Infinite dimensional semiclassical analysis and applications to a model in nuclear magnetic resonance

Amour L.; Jager L.; Nourrigat J.

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Infinite dimensional semiclassical analysis and applications to a model in nuclear magnetic resonance

机译：无限尺寸半导体分析和应用于核磁共振的模型

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We are concerned in this paper with the connection between the dynamics of a model related to nuclear magnetic resonance in Quantum Field Theory (QFT) and its classical counterpart known as the Maxwell-Bloch equations. The model in QFT is a model of quantum electrodynamics considering fixed spins interacting with the quantized electromagnetic field in an external constant magnetic field. This model is close to the common spin-boson model. The classical model goes back to Bloch [Phys. Rev. 70, 460 (1946)]. Our goal is not only to study the derivation of the Maxwell-Bloch equations but also to establish a semiclassical asymptotic expansion of arbitrary high order with control of the error terms of these standard nonlinear classical motion equations. This provides therefore quantum corrections of any order in powers of the semiclassical parameter of the Bloch equations. Besides, the asymptotic expansion for the photon number is also analyzed, and a law describing the photon number time evolution is written down involving the radiation field polarization. Since the quantum photon state Hilbert space (radiation field) is infinite dimensional, we are thus concerned in this article with the issue of semiclassical calculus in an infinite dimensional setting. In this regard, we are studying standard notions as Wick and anti-Wick quantizations, heat operator, Beals characterization theorem, and compositions of symbols in the infinite dimensional context which can have their own interest. Published under license by AIP Publishing.

机译：我们在本文中关注了与量子场理论（QFT）中与核磁共振相关的模型的动态与称为Maxwell-Bloch方程相关的模型之间的关系。 QFT的模型是考虑与外部恒定磁场中的量化电磁场相互作用的固定旋转的量子电动力学模型。该模型接近共同的旋转玻色子模型。经典模型返回到Bloch [phys。 Rev. 70,460（1946）]。我们的目标不仅要研究Maxwell-Bloch方程的推导，还可以使用这些标准非线性经典运动方程的误差项的控制来建立任意高阶的半思法渐近扩展。因此，这提供了Bloch方程的半定数参数的任何顺序的量子校正。此外，还分析了光子数的渐近膨胀，并且描述了涉及辐射场偏振的光子数时间延伸的法律。由于量子光子状态Hilbert空间（辐射场）是无限尺寸的，因此我们在本文中关注了无限尺寸设置中的半导体微分的问题。在这方面，我们正在将标准概念作为灯芯和抗芯的量化，热量运营商，小牛肉表征定理以及可以具有自己兴趣的无限尺寸背景下的符号组成。通过AIP发布在许可证下发布。

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《Journal of Mathematical Physics》 |2019年第7期|共25页
作者
Amour L.; Jager L.; Nourrigat J.;
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Univ Reims LMR FRE 2011 CNRS Moulin Housse BP 1039 F-51687 Reims 2 France;

Univ Reims LMR FRE 2011 CNRS Moulin Housse BP 1039 F-51687 Reims 2 France;

Univ Reims LMR FRE 2011 CNRS Moulin Housse BP 1039 F-51687 Reims 2 France;

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1. Infinite dimensional semiclassical analysis and applications to a model in nuclear magnetic resonance [J] . Amour L., Jager L., Nourrigat J. Journal of Mathematical Physics . 2019,第7期

机译：无限尺寸半导体分析和应用于核磁共振的模型
2. Extraction of spectral information from a short-time signal using filter-diagonalization: Recent developments and applications to semiclassical reaction dynamics and nuclear magnetic resonance signals [J] . Pang JW., Feigon J., Neuhauser D., The Journal of Chemical Physics . 1998,第20期

机译：使用滤波器对角化从短时信号中提取光谱信息：半经典反应动力学和核磁共振信号的最新发展和应用
3. Three-dimensional nuclear magnetic resonance exchange spectroscopy with rotary resonance in rotating solids: Application to tropolone dynamics [J] . Gan ZH., Ernst RR. The Journal of Chemical Physics . 1998,第22期

机译：旋转固体中具有旋转共振的三维核磁共振交换光谱：在对讲机动力学中的应用
4. Prospect Forecast for Precise Processing and Application of Multi-dimensional Nuclear Magnetic Resonance Logging Tool Data [C] . Jiang Zhimin, Dang Yupu, Xue Zhibo, КИТАЙСКО-РОССИЙСКОГО НАУЧНОГО СИМПОЗИУМА . 2017

机译：多维核磁共振测井工具数据精确加工和应用的展望预测
5. Methods in three-dimensional NOE-NOE nuclear magnetic resonance spectroscopy, three-dimensional diffusion-ordered NOESY nuclear magnetic resonance spectroscopy, and studies of methylphosphonate antisense oligonucleotides. [D] . Gozansky, Elliot Kirk. 1997

机译：三维NOE-NOE核磁共振波谱，三维扩散有序NOESY核磁共振波谱以及甲基膦酸酯反义寡核苷酸研究的方法。
6. Magnetic Resonance Imaging with Three-Dimensional Analysis of Left Ventricular Remodeling in Isolated Mitral Regurgitation: Implications beyond Dimensions [O] . Chun G. Schiros, Louis J. Dell’Italia, James D. Gladden, -1

机译：磁共振成像与左心室重新改进左心室重塑三维分析：超越尺寸的含义
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8. Nuclear Magnetic Resonance Identification of Military Nerve Agents and Related Compounds by Two-Dimensional 31P-1H Heteronuclear Overhauser Effect Spectroscopy [R] . Henderson, T. J. 2010

机译：二维31p-1H异核Overhauser效应光谱法鉴定军用神经毒剂及相关化合物的核磁共振

Infinite dimensional semiclassical analysis and applications to a model in nuclear magnetic resonance

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