2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115663Discrete-time evolution operators in integrable quantum lattice models are sometimes more fundamental objects then Hamiltonians. In this paper we study an evolution operator for the one-dimensional integrable q-deformed Bose gas with XXZ-type impurities and find its spectrum. Evolution operators give a new interpretation of known integrable systems, for instance our system describes apparently a simplest laser with a clear resonance peak in the spectrum.Exactly Solvable and Integrable Systemstext