{"title":"On the geometric phase effects on time evolution of the density matrix during modulated radiofrequency pulses","authors":"Dennis J. Sorce , Shalom Michaeli","doi":"10.1016/j.jmr.2025.107840","DOIUrl":null,"url":null,"abstract":"<div><div>In this work the effect of the geometric phase on time evolution of the density matrix was evaluated during nonadiabatic radiofrequency (RF) pulses with <em>Sine</em> amplitude modulation (AM) and <em>Cosine</em> frequency modulation (FM) functions of the RAFF (Relaxations Along a Fictitious Field) family, and the polarization between two energy level ½ spin system coupled by dipolar interaction was evaluated during the application of RF irradiation. The dependencies of the diagonal density matrix elements and the polarization on the rotational correlation times and the time during RF pulses were evaluated. The general treatment of the density matrix elements along with the polarization generated during RF pulses was unavailable thus far, and for the first time was here derived for the nonadiabatic case of the RAFF pulses. The current formalism could be extended to other AM and FM RF waveforms, including the adiabatic RF pulses which are widely used in magnetic resonance (MR). We demonstrate that the sub-geometric phases (SGP) influence the density matrix elements and thus the polarization generated during the application of RF AM and FM pulses. The corrections to describe the SGP influence of the density matrix elements developed in this work could be essential for determination of MR fundamental parameters necessary for evaluation of tissue contrasts <em>in vivo</em> in MRI and for protein dynamics characterization in high resolution NMR, where AM and FM RF pulses are frequently utilized.</div></div>","PeriodicalId":16267,"journal":{"name":"Journal of magnetic resonance","volume":"372 ","pages":"Article 107840"},"PeriodicalIF":2.0000,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of magnetic resonance","FirstCategoryId":"92","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1090780725000126","RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"BIOCHEMICAL RESEARCH METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
In this work the effect of the geometric phase on time evolution of the density matrix was evaluated during nonadiabatic radiofrequency (RF) pulses with Sine amplitude modulation (AM) and Cosine frequency modulation (FM) functions of the RAFF (Relaxations Along a Fictitious Field) family, and the polarization between two energy level ½ spin system coupled by dipolar interaction was evaluated during the application of RF irradiation. The dependencies of the diagonal density matrix elements and the polarization on the rotational correlation times and the time during RF pulses were evaluated. The general treatment of the density matrix elements along with the polarization generated during RF pulses was unavailable thus far, and for the first time was here derived for the nonadiabatic case of the RAFF pulses. The current formalism could be extended to other AM and FM RF waveforms, including the adiabatic RF pulses which are widely used in magnetic resonance (MR). We demonstrate that the sub-geometric phases (SGP) influence the density matrix elements and thus the polarization generated during the application of RF AM and FM pulses. The corrections to describe the SGP influence of the density matrix elements developed in this work could be essential for determination of MR fundamental parameters necessary for evaluation of tissue contrasts in vivo in MRI and for protein dynamics characterization in high resolution NMR, where AM and FM RF pulses are frequently utilized.
期刊介绍:
The Journal of Magnetic Resonance presents original technical and scientific papers in all aspects of magnetic resonance, including nuclear magnetic resonance spectroscopy (NMR) of solids and liquids, electron spin/paramagnetic resonance (EPR), in vivo magnetic resonance imaging (MRI) and spectroscopy (MRS), nuclear quadrupole resonance (NQR) and magnetic resonance phenomena at nearly zero fields or in combination with optics. The Journal''s main aims include deepening the physical principles underlying all these spectroscopies, publishing significant theoretical and experimental results leading to spectral and spatial progress in these areas, and opening new MR-based applications in chemistry, biology and medicine. The Journal also seeks descriptions of novel apparatuses, new experimental protocols, and new procedures of data analysis and interpretation - including computational and quantum-mechanical methods - capable of advancing MR spectroscopy and imaging.