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arXiv quant-ph/9901063quant-ph
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作为统计变量的时间与内禀退相干

Time as a statistical variable and intrinsic decoherence

Rodolfo Bonifacio

摘要:

我们提出了一种新的方法,不增加新的假设标准量子力学的内在退相干。我们推广了Liouville方程,只要求时间演化的动力学半群性质,并放弃了么正性要求。在没有任何近似和统计假设的情况下,我们找到了一个广义的刘维尔方程,它依赖于两个特征时间t1和t2,并在极限t1 = t2 -> 0时简化为通常的方程。然而,对于t1和t2任意小,但有限,我们的方程可以写为一个有限差分方程,预测状态减少到对角形式的能量表示。在宏观极限下,随着系统能量尺度的增大,退相干速率变快。在我们的方法中,演化时间后验地作为具有泊松-伽马函数概率分布的统计变量出现,就好像时间演化将以平均间隔t2随机发生,每个演化具有时间宽度t1。这一观点得到了一个推广的Tam Mandeldarin不等式的证明.与以前的工作Milburn的关系,与激光和微脉塞理论和许多实验测试的例子进行了描述。

英文摘要:

We propose a novel approach to intrinsic decoherence without adding new assumptions to standard quantum mechanics. We generalize the Liouville equation just by requiring the dynamical semigroup property of time evolution and dropping the unitarity requirement. With no approximations and statistical assumptions we find a generalized Liouville equation which depends on two characteristic time t1 and t2 and reduces to the usual equation in the limit t1 = t2 -> 0. However, for t1 and t2 arbitrarily small but finite, our equation can be written as a finite difference equation which predicts state reduction to the diagonal form in the energy representation. The rate of decoherence becomes faster at the macroscopic limit as the energy scale of the system increases. In our approach the evolution time appears, a posteriori, as a statistical variable with a Poisson-gamma function probability distribution as if time evolution would take place randomly at average intervals t2 each evolution having a time width t1. This view point is supported by the derivation of a generalized Tam Mandelstam inequality. The relation with previous work by Milburn, with laser and micromaser theory and many experimental testable examples are described.

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