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Theory of classical metastability in open quantum systems

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Abstract: Metastability is a large separation in timescales in the dynamics, manifesting as the existence of a regime when states of the system appear stationary, before eventual relaxation towards a true stationary state at much larger times. In this talk, I will focus on the emergence of classical metastability, i.e., the case when metastable states can be approximated as probabilistic mixtures of a finite number of states. I will show that a number of classical features follow from this approximation. First, metastable states are mixtures of approximately disjoint states which can be distinguished with negligible error and thus play the role of metastable phases. Second, symmetries of the dynamics correspond to approximate permutations of metastable phases and thus are necessarily discrete. Third, the long-time dynamics – the final relaxation towards the stationary state – is approximated by a classical stochastic dynamics between the metastable phases. Importantly, the classical dynamics is observed not only on average, but also at the level of individual quantum trajectories: coarse-grained continuous measurement records can be viewed as noisy classical trajectories, while their statistics can be approximated by that of the classical dynamics. Finally, I will also briefly explain how to numerically verify the presence of classical metastability in a given open quantum system. Since the proximity to a first-order dissipative phase transition manifests as metastability, the presented results can be used to investigate such transitions – which occur in the thermodynamic limit – already at moderate sizes accessible to numerics.

Reference: arXiv:2006.01227

This talk is part of the Theoretical Physics Seminars series.

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