Research: Asymptotic Exceptional Steady States in Dissipative Dynamics

The complexity of many-body systems in quantum physics is directly reflected in the difficulty of preparing quantum states of interest such as ground states describing the system at zero temperature. In generic dissipative dynamics, this issue manifests in the form of critical slowdown, i.e. the divergence with system size of the time the system needs to approach its steady state. Researchers at TU Dresden and MPIPKS Dresden have now revealed the deeper structure behind this slowdown by demonstrated its direct relation to the asymptotic (with increasing system size) coalescence of the steady state with another eigenstate of the Liouvillian operator governing the dissipative dynamics. This coalescence of eigenstates amounts to an asymptotically non-diagonalizable structure of the Liouvillian, which is a surprising discovery since arriving a such a structure has been known to be mathematically impossible for the steady state of any dynamically stable system. Besides its wide applicability, the qualitatively different response of non-diagonalizable points to perturbations gives immediate physical relevance to the present discovery.  

Y.-M. Hu, J. C. Budich,
Asymptotic Exceptional Steady States in Dissipative Dynamics,
Phys. Rev. Lett. 135, 250402 (2025) (arXiv)