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Author Chang, Zhiwei ♦ Halle, Bertil
Source United States Department of Energy Office of Scientific and Technical Information
Content type Text
Language English
Subject Keyword CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS ♦ BOLTZMANN-VLASOV EQUATION ♦ CORRELATIONS ♦ DIPOLES ♦ MATRICES ♦ RELAXATION ♦ SPACE ♦ SPECTRAL DENSITY ♦ SPHERICAL CONFIGURATION ♦ SPIN ♦ STOCHASTIC PROCESSES ♦ SYMMETRY ♦ TENSORS
Abstract A system of three dipole-coupled spins exhibits a surprisingly intricate relaxation behavior. Following Hubbard’s pioneering 1958 study, many authors have investigated different aspects of this problem. Nevertheless, on revisiting this classic relaxation problem, we obtain several new results, some of which are at variance with conventional wisdom. Most notably from a fundamental point of view, we find that the odd-valued spectral density function influences longitudinal relaxation. We also show that the effective longitudinal relaxation rate for a non-isochronous three-spin system can exhibit an unusual inverted dispersion step. To clarify these and other issues, we present a comprehensive theoretical treatment of longitudinal relaxation in a three-spin system of arbitrary geometry and with arbitrary rotational dynamics. By using the Liouville-space formulation of Bloch-Wangsness-Redfield theory and a basis of irreducible spherical tensor operators, we show that the number of relaxation components in the different cases can be deduced from symmetry arguments. For the isochronous case, we present the relaxation matrix in analytical form, whereas, for the non-isochronous case, we employ a computationally efficient approach based on the stochastic Liouville equation.
ISSN 00219606
Educational Use Research
Learning Resource Type Article
Publisher Date 2015-12-21
Publisher Place United States
Journal Journal of Chemical Physics
Volume Number 143
Issue Number 23


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