2018/07/25 by Pedro Ribeiro, Tomaž Prosen · 1 citation
Physics and Astronomy · #quant-ph #cond-mat.str-el #nlin.SI
paper · pdf · doi:10.1103/physrevlett.122.010401
published as Phys. Rev. Lett. 122, 010401 (2019) · 5 pages, 4 figures
arxiv created 2018/07/25 · arxiv updated 2019/01/09
We consider a collective quantum spin-s in contact with Markovian spin-polarized baths. Using a conserved super-operator charge, a differential representation of the Liouvillian is constructed to find its exact spectrum and eigen-modes. We study the spectral properties of the model in the large-s limit using a semi-classical quantization condition and show that the spectral density may diverge along certain curves in the complex plane. We exploit our exact solution to characterize steady-state properties, in particular at the discontinuous phase transition that arises for unpolarized environments, and to determine the decay rates of coherences and populations. Our approach provides a systematic way of finding integrable Liouvillian operators with non-trivial steady-states as well as a way to study their spectral properties and eigen-modes.