含时增益-损耗主方程的显式闭式传播子
Explicit closed-form propagators for time-dependent gain-loss master equations
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中文总结 AI 辅助
本文针对含时增益-损耗主方程，提出一种显式闭式传播子分解方法，直接确定系数，无需解非线性微分方程组，并应用于玻色子码的动力学评估。
中文摘要 AI 辅助
时间排序是受含时速率主方程支配的驱动开放系统动力学中的一个核心障碍。我们推导了形式为$\mathcal{L}(t)=\alpha(t)A+\beta(t)B$的含时生成元的时序和反时序传播子的显式闭式分解，当对易子$[A,B]$是$A$和$B$的伴随作用的同步本征算子时，即$[A,[A,B]]=\lambda_{A}[A,B]$且$[B,[A,B]]=\lambda_{B}[A,B]$。与称为Wei-Norman分解的解纠缠过程不同，我们的构造直接确定分解系数，无需求解耦合的非线性微分方程组。将此结果应用于玻色子增益-损耗Lindblad方程，我们获得了任意含时增益和损耗速率的精确动力学映射。增益-损耗主方程提供了与热浴耦合的驱动谐振子的规范描述。我们通过推导初始Fock态的Wigner函数的时间演化并将其与独立的相空间结果进行比较来基准测试该构造。我们进一步应用所得的动力学映射来评估二项式玻色子码在驱动增益-损耗动力学下的码空间存活概率。
英文摘要
Time ordering is a central obstacle in driven open-system dynamics governed by master equations with time-dependent rates. We derive explicit closed-form factorizations of the chronological and antichronological propagators for a time-dependent generator of the form $\mathcal{L}(t)=α(t)A+β(t)B$, when the commutator $[A,B]$ is a simultaneous eigenoperator of the adjoint actions of $A$ and $B$, namely $[A,[A,B]]=λ_{A}[A,B]$ and $[B,[A,B]]=λ_{B}[A,B]$. In contrast to the disentangling procedure known as the Wei-Norman decomposition, our construction determines the factorization coefficients directly, without solving a coupled system of nonlinear differential equations. Applying this result to the bosonic gain-loss Lindblad equation, we obtain the exact dynamical map for arbitrary time-dependent gain and loss rates. The gain-loss master equation provides a canonical description of a driven harmonic oscillator coupled to a thermal bath. We benchmark the construction by deriving the time evolution of the Wigner function of an initial Fock state and comparing it with independent phase-space results. We further apply the resulting dynamical map to evaluate the code-space survival probability of a binomial bosonic code under driven gain-loss dynamics.
发表机构
- King’s College London（伦敦国王学院）
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