Speaker
Description
Recent experimental developments in quantum simulators and quantum computers have enabled us to investigate the effects of measurement and dissipation on quantum dynamics. Theoretically, such open quantum systems are often analyzed in terms of the spectra and symmetries of the generators governing the dynamics, provided that the generators are time independent. However, it remains unclear how to analyze open quantum systems governed by time-dependent generators. In this talk, I discuss two topics concerning steady-state structures in open quantum systems beyond time-independent settings.
First, we consider measurement-induced phase transitions, where the dynamics of quantum trajectories cannot be described by time-independent generators because of random measurement outcomes. It is known that measurements in quantum many-body systems can lead to entanglement transitions in quantum trajectories. We show that this transition is accompanied by a spectral transition [1], in analogy with ground-state quantum phase transitions in equilibrium. Here, the relevant spectrum is defined as the Lyapunov spectrum, rather than the eigenvalue spectrum of a time-independent Hamiltonian. We discuss how the Lyapunov spectrum can be useful for characterizing open quantum systems that are not governed by time-independent generators [2–5].
Second, we consider a rigorous classification of steady-state dynamics in time-dependent Gorini-Kossakowski-Sudarshan-Lindblad equations with a recurrence property [6]. We introduce two distinct notions of strong symmetry, namely strong symmetries in the Schrödinger and Heisenberg pictures, and show that they completely characterize four different types of steady-state properties. We also discuss algebraic criteria for a system to have a unique steady state. We demonstrate our results in several examples, including time-quasiperiodically driven many-body systems.
[1] K. Mochizuki and RH, Phys. Rev. Lett. 134, 010410 (2025)
[1] K. Mochizuki and RH, Phys. Rev. Research 6 (1), 013004 (2024)
[1] K. Mochizuki and RH, J. Phys. A: Math. Theor. 58 (26), 265004 (2025)
[4] H. Oshima, K. Mochizuki, RH, Y. Fuji, Phys. Rev. Lett. 134 (24), 240401 (2025)
[5] RH et al., PTEP ptag055 (2026). [Review paper]
[6] H. Yoshida and RH, arXiv:2602.13095 (2026)