Construction of quadratic invariants for time-dependent systems in complex phase space using Struckmeier and Riedel approach

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Reports on Mathematical Physics Pub Date : 2024-08-01 DOI:10.1016/S0034-4877(24)00052-1

Vipin Kumar, S.B. Bhardwaj, Ram Mehar Singh, Shalini Gupta, Fakir Chand

引用次数: 0

Abstract

In this paper, we deal with the construction of quadratic invariants in a complex phase space under the transformation z = (x + iy) and

\bar{z} = (x - i y)

for various time-dependent systems. For this purpose, Struckmeier and Riedel (SR) approach [1, 2] is used. The constructed invariants include an unknown function f₂(t) that is a solution of a third-order differential equation and its coefficients can be determined by the trajectories of the particle. The invariants play an important role in the study of a dynamical system, to access the accuracy in numerical simulations and to investigate the classical and quantum integrability of a system.

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用斯特拉克迈尔和里德尔方法构建复相空间时变系统的二次不变量

在本文中，我们讨论了在 z = (x + iy) 和 z¯=(x-iy) 变换下，为各种时变系统构建复相空间二次不变量的问题。为此，我们采用了 Struckmeier 和 Riedel（SR）方法[1, 2]。构建的不变式包括一个未知函数 f2(t)，它是一个三阶微分方程的解，其系数可由粒子的轨迹确定。不变量在研究动态系统、获得数值模拟的准确性以及研究系统的经典和量子可积分性方面发挥着重要作用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Reports on Mathematical Physics 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.