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 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.
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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
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.
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