AI 中文总结
研究在中心自旋模型中引入PT对称性，通过伪厄密形式和戴森映射研究其对退相干、环境诱导退相干选择及非马尔可夫性的影响，发现γ增加时退相干减缓等现象，且BLP度量有转折点行为。
AI 中文摘要
我们通过添加具有可调厄密性参数γ的PT对称相互作用，将PT对称性引入中心自旋模型。利用伪厄密形式，应用戴森映射将非厄密哈密顿量转换为其厄密表示。发现随着γ增加，退相干减缓，最终在γ = 1时停止。定义一个与度规算符对易的伪厄密可观测量作为自哈密顿量。随着γ趋于1，环境诱导退相干选择逐渐迫使系统选择自哈密顿量的本征态。在强环境 regime中，中心自旋态的稳态纯度随γ增加呈现矛盾的下降。然而，发现一个对应于向自旋浴最大信息耗散的转折点（最小值）。最后，在有限时间内评估了用于量化量子系统非马尔可夫性的Breuer-Laine-Piilo（BLP）度量。在强环境 regime中，BLP度量表现出类似的转折点行为。
英文摘要
We have introduced PT-symmetry to a central spin model by adding a PT-symmetric interaction with a tunable hermiticity parameter $γ$. Using the pseudo-Hermitian formalism, we applied a Dyson map to transform the non-Hermitian Hamiltonian to its Hermitian representation. We have found that the decoherence slows down as $γ$ increases, eventually ceasing at $γ=1$. We define a pseudo-Hermitian observable that commutes with the metric operator to add as the self-Hamiltonian. Einselection gradually forced the system to select the eigenstates of the self-Hamiltonian as $γ\rightarrow1$. The steady-state purity of the central spin states in the strong environment regime exhibits a paradoxical decrease as $γ$ increases. However, a turning point (minimum) corresponding to a maximum information dissipation to the spin bath is found. Finally, the Breuer-Laine-Piilo (BLP) measure, which is used to quantify the non-Markovianity of a quantum system, was evaluated for a finite time. The BLP measure in the strong environment regime exhibited similar turning point behavior, which means that the information backflow reaches a saturation point before declining. This decline signifies the point where PT-symmetry starts shielding the central spin from the environment.
