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矩阵形式的不变本征算符方法以及几种介观电路的本征频率

吴泽 范洪义

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矩阵形式的不变本征算符方法以及几种介观电路的本征频率

吴泽, 范洪义

The invariant eigen-operator method in matrix form and the eigenfrequency of several mesoscopic circuits

Wu Ze, Fan Hong-Yi
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  • 本文把不变本征算符方法(invariant eigen-operator, IEO方法)推广到了基于拉格朗日量的矩阵形式, 将以往计算的思路和过程用简约的矩阵形式表示出来, 这对大规模复杂多回路的介观电路的计算有着重要的意义. 此外用该方法计算了三个LC介观电路的本征频率, 包括存在互感和不存在互感的两种情形. 通过计算结果得出了这些电路的相关性质, 说明了本征频率只与介观电路本身的元件性质有关.
    The Invariant Eigen-operator (IEO) method is widely used in solving the eigenfrequencies of the coulped quantum mesoscopic circuits. The previous IEO method is complicated but stylized, we always wasted much time in this boring processes. Here we extended the IEO method to the matrix form based on Lagrangian of the complex mesoscopic circuits, and express the ideas and processes of the previous calculations of the IEO method in a very simple matrix form. The mathematical methods we used is the indicator representation of the matrix, and we got a very simple and convenient matrix form of the IEO method. This form has important significance for the calculation of large-scale complex multi-loop mesoscopic circuits. Moreover, the matrix form of the IEO method is very friendly to the programming implementation of the complex quantum mesoscopic LC circuits, it is probably a most optimal algorithm for calculating the eigenfrequencies of the quantum mesoscopic LC circuits. In addition, with some help of computer programs, we used this method to calculate the eigenfrequencies of three LC mesoscopic circuits, including two cases with and without mutual inductance. We revealed some relevant properties of these circuits by calculating results, indicating that the eigenfrequency is only related to the element properties of the mesoscopic circuit itself. Finally, we found that this method can also be used in other areas like atom-light coupling systems and solid state physics.
      通信作者: 范洪义, fhym@ustc.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 11775208)资助的课题
      Corresponding author: Fan Hong-Yi, fhym@ustc.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11775208)
    [1]

    Fan H Y, Li C 2004 Phys. Lett. A 321 75Google Scholar

    [2]

    任益充, 范洪义 2013 物理学报 62 156301Google Scholar

    Ren Y C, Fan H Y 2013 Acta Phys. Sin. 62 156301Google Scholar

    [3]

    范洪义, 吴昊, 袁洪春 2011 量子力学的不变本征算符方法 (上海: 上海交通大学出版社) 第175−178页

    Fan H Y, Wu H, Yuan H C 2011 Invariant Eigen-Operator Method in Quantum Mechanics (Shanghai: Shanghai Jiao Tong University Press) pp175−178 (in Chinese)

    [4]

    Fan H Y, Wu H, Xu X F 2005 Int. J. Mod. Phys. B 19 4073Google Scholar

    [5]

    Fan H Y, Tang X B 2007 Commun. Theor. Phys. 47 865Google Scholar

    [6]

    Ren G, Fan H Y 2009 Int. J. Phys. 48 2016Google Scholar

    [7]

    Fan H Y, Wang T T 2007 Int. J. Mod. Phys. B 21 1961Google Scholar

    [8]

    Song T Q, Fan H Y 2006 Mod. Phys. Lett. A 21 451Google Scholar

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    Liu Y M 2009 Int. J. Theor. Phys. 48 2372Google Scholar

    [10]

    Fan H Y, Tang X B 2006 Commun. Theor. Phys. 46 603Google Scholar

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    Fan H Y, Tang X B, Hu H P 2008 Commun. Theor. Phys. 50 674Google Scholar

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    Fan H Y, Wu H 2007 Mod. Phys. Lett. B 21 1751Google Scholar

    [13]

    Fan H Y, Wu H 2008 Commun. Theor. Phys. 49 50Google Scholar

    [14]

    Tang X B, Fan H Y 2010 Int. J. Theor. Phys. 49 877Google Scholar

    [15]

    Fan H Y, Wu H 2009 Int. J. Mod. Phys. B 23 234

    [16]

    Fan H Y, Wang T T, Yang Y L 2006 Int. J. Mod. Phys. B 20 5417Google Scholar

    [17]

    Song T Q, Zhu J Y, Fan H Y 2003 Commun. Theor. Phys. 39 91Google Scholar

    [18]

