Spectra of generators of Markovian evolution in the thermodynamic limit: From non-Hermitian to full evolution via tridiagonal Laurent matrices
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866915520284983296 |
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| author | Klausen, Frederik Ravn |
| author_facet | Klausen, Frederik Ravn |
| contents | It is shown that generators of single-particle, translation-invariant Lindblad operators on the infinite line are unitarily equivalent to direct integrals of finite-range bi-infinite Laurent operator with finite-range perturbations. This representation enables rigorous calculation of spectra for local dissipation such as dephasing and incoherent hopping, and yields proofs of gaplessness, absence of residual spectrum and a condition for convergence of finite volume spectra to their infinite volume counterparts. The analysis relies on new results on the spectra of direct integrals of non-normal operators which may be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_09879 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Spectra of generators of Markovian evolution in the thermodynamic limit: From non-Hermitian to full evolution via tridiagonal Laurent matrices Klausen, Frederik Ravn Mathematical Physics Spectral Theory Quantum Physics 81V99, 46N50, 82C10, 47A10 It is shown that generators of single-particle, translation-invariant Lindblad operators on the infinite line are unitarily equivalent to direct integrals of finite-range bi-infinite Laurent operator with finite-range perturbations. This representation enables rigorous calculation of spectra for local dissipation such as dephasing and incoherent hopping, and yields proofs of gaplessness, absence of residual spectrum and a condition for convergence of finite volume spectra to their infinite volume counterparts. The analysis relies on new results on the spectra of direct integrals of non-normal operators which may be of independent interest. |
| title | Spectra of generators of Markovian evolution in the thermodynamic limit: From non-Hermitian to full evolution via tridiagonal Laurent matrices |
| topic | Mathematical Physics Spectral Theory Quantum Physics 81V99, 46N50, 82C10, 47A10 |
| url | https://arxiv.org/abs/2206.09879 |