从纯耗散出发的哈密顿动力学
Hamiltonian dynamics from pure dissipation
- University of Copenhagen（哥本哈根大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文展示纯耗散可模拟哈密顿动力学，通过非简并跳跃算子和可控耗散生成器，在钻石范数下以O(t²/ε)时间逼近哈密顿动力学，揭示了耗散动力学的基本退相干成本。
AI中文摘要：
封闭与开放量子动力学的根本差异在于环境相互作用：封闭系统完全孤立，受幺正哈密顿量动力学可逆演化；开放系统持续与外部浴耦合，导致不可逆耗散与信息丢失。本文展示内部哈密顿量动力学可通过外部纯耗散
英文摘要：
The fundamental difference between closed and open quantum dynamics lies in their environmental interaction: closed systems are perfectly isolated and evolve reversibly under unitary Hamiltonian dynamics, whereas open systems continuously couple to an external bath, resulting in irreversible dissipation and information loss. In this work, we show internal Hamiltonian dynamics can be "faked`` via external pure dissipation, i.e., Lindbladians without a coherent Hamiltonian part. More concretely, we show that, in a GKSL representation with zero explicit Hamiltonian term but nontraceless jump operators, bounded-norm dissipative generators can approximate Hamiltonian dynamics within $ε$ error in diamond norm using $\mathcal{O}(t^2/ε)$ evolution time. We further prove that for time-independent dynamics this $\mathcal{O}(t^2/ε)$ scaling is in the worst case, necessary and optimal from a geometric perspective, which captures the fundamental decoherence cost for catching up with the speed of Hamiltonian dynamics. Our construction leads to various implications, including the BQP-completeness of purely dissipative dynamics even before reaching approximate equilibrium, a Zeno-adjacent state-independent freezing effect, the no super-quadratic fast-forwarding theorem of a class of purely dissipative dynamics, and reducing Lindbladian simulation cost via gauge changing.