    Fan H Y, Tang X B 2006 Commun. Theor. Phys. 45 1003Google Scholar

    [19]

    Fan H Y, Gui W J, Gui J Z 2007 Int. J. Mod. Phys. B 21 737Google Scholar

    [20]

    Yu T X, Fan H Y 2010 Commun. Theor. Phys. 53 257Google Scholar

    [21]

    Meng X G, Wang J S, Zhai Y, Fan H Y 2008 Chin. Phys. Lett. 25 1205Google Scholar

    [22]

    张科, 范承玉, 范洪义 2018 物理学报 67 170301Google Scholar

    Zhang K, Fan C Y, Fan H Y, 2018 Acta Phys. Sin. 67 170301Google Scholar

  • 图 1  两回路$ L\text{-}C$介观电路

    Fig. 1.  Two-loop $L\text{-}C$ mesoscopic circuit

    图 2  无互感的$ L\text-C$介观电路

    Fig. 2.  $ L\text{-}C$ mesoscopic circuit without mutual inductance

    图 3  带互感的$ L\text-C$介观电路

    Fig. 3.  $ L\text-C$ mesoscopic circuit with mutual inductance 2m.

  • [1]

    Fan H Y, Li C 2004 Phys. Lett. A 321 75Google Scholar

    [2]

    任益充, 范洪义 2013 物理学报 62 156301Google Scholar

    Ren Y C, Fan H Y 2013 Acta Phys. Sin. 62 156301Google Scholar

    [3]

    范洪义, 吴昊, 袁洪春 2011 量子力学的不变本征算符方法 (上海: 上海交通大学出版社) 第175−178页

    Fan H Y, Wu H, Yuan H C 2011 Invariant Eigen-Operator Method in Quantum Mechanics (Shanghai: Shanghai Jiao Tong University Press) pp175−178 (in Chinese)

    [4]

    Fan H Y, Wu H, Xu X F 2005 Int. J. Mod. Phys. B 19 4073Google Scholar

    [5]

    Fan H Y, Tang X B 2007 Commun. Theor. Phys. 47 865Google Scholar

    [6]

    Ren G, Fan H Y 2009 Int. J. Phys. 48 2016Google Scholar

    [7]

    Fan H Y, Wang T T 2007 Int. J. Mod. Phys. B 21 1961Google Scholar

    [8]

    Song T Q, Fan H Y 2006 Mod. Phys. Lett. A 21 451Google Scholar

    [9]

    Liu Y M 2009 Int. J. Theor. Phys. 48 2372Google Scholar

    [10]

    Fan H Y, Tang X B 2006 Commun. Theor. Phys. 46 603Google Scholar

    [11]

    Fan H Y, Tang X B, Hu H P 2008 Commun. Theor. Phys. 50 674Google Scholar

    [12]

    Fan H Y, Wu H 2007 Mod. Phys. Lett. B 21 1751Google Scholar

    [13]

    Fan H Y, Wu H 2008 Commun. Theor. Phys. 49 50Google Scholar

    [14]

    Tang X B, Fan H Y 2010 Int. J. Theor. Phys. 49 877Google Scholar

    [15]

    Fan H Y, Wu H 2009 Int. J. Mod. Phys. B 23 234

    [16]

    Fan H Y, Wang T T, Yang Y L 2006 Int. J. Mod. Phys. B 20 5417Google Scholar

    [17]

    Song T Q, Zhu J Y, Fan H Y 2003 Commun. Theor. Phys. 39 91Google Scholar

    [18]

    Fan H Y, Tang X B 2006 Commun. Theor. Phys. 45 1003Google Scholar

    [19]

    Fan H Y, Gui W J, Gui J Z 2007 Int. J. Mod. Phys. B 21 737Google Scholar

    [20]

    Yu T X, Fan H Y 2010 Commun. Theor. Phys. 53 257Google Scholar

    [21]

    Meng X G, Wang J S, Zhai Y, Fan H Y 2008 Chin. Phys. Lett. 25 1205Google Scholar

    [22]

    张科, 范承玉, 范洪义 2018 物理学报 67 170301Google Scholar

    Zhang K, Fan C Y, Fan H Y, 2018 Acta Phys. Sin. 67 170301Google Scholar

计量
  • 文章访问数:  5313
  • PDF下载量:  53
  • 被引次数: 0
出版历程
  • 收稿日期:  2019-05-03
  • 修回日期:  2019-08-30
  • 上网日期:  2019-11-01
  • 刊出日期:  2019-11-20

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