Non-Ergodic Nuclear Depolarization in Nano-Cavities

Abstract

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 $4\pi /g$ ($2\pi /g$) 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 $<(\delta g{)}^2{>}^{-1/2}$, where the $<(\delta g{)}^2>$ 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.

26 pages, 3 figures

References in corpus (1)

• Nuclear Spin Qubit Dephasing Time in the Integer Quantum Hall Effect Regime

Cited by in corpus (12)

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• Quantum correlations in a system of nuclear s=1/2 spins in a strong magnetic field
• Many-particle Entanglement in Multiple Quantum NMR Spectroscopy
• NMR dynamics of quantum discord for spin-carrying gas molecules in a closed nanopore
• NMR line shapes of a gas of nuclear spin-1/2 molecules in fluctuating nano-containers
• The multiple quantum NMR dynamics in systems of equivalent spins with the dipolar ordered initial state
• Multiple quantum NMR dynamics in a gas of spin-carrying molecules in fluctuating nanopores
• Multiple quantum NMR of spin-carrying molecules in nanopores: high order corrections to the two-spin/two-quantum Hamiltonian
• Many-spin entanglement in multiple quantum NMR with a dipolar ordered initial state
• Geometric measure for two-qubit CS-states: an exactly solvable model
• A showing of entangling and discording power for cooper-pair gate