Luminary Research Archive
Luminary Research ArchiveIndependent scholarship
Luminary Portal

All Research

Research

135 papers
Browse papers
  1. Bose gases in weakly twisted annular-sector waveguidesScott SchubrEdition 2 · 2026-10-27 Public
  2. Sharp convergence of heat-kernel Sinkhorn metricsScott SchubrEdition 2 · 2026-10-27 Public
  3. Positive heat-flow observations on spherical shells: cutoffs, optimal preparation and concentrationScott SchubrEdition 2 · 2026-10-27 Public
  4. Leading bias and positive correction of heat-kernel Sinkhorn metricsScott SchubrEdition 2 · 2026-10-27 Public
  5. Self-concordance and allocation for spatial power sumsScott SchubrEdition 2 · 2026-10-27 Public
  6. Curvature classification and certified Sinkhorn metrics for Fourier density modelsScott SchubrEdition 2 · 2026-10-27 Public
  7. Mean ergodic convergence from near-diagonal subadditivityScott SchubrEdition 2 · 2026-10-27 Public
  8. Quantitative Null-Space Compression for a Weighted Weil OperatorScott SchubrEdition 2 · 2026-10-27 Public
  9. Mixed-state escape bounds and proper agnostic learning of stabilizer states in odd-prime dimensionsScott SchubrEdition 3 · 2026-10-27 Public
  10. Degree laws and edge correlations for random forestsScott SchubrEdition 2 · 2026-10-27 Public
  11. Polynomial cores and inertia under Carleman moment boundsScott SchubrEdition 2 · 2026-10-27 Public
  12. Certified source elimination for localized odd Weil formsScott SchubrEdition 2 · 2026-10-27 Public
  13. Covariance-Spectrum Certificates for Homogeneous Stable Count LawsScott SchubrEdition 7 · 2026-10-27 Public
  14. Trace-perturbed minimizers of the mixed discriminantScott SchubrEdition 2 · 2026-10-27 Public
  15. Finite-projection holomorphic stabilization of contractible affine hypersurfacesScott SchubrEdition 3 · 2026-10-27 Public
  16. Sharp noise transitions for an adaptive single-copy stabilizer-learning processScott SchubrEdition 2 · 2026-10-27 Public
  17. Single-copy learning of noisy stabilizers by certified filteringScott SchubrEdition 2 · 2026-10-27 Public
  18. Exponential growth of sparse Euler products and normal graded domainsScott SchubrEdition 2 · 2026-10-27 Public
  19. Single-time boundary heat-flux rigidity for smooth domainsScott SchubrEdition 3 · 2026-10-27 Public
  20. Sharp all-times heat-content comparison and concentration on compact metric graphsScott SchubrEdition 2 · 2026-10-27 Public
  21. Finite Persistent Memory in Exact Sampling: Countable Rigidity and Algebraic Memory BoundsScott SchubrEdition 2 · 2026-10-27 Public
  22. Phase transitions and effective curvature bounds in Fourier density modelsScott SchubrEdition 2 · 2026-10-27 Public
  23. Energy-Filtered Dynamical Localization in Constructive Dirichlet TowersScott SchubrEdition 2 · 2026-10-27 Public
  24. Sharp fourth-root concavity for lattice counts on smooth toric Fano threefoldsScott SchubrEdition 2 · 2026-10-27 Public
PublicEdition 2

Bose gases in weakly twisted annular-sector waveguides

Scott Schubr

Original PDF · First-page preview

Loading original first page…

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.

Read the full paper in the original PDF.