Propagation of Condensation via Neumann Localization in the Dilute Bose Gas
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911566622883840 |
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| author | Junge, Lukas |
| author_facet | Junge, Lukas |
| contents | We prove a Neumann localization inequality for the Laplacian that includes a spectral gap. This result is obtained by partitioning a cube into overlapping families of subcubes and analysing the associated projection operators. The resulting operator inequality goes through a discrete Neumann Laplacian on the lattice of boxes and yields a quantitative spectral gap estimate. As an application, we consider the dilute Bose gas with Neumann boundary conditions. Combining the localization method with recently established free-energy lower bounds, we propagate strong condensation estimates from the Gross Pitaevskii scale to larger boxes of side length $R\sim a(ρa^3)^{-\frac{3}{4}-η}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_20776 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Propagation of Condensation via Neumann Localization in the Dilute Bose Gas Junge, Lukas Mathematical Physics Spectral Theory 81Q10 (Primary) 47B25 (Secondary) We prove a Neumann localization inequality for the Laplacian that includes a spectral gap. This result is obtained by partitioning a cube into overlapping families of subcubes and analysing the associated projection operators. The resulting operator inequality goes through a discrete Neumann Laplacian on the lattice of boxes and yields a quantitative spectral gap estimate. As an application, we consider the dilute Bose gas with Neumann boundary conditions. Combining the localization method with recently established free-energy lower bounds, we propagate strong condensation estimates from the Gross Pitaevskii scale to larger boxes of side length $R\sim a(ρa^3)^{-\frac{3}{4}-η}$. |
| title | Propagation of Condensation via Neumann Localization in the Dilute Bose Gas |
| topic | Mathematical Physics Spectral Theory 81Q10 (Primary) 47B25 (Secondary) |
| url | https://arxiv.org/abs/2603.20776 |