New approach to describe two coupled spins in a variable magnetic field

Yuri Belousov, R. Grimaudo, A. Messina, A. Migliore, A. Sergi
{"title":"New approach to describe two coupled spins in a variable magnetic field","authors":"Yuri Belousov, R. Grimaudo, A. Messina, A. Migliore, A. Sergi","doi":"10.1063/5.0055009","DOIUrl":null,"url":null,"abstract":"We propose a method to describe the evolution of two spins coupled by hyperfine interaction in an external time-dependent magnetic field. We apply the approach to the case of hyperfine interaction with axial symmetry, which can be solved exactly in a constant, appropriately oriented magnetic field. In order to treat the nonstationary dynamical problem, we modify the time-dependent Schrodinger equation through a change of representation that, by exploiting an instantaneous (adiabatic) basis makes the time-dependent Hamiltonian diagonal at any time instant. The solution of the transformed time-dependent Schrodinger in the form of chronologically ordered exponents with transparent pre-exponential coefficients is reported. This solution is highly simplified when an adiabatically varying magnetic field perturbs the system. The approach here proposed may be used for the perturbative treatment of other dynamical problems with no exact solution.","PeriodicalId":8484,"journal":{"name":"arXiv: Quantum Physics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2020-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Quantum Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1063/5.0055009","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 4

Abstract

We propose a method to describe the evolution of two spins coupled by hyperfine interaction in an external time-dependent magnetic field. We apply the approach to the case of hyperfine interaction with axial symmetry, which can be solved exactly in a constant, appropriately oriented magnetic field. In order to treat the nonstationary dynamical problem, we modify the time-dependent Schrodinger equation through a change of representation that, by exploiting an instantaneous (adiabatic) basis makes the time-dependent Hamiltonian diagonal at any time instant. The solution of the transformed time-dependent Schrodinger in the form of chronologically ordered exponents with transparent pre-exponential coefficients is reported. This solution is highly simplified when an adiabatically varying magnetic field perturbs the system. The approach here proposed may be used for the perturbative treatment of other dynamical problems with no exact solution.
描述变磁场中两个耦合自旋的新方法
我们提出了一种描述在外时变磁场中由超精细相互作用耦合的两个自旋演化的方法。我们将该方法应用于具有轴对称的超精细相互作用的情况,这种情况可以在恒定的、适当定向的磁场中精确求解。为了处理非平稳动力学问题,我们通过变换表示来修正时变薛定谔方程,利用瞬时(绝热)基使时变哈密顿对角线在任何时刻都是瞬时的。本文报道了具有透明指数前系数的时间顺序指数形式的变换时相关薛定谔方程的解。当一个绝热变化的磁场扰动系统时,该解高度简化。本文提出的方法可用于其他无精确解的动力学问题的微扰处理。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信