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

2022/06/20 by Klausen, Frederik Ravn
#46N50 #47A10 #81V99 #82C10 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2206.09879

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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