Abstract
There are two important related research areas that I propose to investigate. First, we plan to develop an efficient numerical integrator based on Fer expansion for solid-state NMR simulation of experiments. Second, we intend to extend the method to solve quantum Liouville equation and quantum Fokker-Planck equation in order to improve the understanding of the dynamics of quantum systems subject to dissipation due to its relation to macroscopic quantum phenomena. The goal of the proposed research is to study a numerical integrator based on Fer expansion (Fer integrators of higher orders) in the integration of the time-dependent Schrodinger equation (TDSE) which is a central problem to nuclear magnetic resonance in general and solid-state NMR (SSNMR) in particular. The Fer integrator will provide to experts in quantum mechanics, NMR spectroscopy, and spin dynamics researchers, additional means for controlling spin dynamics in SSNMR. The efficient diagram will be used to compare the different orders of the Fer integrators obtained.
Highlights
The goal of the proposed research is to study a numerical integrator based on Fer expansion (Fer integrators of higher orders) in the integration of the time-dependent Schrodinger equation (TDSE) which is a central problem to nuclear magnetic resonance in general and solid-state NMR (SSNMR) in particular
The overall goals are: a) to develop Fer integrators of higher orders; b) to use the efficient diagram to compare the different orders of the Fer integrators obtained, for use in solid-state NMR; c) the efficiency plot is obtained by carrying out the numerical integration with different time steps, corresponding to different numbers of evaluations of the Hamiltonian H(t) (For each run, one compares the corresponding approximation with the exact solution, and plots the error as a function of the total number of matrix evaluations)
We plan to apply the efficient numerical integrator based on Fer expansion to the following specific solid-state NMR experiments which are of major interest in the NMR community
Summary
The goal of the proposed research is to study a numerical integrator based on Fer expansion (Fer integrators of higher orders) in the integration of the time-dependent Schrodinger equation (TDSE) which is a central problem to nuclear magnetic resonance in general and solid-state NMR (SSNMR) in particular. Solving the Schrodinger equation towards obtaining propagators is a central problem to NMR in general and solid-state NMR in particular. The applications of the Fokker-Planck equation[4] to solid-state NMR are considered. I intend to extend the method to solve quantum Liouville equation[5] and quantum Fokker-Planck equation in order to improve the understanding of the dynamics of quantum systems subject to dissipation due to its relation to macroscopic quantum phenomena
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