has all-mode oscillator resolvent occupation law. Canonical proof excluded from public paper.

Reproduction notes

The exact publication package includes the 10-page manuscript, editable LaTeX sources, reader/build instructions, citation metadata, public checksums and any necessary mathematical or computational supplements. Keep its 6 members together and follow the included README for dependencies, build commands and any finite verification programs. Published finite checks support the stated arguments; they do not replace universal analytic proofs or establish external human refereeing.

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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.

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Scott Schubr. (2026). Bose gases in weakly twisted annular-sector waveguides (Version 1). Luminary Research Archive. https://research.luminaryoddities.com/bose-gases-in-weakly-twisted-annular-sector-waveguides/v/1

BibTeX
@techreport{luminary_bose_gases_in_weakly_twisted_annular_sector_waveguides_v1,
  title = {Bose gases in weakly twisted annular-sector waveguides},
  author = {Scott Schubr},
  year = {2026},
  institution = {Luminary Research Archive},
  type = {Research Article},
  note = {Version 1},
  url = {https://research.luminaryoddities.com/bose-gases-in-weakly-twisted-annular-sector-waveguides/v/1}
}

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