论文标题
lindblad方程
Density Matrix Formalism for PT-Symmetric Non-Hermitian Hamiltonians with the Lindblad Equation
论文作者
论文摘要
In the presence of Lindblad decoherence, i.e. dissipative effects in an open quantum system due to interaction with an environment, we examine the transition probabilities between the eigenstates in the two-level quantum system described by non-Hermitian Hamiltonians with the Lindblad equation, for which the parity-time-reversal (PT) symmetry is conserved.首先，开发了PT-对称非富尔顿系统系统的密度矩阵形式主义。结果表明，lindblad运算符$ l^{} _ j $是伪hermitian，即，$ηl^{} _jη^{ - 1} = l^\ dagger_j $ at $η$，$η$是线性和阳性的，是一个线性和阳性的标准，并尊重pt insemmetry，and symmetry and n n y n y n n y n n n y n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n YERNICERNIRE。我们证明了一般密度矩阵$ρ^{} _ {\ rm g}（t）\equivρ（t）η$，而不是标准化的密度矩阵$ρ^{} _ {\ rm n}（\ rm n}（t）（t）\ equiv equiv equiv equiv pρ（t）/{根据线性要求计算过渡概率。其次，密度基质形式主义用于在普通非对称的非铁汉顿人的一般情况下得出过渡概率。在某些具体示例中，我们计算过过渡概率的紧凑分析公式，并使用数值插图探索其主要特征。在没有Lindblad econerence的情况下，我们还使用状态向量进行比较，并使用状态向量进行比较。
In the presence of Lindblad decoherence, i.e. dissipative effects in an open quantum system due to interaction with an environment, we examine the transition probabilities between the eigenstates in the two-level quantum system described by non-Hermitian Hamiltonians with the Lindblad equation, for which the parity-time-reversal (PT) symmetry is conserved. First, the density matrix formalism for PT-symmetric non-Hermitian Hamiltonian systems is developed. It is shown that the Lindblad operators $L^{}_j$ are pseudo-Hermitian, namely, $ηL^{}_j η^{-1} = L^\dagger_j$ with $η$ being a linear and positive-definite metric, and respect the PT symmetry as well. We demonstrate that the generalized density matrix $ρ^{}_{\rm G}(t) \equiv ρ(t) η$, instead of the normalized density matrix $ρ^{}_{\rm N}(t) \equiv ρ(t)/{\rm tr}\left[ρ(t)\right]$, should be implemented for the calculation of the transition probabilities in accordance with the linearity requirement. Second, the density matrix formalism is used to derive the transition probabilities in general cases of PT-symmetric non-Hermitian Hamiltonians. In some concrete examples, we calculate compact analytical formulas for the transition probabilities and explore their main features with numerical illustrations. We also make a comparison between our present results and our previous ones using state vectors in the absence of Lindblad decoherence.
