arXiv 0806.37862008-06quant-phcond-mat.other

自旋环境中量子比特的非马尔可夫动力学和冯诺伊曼熵演化

Non-Markovian dynamics and von Neumann entropy evolution of a qubit in a spin environment

J. Rodríguez Garzón, R. M. Gutiérrez

备注：: 10 pages, 5 figures, revised interpretation, updated references

摘要：

在热力学极限下，研究了N个自旋为1/2的粒子在局域磁场中的动力学行为。自旋之间的相互作用是海森堡XY型，浴被认为是一个完美的热库。在这种情况下，得到了不同温度下约化密度矩阵的布居演化。玻恩近似，但不是一个马尔可夫近似的非马尔可夫动力学。通过冯诺伊曼熵得到系统混合方式的度量。对于低温，结果表明，有振荡的人口和冯诺伊曼熵，表明中心自旋成为一个纯态的特征时间周期，它是可能的提取或恢复信息。在高温下，演化显示出最终的最大混合态，熵S=ln 2，这是预期的两个能级系统。

英文摘要：

The dynamics of a central spin-1/2 in presence of a local magnetic field and a bath of N spin-1/2 particles is studied in the thermodynamic limit. The interaction between the spins is Heisenberg XY type and the bath is considered to be a perfect thermal reservoir. In this case, the evolution of the populations of the reduced density matrix are obtained for different temperatures. A Born approximation is made but not a Markov approximation resulting a non-Markovian dynamics. The measure of the way that the system mixes is obtained by means of the von Neumann entropy. For low temperatures, results show that there are oscillations of populations and of the von Neumann entropy, indicating that the central spin becomes a pure state with characteristic time periods in which it is possible to extract or recuperate information. In the regime of high temperatures, the evolution shows a final maximum mixed state with entropy S=ln 2 as it is expected for a two level system.

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摘要：

英文摘要：

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