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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Online-Zugang: | https://arxiv.org/abs/2605.26586 |
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| _version_ | 1866918523632091136 |
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| author | Ohzeki, Masayuki |
| author_facet | Ohzeki, Masayuki |
| contents | Analytic continuation from imaginary-time Green's functions to real-frequency spectra is a central ill-posed inverse problem in quantum many-body physics. We show that the thermal kernel admits an analytical generalized singular-value structure once its purely dynamical part is separated from the statistical weight imposed by the heat bath. The dynamical kernel is the imaginary-bandwidth continuation of Slepian's finite Fourier transform and is governed by the same Sturm-Liouville algebra that yields prolate spheroidal wave functions. Fermionic and bosonic statistics then enter as gauge transformations of the frequency-space inner product, producing self-adjoint effective potentials but no numerical kernel diagonalization. The Shannon number, $N_c=β\wmax/π$, fixes the upper information capacity of this pure Laplace channel. Finally, the optimal sampling points are obtained as eigenvalues of a Legendre colleague matrix, giving a deterministic compressed-sensing grid without iterative root searches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_26586 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Analytical Singular-Value Structure of Analytic-Continuation Kernels from Slepian Information Theory Ohzeki, Masayuki Quantum Physics Strongly Correlated Electrons Analytic continuation from imaginary-time Green's functions to real-frequency spectra is a central ill-posed inverse problem in quantum many-body physics. We show that the thermal kernel admits an analytical generalized singular-value structure once its purely dynamical part is separated from the statistical weight imposed by the heat bath. The dynamical kernel is the imaginary-bandwidth continuation of Slepian's finite Fourier transform and is governed by the same Sturm-Liouville algebra that yields prolate spheroidal wave functions. Fermionic and bosonic statistics then enter as gauge transformations of the frequency-space inner product, producing self-adjoint effective potentials but no numerical kernel diagonalization. The Shannon number, $N_c=β\wmax/π$, fixes the upper information capacity of this pure Laplace channel. Finally, the optimal sampling points are obtained as eigenvalues of a Legendre colleague matrix, giving a deterministic compressed-sensing grid without iterative root searches. |
| title | Analytical Singular-Value Structure of Analytic-Continuation Kernels from Slepian Information Theory |
| topic | Quantum Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2605.26586 |