Coherence-Controlled Quantum Zeno Dynamics from Exact Reset Maps

Abstract: We develop an exact framework for quantum Zeno and anti-Zeno dynamics in a broad class of open systems, whose microscopic Hamiltonians are quadratic in bosonic or fermionic operators. We treat the environment through an exact stroboscopic resetting scheme acting at the level of the single-particle density matrix (SPDM). Within this framework, we consider two cases: a repeated-interaction (RI) protocol, in which the environment block is rethermalized and all system-environment coherences are erased after each step, and an evolving-correlation (EC) protocol, in which only the environment block is reset while system-environment coherences are preserved. For RI, we derive a general short-time Zeno law for the survival probability of a single-particle excitation and show that the corresponding decay rate scales linearly with the reset interval, implying Zeno freezing in the limit of infinitely frequent resets. Beyond the short-time regime, we formulate the RI dynamics directly in terms of the exact one-cycle propagator, which allows us to analyze finite-$τ$ anti-Zeno windows without additional approximations. For EC, we obtain a continuous-reset description in which the kept single-particle correlators obey a finite-dimensional linear differential equation. In this case the drift in the system block remains finite in the frequent-reset limit, so strict freezing is absent. We illustrate these results for a single fermionic level coupled to a semi-infinite tight-binding chain acting as a structured bath. Our results identify coherence erasure versus coherence retention as the key factor controlling the reset-induced Zeno physics.