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On the generality of symmetry breaking and dissipative freezing in quantum trajectories

by Joseph Tindall, Dieter Jaksch, Carlos Sánchez Muñoz

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Submission summary

Authors (as Contributors): Dieter Jaksch · Joseph Tindall
Submission information
Arxiv Link: (pdf)
Date accepted: 2022-10-13
Date submitted: 2022-09-23 16:13
Submitted by: Tindall, Joseph
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Quantum Physics
Approaches: Theoretical, Computational


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.

Published as SciPost Phys. Core 6, 004 (2023)

List of changes

1) Fixed a typo concerning the α’s below Eq. (14)
2) Fixed a typo in Section 2.5
3) We have notated the freeze-time as $t_{f}$.
4) We have discussed that determining Eq. (26) generally requires diagonalization of the full Liouvillian. We have noted, however, that there exists a more simple case – based on simple relations involving the Lindblad and Hamiltonian operators – where it is known to be true. Moreover, we have reemphasized our argument that our results demonstrate that a single trajectory can demonstrate clear evidence of Eq. (26) – which is much more computationally efficient than diagonalization of the full Liouvillian.
5) We have removed the circular argument on page 17.
6) We have made it clear, in Section 2.4, that the steady state in a given symmetry subspace need not be unique.
7) We have made the argument (that one of $p^{(i)} (α_{1},t)$ and $p^{(i)} (α_{2},t)$ will be of order $\epsilon^{2}$ at the freeze-time) at the beginning of page 11 clearer.
8) We have made extensive grammatical changes in line with the referee’s suggestions.
9) We have removed the mention of qudits and made it clear we are referring to two particles of spin 3/2. We have also specified the Hilbert space dimension.
10) We have made the caption of Fig. 2 clearer and in-line with Eq. (1).

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