dorsal/arxiv
View SchemaNon-Ergodic Nuclear Depolarization in Nano-Cavities
| Authors | E. B. Fel'dman, M. G. Rudavets |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0306055 |
| URL | https://arxiv.org/abs/quant-ph/0306055 |
| DOI | 10.1134/1.1675888 |
| Journal | JETP V98 N2 (2004) pp 207-219 |
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.
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"abstract": "Recently, it has been observed that the effective dipolar interactions\nbetween nuclear spins of spin-carrying molecules of a gas in a closed\nnano-cavities are independent of the spacing between all spins. We derive exact\ntime-dependent polarization for all spins in spin-1/2 ensemble with spatially\nindependent effective dipolar interactions. If the initial polarization is on a\nsingle (first) spin,$P_1(0)= 1$ then the exact spin dynamics of the model is\nshown to exhibit a periodical short pulses of the polarization of the first\nspin, the effect being typical of the systems having a large number, $N$, of\nspins. If $N \\gg 1$, then within the period $4\\pi/g$ ($2\\pi/g$) for odd (even)\n$N$-spin clusters, with $g$ standing for spin coupling, the polarization of\nspin 1 switches quickly from unity to the time independent value, 1/3, over the\ntime interval about $(g\\sqrt{N})^{-1}$, thus, almost all the time, the spin 1\nspends in the time independent condition $P_1(t)= 1/3$. The period and the\nwidth of the pulses determine the volume and the form-factor of the ellipsoidal\ncavity. The formalism is adopted to the case of time varying nano-fluctuations\nof the volume of the cavitation nano-bubbles. If the volume $V(t)$ is varied by\nthe Gaussian-in-time random noise then the envelope of the polarization peaks\ngoes irreversibly to 1/3. The polarization dynamics of the single spin exhibits\nthe Gaussian (or exponential) time dependence when the correlation time of the\nfluctuations of the nano-volume is larger (or smaller) than the $\u003c(\\delta g)^2\n\u003e^{-1/2} $, where the $\u003c(\\delta g)^2\u003e$ is the variance of the $g(V(t))$\ncoupling. Finally, we report the exact calculations of the NMR line shape for\nthe $N$-spin gaseous aggregate.",
"arxiv_id": "quant-ph/0306055",
"authors": [
"E. B. Fel\u0027dman",
"M. G. Rudavets"
],
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"doi": "10.1134/1.1675888",
"journal_ref": "JETP V98 N2 (2004) pp 207-219",
"title": "Non-Ergodic Nuclear Depolarization in Nano-Cavities",
"url": "https://arxiv.org/abs/quant-ph/0306055"
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