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arXiv quant-ph/0202169quant-ph
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海森堡模型中的退相干

Decoherence in the Heisenberg model

Olavi Dannenberg

摘要:

为了阐明封闭量子系统中退相干的概念,我们研究了一个简化的海森堡自旋模型。为此,我们定义了一个新的概念:退相干函数ψ(t),它描述了整个系统中退相干的动力学,并与所有粒子的总(冯诺依曼)熵。正如预期的那样,退相干既被理解为由系统动力学引起的统计过程,也被理解为熵的问题。此外,退相干时间的概念也适用于封闭系统,我们已经解决了它在1/r型势场中关于粒子数N、密度ρ和空间维数D的海森堡模型中的行为。我们还研究了在这类系统中发生的庞加莱递归:在N=1000粒子系统中,递归时间接近宇宙年龄的量级。这促使我们得出结论,退相干不仅在实践中,而且在原则上是量子经典问题的解决方案。

英文摘要:

We study a simplified Heisenberg spin model in order to clarify the idea of decoherence in closed quantum systems. For this purpose, we define a new concept: the decoherence function Ξ(t), which describes the dynamics of decoherence in the whole system, and which is linked with the total (von Neumann) entropy of all particles. As expected, decoherence is understood both as a statistical process that is caused by the dynamics of the system, and also as a matter of entropy. Moreover, the concept of decoherence time is applicable in closed systems and we have solved its behaviour in the Heisenberg model with respect to particle number N, density ρand spatial dimension D in a 1/r -type of potential. We have also studied the Poincare recurrences occurring in these types of systems: in an N=1000 particle system the recurrence time is close to the order of the age of the universe. This encourages us to conclude that decoherence is the solution for quantum-classical problems not only in practice, but also in principle.

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