Spectra of generators of Markovian evolution in the thermodynamic limit: From non-Hermitian to full evolution via tridiagonal Laurent matrices

• URL: http://arxiv.org/abs/2206.09879v3
• Date: Mon, 29 Sep 2025 15:48:43 GMT
• Title: Spectra of generators of Markovian evolution in the thermodynamic limit: From non-Hermitian to full evolution via tridiagonal Laurent matrices
• Authors: Frederik Ravn Klausen,
• Abstract summary: 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: 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.

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