Continuous Floquet theory in solid-state NMR.

Area of Science:

• Physical Chemistry
• Quantum Mechanics
• Spectroscopy

Background:

• Traditional Floquet theory requires periodic Hamiltonians, limiting its application to certain nuclear magnetic resonance (NMR) experiments.
• Observable effects in solid-state NMR experiments with non-continuous Hamiltonians are not fully captured by traditional Floquet theory.
• There is a need for theoretical frameworks that can accurately describe complex NMR experiments with multiple modulation frequencies.

Purpose of the Study:

• To present the application of continuous Floquet theory in solid-state nuclear magnetic resonance (NMR).
• To extend the capabilities of Floquet theory for describing non-continuous Hamiltonians in NMR.
• To provide tools for analyzing NMR experiments with multiple modulation frequencies.

Main Methods:

• Development of closed-form expressions for computing first- and second-order effective Hamiltonians.
• Integration of continuous Floquet theory with existing NMR theoretical frameworks.
• Investigation of several solid-state NMR experiments using the developed theory.

Main Results:

• Continuous Floquet theory successfully describes observable effects in solid-state NMR experiments with non-continuous Hamiltonians.
• Closed-form expressions for effective Hamiltonians streamline theoretical calculations and experimental design.
• The duration of pulse schemes significantly impacts resonance condition widths and near-resonance behavior in NMR experiments.

Conclusions:

• Continuous Floquet theory offers a powerful extension to traditional Floquet theory for solid-state NMR.
• The developed theoretical framework facilitates the analysis of complex NMR experiments with multiple modulation frequencies.
• Understanding pulse scheme duration is crucial for optimizing solid-state NMR experiments and interpreting results.