论文标题
非热汉密尔顿和林德布拉德进化之间的持续转变
A continuous transformation between non-Hermitian Hamiltonian and Lindbladian evolution
论文作者
论文摘要
非热汉密尔顿人和Lindblad操作员是描述与不同种类环境相互作用的量子系统的一些最重要的动力学生成器。第一种类型与保守的进化不同，它是导致粒子衰变的反省术语，而第二种类型的术语则以lindblad形式的耗散算子差异，可以用浴缸进行能量交换。但是，尽管在某些情况下，两种类型的地图可用于描述相同的可观察到的可观察，但它们形成了一个不相交的集合。在这项工作中，我们提出了一个$ l_ \ text {mixed}（z，ρ_s）= -i [h，ρ_s] + \ sum_i \ left（\ frac {γ_{c，i}} {z +γ_{z +γ_{c，i} f _ii} f_iipect f_i i^i的{ - \ frac {1} {2} \ {f_i^{\ dagger} f_i，ρ_s\} _+\ right）$，它取决于一般的能量$ z $，并且具有可调参数$γ_c$，该$ $γ_c$决定损失的粒子密度丢失的程度。它具有非限制的限制（$γ_C\ to $ $γ_c\ to $）和Lindbladian Dynamics（$γ_C\ to \ infty $）。中间制度会进化密度矩阵，从而使$ 0 \ leq \ text {tr}（ρ_s）\ leq 1 $。我们在辅助连续歧管的帮助下得出发电机，以充当粒子密度的水槽。进化描述了可以将粒子密度和能量与其环境交换的系统。我们为两个级别的系统和具有连贯的人口捕获点的五级级别系统的功能说明了其功能。
Non-Hermitian Hamiltonians and Lindblad operators are some of the most important generators of dynamics for describing quantum systems interacting with different kinds of environments. The first type differs from conservative evolution by an anti-Hermitian term that causes particle decay, while the second type differs by a dissipation operator in Lindblad form that allows energy exchange with a bath. However, although under some conditions the two types of maps can be used to describe the same observable, they form a disjoint set. In this work, we propose a generalized generator of dynamics of the form $L_\text{mixed}(z,ρ_S) = -i[H,ρ_S] + \sum_i \left(\frac{Γ_{c,i}}{z+Γ_{c,i}}F_iρ_S F_i^{\dagger} -\frac{1}{2} \{F_i^{\dagger} F_i,ρ_S \}_+\right)$ that depends on a general energy $z$, and has a tunable parameter $Γ_c$ that determines the degree of particle density lost. It has as its limits non-Hermitian ($Γ_c \to 0$) and Lindbladian dynamics ($Γ_c \to \infty$). The intermediate regime evolves density matrices such that $0 \leq \text{Tr} (ρ_S) \leq 1$. We derive our generator with the help of an ancillary continuum manifold acting as a sink for particle density. The evolution describes a system that can exchange both particle density and energy with its environment. We illustrate its features for a two level system and a five $M$ level system with a coherent population trapping point.
