Spectroscopic signatures of a Liouvillian exceptional spectral phase in a collective spin

2026/02/28 by Rafael A. Molina
Physics and Astronomy · #Emission spectrum #Excitation #Phase (matter) #Quantum Mechanics and Non-Hermitian Physics #Quantum many-body systems #Relaxation (psychology) #Spectral properties #Spectrum (functional analysis) #Spin (aerodynamics) #Topological Materials and Phenomena #cond-mat.mes-hall #quant-ph

paper · pdf · doi:10.21468/scipostphyscore.9.3.045

published as SciPost Phys. Core 9, 045 (2026) · Submission to SciPost Physics Core. Expanded discussion and appendices

arxiv created 2026/04/25 · openalex publication_date 2026/07/30 · openalex created_date 2026/07/31 · openalex updated_date 2026/08/02 · arxiv updated 2026/08/05

Abstract

Non-Hermitian degeneracies of Lindblad generators (Liouvillian exceptional points) can induce non-exponential relaxation and higher-order poles in dynamical response functions. A collective spin coupled to a polarized Markovian bath exhibits an exceptional spectral phase in which defective Liouvillian modes imprint super-Lorentzian features in frequency-resolved spectra. We compute the emission spectrum via the Liouvillian resolvent, identify symmetry-sector selection rules, and demonstrate that exceptional-point signatures are strongly state-dependent: they are suppressed in steady-state fluorescence yet become unambiguous for generic (infinite-temperature or random) initial states. Our results provide an experimentally accessible spectroscopic diagnostic of many-body Liouvillian exceptional phases and clarify when steady-state emission can (and cannot) reveal them.

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