研究発表

Recent experimental advance in cold-atomic physics enables us to implement well- controlled dissipation in quantum many-body systems. It is therefore a fascinating problem to explore generic phenomena arising from the interplay between interactions in many-body systems and dissipation. Theoretically, the time evolution of a Markovian open quantum system is generated by the Liouvillian of the Lindblad form, whose spectral properties (e.g., the relation between the spectral gap and the relaxation time [1-4]) have been intensively studied up to now. In this talk, I focus on the spectral gap of the Liouvillian (the Liouvillian gap) in the weak dissipation limit. I argue that the Liouvillian gap under a weak bulk dissipation often exhibits a singularity in the thermodynamic limit, which is closely related with the irreversible relaxation that is observed in the chaotic quantum many- body system completely isolated from the environment. References [1] M. Žnidarič, Phys. Rev. E 92, 042143 (2015) [2] T. Mori and T. Shirai, Phys. Rev. Lett. 125, 230604 (2020) [3] T. Haga, M. Nakagawa, R. Hamazaki, and M. Ueda, Phys. Rev. Lett. 127, 070402 (2021) [4] T. Mori and T. Shirai, Phys. Rev. Lett. 130, 230404 (2023)

Open-system analysis of thermalization in isolated quantum systems Eigenstate thermalization hypothesis (ETH) explains why an isolated quantum system eventually thermalizes, but it does not tell us much about the timescale of the onset of thermalization. Since the time evolution is unitary, all the eigenvalues of the time evolution operator lie on the unit circle in complex plane. It means that we cannot estimate the thermalization timescale by looking at eigenvalues of the time evolution operator. In this talk, I argue that an open-system analysis based on the Lindblad quantum master equation gives an estimate of the thermalization timescale of the isolated system [1]. More specifically, we consider a kicked Ising chain under bulk dissipation and investigate the Liouvillian gap, which is the spectral gap of the generator of the dynamics, in the weak dissipation limit. We show that the Liouvillian gap can remain finite even in the weak dissipation limit if the thermodynamic limit is taken first. This finite value of the Liouvillian gap in the weak dissipation limit gives the exponential decay rate of the isolated system. This result is reminiscent of Ruelle-Pollicott resonances in classical chaos. Indeed, we argue that the finite Liouvillian gap in the weak dissipation limit is interpreted as a quantum Ruelle-Pollicott resonance. For static systems with the time-independent Hamiltonian, a special care is needed. I also explain how we can extract exponential decays hidden in the unitary time evolution of a static system. [1] T. Mori, arXiv:2311.10304

In recent years, open quantum many-body systems have received much attention due to experimental progress that allows us to introduce well-controlled dissipation to quantum many-body systems. A quantum Markov process is generated by the Liouvillian superoperator of the Lindblad form. An important quantity characterizing dissipative quantum dynamics is the Liouvillian gap, i.e., the spectral gap of the Liouvillian. The Liouvillian gap characterizes the asymptotic decay rate in the long-time regime. It was shown that a finite Liouvillian gap in the thermodynamic limit implies exponential decay of correlations in the steady state. As a consequence, a vanishing Liouvillian gap is used as a signature of a dissipative phase transition. In this talk, I focus on the Liouvillian gap of open quantum many-body systems in the weak dissipation limit. I argue that, counterintuitively, the thermodynamic limit of the Liouvillian gap in a chaotic open Floquet system (i.e., the Hamiltonian of the system of interest periodically depends on time) converges to a nonzero value in the weak dissipation limit. This nontrivial value of the Liouvillian gap is identified as the intrinsic decay rate of the underlying isolated quantum system. I also discuss an analogous result for open static systems, in which the Hamiltonian does not depend on time.