Asymptotic Similarity of Time Correlation Functions and Shape of the 13C and 29Si NMR Spectra in Diamond and Silicon

Solid-State NMR Free Induction Decay, Simulated by the System of Classical Magnetic Moments and Quantum Correlations

“…problem have been published. However, we do not consider here all the variety of developed approaches and methods applied to this problem (see, for example, [9,10] and the literature cited there), but dwell on the most important ones.…”

“…In the indicated high-temperature approximation, for mutual information (9), we obtain (10) Mutual information ( 9) is a measure of the total correlations, which are the sum of the classical and quantum correlations. To calculate the classical correlations of two random variables-the orientations of two magnetic moments in our case-it is necessary to find the probability distribution of their values.…”

“…The mutual information calculated by formulas (10), (13), and (15) for this matrix will serve as a measure of the classical correlations. However, the obtained value depends on the chosen basis (11).…”

“…To simplify the analysis, we assume that all spins occupy equivalent positions in the lattice, then In this case (22) Expression ( 22) differs from the analogous expression for an isolated pair of spins obtained in [23] by replacing by and β by Therefore, omitting the intermediate calculations, we present the final results at once. First, for the mutual information (10), we obtain (23) where Secondly, for the classical (C ij ) and quantum (quantum discord D ij ) parts of the correlations at we have (24) Result (24) was obtained using the Neumann orthogonal measurement (13) along one of the spins with projectors (12). Finally, for the classical (J ij ) and quantum (Q ij ) parts of the correlations at , we find (25) (26) where…”

The exact solution for the free induction decay in a quasi-one-dimensional system in a multi-pulse NMR experiment

“…Although the development of the theoretical methods for calculation of the FID began long ago [2], the complete solution of the problem is yet to be obtained and is the subject of ongoing research [5,6]. More progress was achieved in one-dimensional systems where an expression of the 19 F FID was calculated by exactly diagonalizing the Hamiltonian of the closed linear chain of five spins with nearest and next-nearest neighbor interactions [7].The effect of other nuclei was taken into account using a Gaussian broadening function of calculated multiplets [7].…”