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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.