Abstract
In this letter we point out that the Lindblad spectrum of a quantum many-body system displays a segment structure and exhibits two different energy scales in the strong dissipation regime. One energy scale determines the separation between different segments, being proportional to the dissipation strength, and the other energy scale determines the broadening of each segment, being inversely proportional to the dissipation strength. Ultilizing a relation between the dynamics of the second R\'enyi entropy and the Lindblad spectrum, we show that these two energy scales respectively determine the short- and the long-time dynamics of the second R\'enyi entropy starting from a generic initial state. This gives rise to opposite behaviors, that is, as the dissipation strength increases, the short-time dynamics becomes faster and the long-time dynamics becomes slower. We also interpret the quantum Zeno effect as specific initial states that only occupy the Lindblad spectrum around zero, for which only the broadening energy scale of the Lindblad spectrum matters and gives rise to suppressed dynamics with stronger dissipation. We illustrate our theory with two concrete models that can be experimentally verified.
Highlights
For a closed quantum system, the energy spectrum of its Hamiltonian fully determines the timescales of its dynamics
Utilizing an approximate relation between the dynamics of the second Rényi entropy and the Lindblad spectrum, we show that these two energy scales respectively determine the short-time and long-time dynamics of the second Rényi entropy starting from a generic initial state
The spectrum of the Hamiltonian alone can no longer determine the timescales of the entire dynamics, and a natural question is what energy scales set the timescales of dynamics of an open quantum system
Summary
For a closed quantum system, the energy spectrum of its Hamiltonian fully determines the timescales of its dynamics. One intuition is from the perturbation theory when the dissipation strength is weaker compared with the typical energy scales of the Hamiltonian [2] In this regime, treating the dissipation perturbatively gives rise to a scenario in which the dissipation dynamics become faster when the dissipation. Since the measurement can be understood in terms of dissipations in the Lindblad master equation, it provides another scenario in which the dissipation dynamics is suppressed when the dissipation becomes stronger when the dissipation strength is stronger than the typical energy scales of the Hamiltonian It seems that these two scenarios respectively apply to different parameter regimes, and the results are qualitatively opposite to each other. The dynamics always become slow when the dissipation strength increases, giving rise to the quantum Zeno effect
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