Evolution operators for quantum chains

Discrete-time evolution operators in integrable quantum lattice models are sometimes more fundamental objects than 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. (fast track communications)