纳米腔中非遍历的核去极化
Non-Ergodic Nuclear Depolarization in Nano-Cavities
摘要：
最近，人们已经观察到，在封闭的纳米腔中的气体的自旋携带分子的核自旋之间的有效偶极相互作用与所有自旋之间的间距无关。我们推导出了自旋1/2系综中所有自旋在有效偶极相互作用与空间无关的情况下的精确的含时极化。如果初始极化是在一个单一的（第一个）自旋，$P_1(0)= 1$，然后该模型的确切的自旋动力学显示，表现出一个周期性的短脉冲的极化的第一个自旋，效果是典型的系统具有大量的，$N$，自旋。如果$N \gg 1$，那么在周期$4π/g$（$2π/g$）内，对于奇（偶）$N$ -自旋团簇，$g$代表自旋耦合，自旋1的极化在大约$(g\sqrt{N})^{-1}$的时间间隔内从1迅速切换到与时间无关的值1/3，因此，几乎所有的时间，自旋1都处于与时间无关的条件$P_1(t)= 1/3$。脉冲的周期和宽度决定了椭圆形腔的体积和形状因子。该方法适用于空化气泡体积随时间变化的情况。如果音量$V(t)$被时间上的高斯随机噪声改变，则极化峰值的包络不可逆地变为1/3。当纳米体积涨落的相关时间大于（或小于）$<(δg)^2 >^{-1/2} $时，单自旋的极化动力学表现出高斯（或指数）时间依赖性，其中$<(δg)^2>$是$g(V(t))$耦合的方差.最后，我们报道了$N$ -自旋气体聚集体的NMR谱线形状的精确计算.
英文摘要：
Recently, it has been observed that the effective dipolar interactions between nuclear spins of spin-carrying molecules of a gas in a closed nano-cavities are independent of the spacing between all spins. We derive exact time-dependent polarization for all spins in spin-1/2 ensemble with spatially independent effective dipolar interactions. If the initial polarization is on a single (first) spin,$P_1(0)= 1$ then the exact spin dynamics of the model is shown to exhibit a periodical short pulses of the polarization of the first spin, the effect being typical of the systems having a large number, $N$, of spins. If $N \gg 1$, then within the period $4π/g$ ($2π/g$) for odd (even) $N$-spin clusters, with $g$ standing for spin coupling, the polarization of spin 1 switches quickly from unity to the time independent value, 1/3, over the time interval about $(g\sqrt{N})^{-1}$, thus, almost all the time, the spin 1 spends in the time independent condition $P_1(t)= 1/3$. The period and the width of the pulses determine the volume and the form-factor of the ellipsoidal cavity. The formalism is adopted to the case of time varying nano-fluctuations of the volume of the cavitation nano-bubbles. If the volume $V(t)$ is varied by the Gaussian-in-time random noise then the envelope of the polarization peaks goes irreversibly to 1/3. The polarization dynamics of the single spin exhibits the Gaussian (or exponential) time dependence when the correlation time of the fluctuations of the nano-volume is larger (or smaller) than the $<(δg)^2 >^{-1/2} $, where the $<(δg)^2>$ is the variance of the $g(V(t))$ coupling. Finally, we report the exact calculations of the NMR line shape for the $N$-spin gaseous aggregate.
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