{"title":"随机非线性磁场下自旋相演化的有效相扩散","authors":"Guoxing Lin","doi":"10.1103/physreve.110.034119","DOIUrl":null,"url":null,"abstract":"The general theoretical description of spin self-diffusion under a nonlinear gradient magnetic field is proposed, which extends the effective phase diffusion method for a linear gradient field. Based on the phase diffusion, the proposed method reveals the general features of phase evolutions in nonlinear gradient fields. There are three types of phase evolutions: phase diffusion, float phase evolution, and shift evolution based on the starting position. For spin diffusion near the origin of the nonlinear field, these three phase evolutions significantly affect the nuclear magnetic resonance (NMR) signal. The traditional methods have difficulties in handling these three-phase evolutions. Notably, the phase from float phase evolution is missed or misplaced in traditional methods, which leads to incorrect NMR signal attenuation or phase shift. The method here shows that the diffusing and float phase evolutions come from the first and second derivatives of the gradient field. Based on these three phase evolutions, the phase variance and corresponding NMR signal attenuation are obtained, as demonstrated by calculating the phase diffusions under both parabolic and cubic fields. The results indicate that signal attenuation obeys Gaussian attenuation for a short time, then changes to follow Lorentzian or Mittag-Leffler function attenuations as time increases, significantly different from Gaussian attenuation. For spins starting diffusion far away from the origin of the field gradient, the signal attenuation is Gaussian, but the float phase still has an important effect on the total phase shift of even-order gradient fields, which could be used to measure the diffusion coefficient directly. Random walk simulations were performed, which support the obtained theoretical results. General theoretical expressions are obtained, which can handle random order nonlinear gradient fields. The results could help develop advanced experimental techniques based on a nonlinear gradient field in NMR and magnetic resonance imaging.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":null,"pages":null},"PeriodicalIF":2.4000,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Effective phase diffusion for spin phase evolution under random nonlinear magnetic field\",\"authors\":\"Guoxing Lin\",\"doi\":\"10.1103/physreve.110.034119\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The general theoretical description of spin self-diffusion under a nonlinear gradient magnetic field is proposed, which extends the effective phase diffusion method for a linear gradient field. Based on the phase diffusion, the proposed method reveals the general features of phase evolutions in nonlinear gradient fields. There are three types of phase evolutions: phase diffusion, float phase evolution, and shift evolution based on the starting position. For spin diffusion near the origin of the nonlinear field, these three phase evolutions significantly affect the nuclear magnetic resonance (NMR) signal. The traditional methods have difficulties in handling these three-phase evolutions. Notably, the phase from float phase evolution is missed or misplaced in traditional methods, which leads to incorrect NMR signal attenuation or phase shift. The method here shows that the diffusing and float phase evolutions come from the first and second derivatives of the gradient field. Based on these three phase evolutions, the phase variance and corresponding NMR signal attenuation are obtained, as demonstrated by calculating the phase diffusions under both parabolic and cubic fields. The results indicate that signal attenuation obeys Gaussian attenuation for a short time, then changes to follow Lorentzian or Mittag-Leffler function attenuations as time increases, significantly different from Gaussian attenuation. For spins starting diffusion far away from the origin of the field gradient, the signal attenuation is Gaussian, but the float phase still has an important effect on the total phase shift of even-order gradient fields, which could be used to measure the diffusion coefficient directly. Random walk simulations were performed, which support the obtained theoretical results. General theoretical expressions are obtained, which can handle random order nonlinear gradient fields. The results could help develop advanced experimental techniques based on a nonlinear gradient field in NMR and magnetic resonance imaging.\",\"PeriodicalId\":20085,\"journal\":{\"name\":\"Physical review. E\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.4000,\"publicationDate\":\"2024-09-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Physical review. E\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1103/physreve.110.034119\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical review. E","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physreve.110.034119","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
Effective phase diffusion for spin phase evolution under random nonlinear magnetic field
The general theoretical description of spin self-diffusion under a nonlinear gradient magnetic field is proposed, which extends the effective phase diffusion method for a linear gradient field. Based on the phase diffusion, the proposed method reveals the general features of phase evolutions in nonlinear gradient fields. There are three types of phase evolutions: phase diffusion, float phase evolution, and shift evolution based on the starting position. For spin diffusion near the origin of the nonlinear field, these three phase evolutions significantly affect the nuclear magnetic resonance (NMR) signal. The traditional methods have difficulties in handling these three-phase evolutions. Notably, the phase from float phase evolution is missed or misplaced in traditional methods, which leads to incorrect NMR signal attenuation or phase shift. The method here shows that the diffusing and float phase evolutions come from the first and second derivatives of the gradient field. Based on these three phase evolutions, the phase variance and corresponding NMR signal attenuation are obtained, as demonstrated by calculating the phase diffusions under both parabolic and cubic fields. The results indicate that signal attenuation obeys Gaussian attenuation for a short time, then changes to follow Lorentzian or Mittag-Leffler function attenuations as time increases, significantly different from Gaussian attenuation. For spins starting diffusion far away from the origin of the field gradient, the signal attenuation is Gaussian, but the float phase still has an important effect on the total phase shift of even-order gradient fields, which could be used to measure the diffusion coefficient directly. Random walk simulations were performed, which support the obtained theoretical results. General theoretical expressions are obtained, which can handle random order nonlinear gradient fields. The results could help develop advanced experimental techniques based on a nonlinear gradient field in NMR and magnetic resonance imaging.
期刊介绍:
Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.