Petitjean C, Jacquod Ph
Département de Physique Théorique, Université de Genève, CH-1211 Genèva 4, Switzerland.
Phys Rev Lett. 2006 Sep 22;97(12):124103. doi: 10.1103/PhysRevLett.97.124103. Epub 2006 Sep 20.
In echo experiments, imperfect time-reversal operations are performed on a subset of the total number of degrees of freedom. To capture the physics of these experiments, we introduce a partial fidelity M(B)(t), the Boltzmann echo, where only part of the system's degrees of freedom can be time reversed. We present a semiclassical calculation of M(B)(t). We show that, as the time-reversal operation is performed more and more accurately, the decay rate of M(B)(t) saturates at a value given by the decoherence rate of the controlled degrees of freedom due to their coupling to uncontrolled ones. We connect these results with NMR spin echo experiments.
在回波实验中，对总自由度的一个子集进行了不完美的时间反演操作。为了捕捉这些实验的物理过程，我们引入了部分保真度(M(B)(t))，即玻尔兹曼回波，其中只有系统自由度的一部分可以进行时间反演。我们给出了(M(B)(t))的半经典计算。我们表明，随着时间反演操作越来越精确，(M(B)(t))的衰减率会饱和到一个由受控自由度由于与不受控自由度耦合而产生的退相干率所给定的值。我们将这些结果与核磁共振自旋回波实验联系起来。
