Preservation of positivity by dynamical coarse graining
Preservation of positivity by dynamical coarse graining
复制标题
DOI：
10.1103/physreva.78.022106
复制
发表时间：
2008-04
影响因子：
2.9
通讯作者：
G. Schaller;T. Brandes
中科院分区：
文献类型：
--
作者：
G. Schaller;T. Brandes
我们比较了不同的量子主方程的约化密度矩阵的时间演化。广泛应用的长期近似（旋转波近似）与Born-Markov近似相结合，生成一个Lindblad型主方程，确保完全正向和稳定的演化，通常适用于光学浴。然而，对于声子浴，预期长期近似是无效的。通常的马尔可夫主方程一般不保持密度矩阵的正性。作为一个解决方案，我们提出了一个动态适应的粗粒度时间尺度的粗粒度方法。对于一些简单的例子，我们证明，这保留了积分微分玻恩方程的精度。对于大的时候，我们分析表明，长期近似主方程恢复。该方法原则上可以扩展到具有动态变化的系统哈密顿量的系统，这对于绝热量子计算特别感兴趣。我们给出了一些数值例子的自旋玻色子模型的情况下，自旋系统热化迅速，热化没有达到的其他例子。
We compare different quantum master equations for the time evolution of the reduced density matrix. The widely applied secular approximation (rotating wave approximation) applied in combination with the Born-Markov approximation generates a Lindblad-type master equation ensuring for completely positive and stable evolution and is typically well applicable for optical baths. For phonon baths however, the secular approximation is expected to be invalid. The usual Markovian master equation does not generally preserve positivity of the density matrix. As a solution we propose a coarse-graining approach with a dynamically adapted coarse-graining time scale. For some simple examples we demonstrate that this preserves the accuracy of the integro-differential Born equation. For large times we analytically show that the secular approximation master equation is recovered. The method can in principle be extended to systems with a dynamically changing system Hamiltonian, which is of special interest for adiabatic quantum computation. We give some numerical examples for the spin-boson model of cases where a spin system thermalizes rapidly, and other examples where thermalization is not reached.