Bose gases in weakly twisted annular-sector waveguides
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Abstract
We derive spectral, thermodynamic and one-body density-matrix opening limits for 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. For p>1, at particle scale c^(-2/(p+1)), the scaled one-body operator converges in trace norm to the tensor product of the transverse ground-state projector and an anharmonic-oscillator resolvent, and its straightened position density converges in L¹. At the natural c^(-1/p) scale the critical scaled density is finite exactly for 0<p<1; the excess occupies the single ground mode. This critical density retains every transverse band of an explicit operator-valued symbol. A sector-specific uniform harmonic comparison identifies the marginal c^(-1)log(1/c) scale. At the natural and marginal scales we prove operator-norm convergence to the condensate and compute the exact trace-norm defect carried by the normal component. The proof establishes actual scaled eigenprojector convergence, an intermediate count and a full fixed-time heat-trace limit, controlling singular excited occupations as the spectral gap closes. All statistical statements concern grand-canonical means. Power-trap criteria and free-Gibbs operator limits are classical; the result transfers them, including a spatial profile, to this actual nonseparable confining geometric 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
- none
Scope
Actual geometric spectral, full-band thermodynamic and one-body opening limits for weakly twisted annular-sector Dirichlet tubes. Dense p > 1 trace-norm covariance and straightened L1 density limits coexist with natural/marginal operator-norm condensate limits and exact residual normal trace mass; all statistical conclusions concern grand-canonical means.
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
The 13-page manuscript and complete editable source are supplied in a 6-member public package. README.md gives build instructions, dependencies and reproduction scope. Build reproduction is qualified by the compiler, support files and timestamp settings specified in the supplied instructions. The mathematical conclusions have analytic proofs; accompanying finite checks, where present, retain the limited scopes stated in the package.