The Clifford Algebra of the Density Matrix: An Elementary Approach

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-06-29 DOI:10.1007/s00006-024-01337-8

Pedro Amao, Hernan Castillo

引用次数: 0

Abstract

This work studies the Clifford algebra approach to the density matrix. We discuss elementary examples of pure and mixed states by writing the density matrix as an element of the Clifford algebra of the three-dimensional space \(Cl_3\). We also revisit the phenomenon of Larmor precession within the framework of Clifford algebra. Additionally, we discuss the geometrical interpretation of the so-called Clifford Density Element (CDE) for pure states in analogy to the Bloch sphere of conventional quantum theory. Finally, we discuss the dynamics of the CDE, which obeys an algebraic form of the Liouville von–Neumann equation.

Abstract Image

查看原文本刊更多论文

密度矩阵的克利福德代数：初级方法

这项工作研究了密度矩阵的克利福德代数方法。通过把密度矩阵写成三维空间 \(Cl_3\) 的克利福德代数的一个元素，我们讨论了纯态和混合态的基本例子。我们还在克利福德代数的框架内重温了拉莫尔前驱现象。此外，我们还讨论了所谓的克利福德密度元（CDE）对纯态的几何解释，它类似于传统量子理论中的布洛赫球。最后，我们讨论了 CDE 的动力学，它服从柳维尔-冯-牛曼方程的代数形式。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.