Non-ergodic Nuclear Depolarization in Nano-cavities

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 spin1 2 ensemble with spatially independent effective dipolar interactions. If the initial polarization is on a single (first) spin,P1(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 ≫ 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 √ N)−1 , thus, almost all the time, the spin 1 spends in the time independent condition P1(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. PACS numbers: 05.30.-d, 76.20.+q