论文标题
红场方程的完全积极，简单，可能高度准确
Completely Positive, Simple, and Possibly Highly Accurate Approximation of the Redfield Equation
论文作者
论文摘要
在这里，我们提出了一个lindblad主方程，该方程近似于Redfield方程，这是一个源自第一原理的众所周知的主方程，而没有显着损害Redfield方程的适用性范围。该近似值不是全尺寸的粗粒，而是在红场方程中截断了术语，该项在量子系统的典型时间尺度上平均耗尽。此近似值的第一步是正确地将哈密顿量系统重新归一化，以对称由于环境耦合而导致状态的损失和损失。在第二步中，我们将光谱密度的算术平均值与几何损失交换，从而恢复了完全的阳性。这种完全积极的近似值，游戏（几何弧度主方程），在其时间无关，与时间相关和浮标形式之间具有适应性。在确切可解决的三级Jaynes-Cummings模型中，我们发现近似状态的误差几乎比求解粗粒的随机主方程获得的数量级低。作为一个测试床，我们使用铁磁Heisenberg旋转链，在多达25个旋转之间与远程偶极偶极子耦合，并研究各种主方程之间的差异。我们发现，每个计算资源的精度最高。
Here we present a Lindblad master equation that approximates the Redfield equation, a well known master equation derived from first principles, without significantly compromising the range of applicability of the Redfield equation. Instead of full-scale coarse-graining, this approximation only truncates terms in the Redfield equation that average out over a time-scale typical of the quantum system. The first step in this approximation is to properly renormalize the system Hamiltonian, to symmetrize the gains and losses of the state due to the environmental coupling. In the second step, we swap out an arithmetic mean of the spectral density with a geometric one, in these gains and losses, thereby restoring complete positivity. This completely positive approximation, GAME (geometric-arithmetic master equation), is adaptable between its time-independent, time-dependent, and Floquet form. In the exactly solvable, three-level, Jaynes-Cummings model, we find that the error of the approximate state is almost an order of magnitude lower than that obtained by solving the coarse-grained stochastic master equation. As a test-bed, we use a ferromagnetic Heisenberg spin-chain with long-range dipole-dipole coupling between up to 25-spins, and study the differences between various master equations. We find that GAME has the highest accuracy per computational resource.
