Recently, several studies involving open quantum systems which possess a strong symmetry have observed that every individual trajectory in the Monte Carlo unravelling of the master equation will dynamically select a specific symmetry sector to 'freeze' into in the long-time limit. This phenomenon has been termed 'dissipative freezing', and in this paper we argue, by presenting several simple mathematical perspectives on the problem, that it is a general consequence of the presence of a strong symmetry in an open system with only a few exceptions. Using a number of example systems we illustrate these arguments, uncovering an explicit relationship between the spectral properties of the Liouvillian in off-diagonal symmetry sectors and the time it takes for freezing to occur. In the limiting case that eigenmodes with purely imaginary eigenvalues are manifest in these sectors, freezing fails to occur. Such modes indicate the preservation of information and coherences between symmetry sectors of the system and can lead to phenomena such as non-stationarity and synchronisation. The absence of freezing at the level of a single quantum trajectory provides a simple, computationally efficient way of identifying these traceless modes.
Cited by 1
Li et al., Synchronization of persistent oscillations in spin systems with nonlocal dissipation
Phys. Rev. A 107, 032219 (2023) [Crossref]
Authors / Affiliations: mappings to Contributors and OrganizationsSee all Organizations.
- 1 University of Oxford
- 2 Flatiron Institute
- 3 Institut für Laserphysik [ILP]
- 4 Hamburg Centre for Ultrafast Imaging
- 5 Universidad Autónoma de Madrid / Autonomous University of Madrid [UAM]