Środowiskowe Seminarium z Informacji i Technologii Kwantowych
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2021-06-10 (11:15) 
Katarzyna Macieszczak (University of Cambridge)
Operational approach to metastability in open quantum systems
Zoom link: https://zoom.us/j/6526721604?pwd=Y0pPdE9vT1hNWWNiZVBMaEVOeHN2dz09
Metastability is a phenomenon of a large separation in dynamical timescales, leading to a prolonged temporal regime when system states appear stationary before eventually relaxing towards a true, usually unique, steady state. For classical equilibrium dynamics, metastability can be understood as a consequence of multiple local minima present in the system free energy function, but for non-equilibrium dynamics such a general description linking dynamic and static properties is elusive. In this talk, I will introduce an information-theoretic approach of quantifying how non-stationary an open quantum system is during a given time regime [1]. Despite its abstractness, this approach arises directly from experimental considerations of how the averages of observables change with time in a finitely dimensional system. For dynamics governed by a master equation, I will then draw upon a simple but powerful analogy with exponential decay, to investigate regimes when such changes are negligible according to the logarithmic scale of time, and thus the system can be viewed as approximately stationary. I will show that a distinct regime of approximate stationarity may arise beyond the initial and final regimes of the dynamics, which provides a quantitative description of the phenomenon of metastability in open quantum systems. I will also explain how metastability relates to the separation in the real part of the master operator spectrum and connect to earlier results of the spectral theory of metastability [2].
[1] arXiv:2104.05095 (2021).
[2] Phys. Rev. Lett. 116, 240404 (2016).
Metastability is a phenomenon of a large separation in dynamical timescales, leading to a prolonged temporal regime when system states appear stationary before eventually relaxing towards a true, usually unique, steady state. For classical equilibrium dynamics, metastability can be understood as a consequence of multiple local minima present in the system free energy function, but for non-equilibrium dynamics such a general description linking dynamic and static properties is elusive. In this talk, I will introduce an information-theoretic approach of quantifying how non-stationary an open quantum system is during a given time regime [1]. Despite its abstractness, this approach arises directly from experimental considerations of how the averages of observables change with time in a finitely dimensional system. For dynamics governed by a master equation, I will then draw upon a simple but powerful analogy with exponential decay, to investigate regimes when such changes are negligible according to the logarithmic scale of time, and thus the system can be viewed as approximately stationary. I will show that a distinct regime of approximate stationarity may arise beyond the initial and final regimes of the dynamics, which provides a quantitative description of the phenomenon of metastability in open quantum systems. I will also explain how metastability relates to the separation in the real part of the master operator spectrum and connect to earlier results of the spectral theory of metastability [2].
[1] arXiv:2104.05095 (2021).
[2] Phys. Rev. Lett. 116, 240404 (2016).