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Behavior of a constrained particle on superintegrability of the two-dimensional complex Cayley–Klein space and its thermodynamic properties
Physica A: Statistical Mechanics and its Applications ( IF 3.3 ) Pub Date : 2021-03-19 , DOI: 10.1016/j.physa.2021.125935
A. Najafizade , H. Panahi

In this paper, we study the motion of a particle on a family of superintegrable Hamiltonians of the unitary groups in Cayley–Klein space. This possibility is provided through the general commutator relations between generators from its respective group. Hence, by converting coordinates from Cartesian space to Eulerian parameterization, the obtained metric in terms of the new coordinates is equal to the same Lagrangian of geodesic motion. On the other hand, by reducing the SUκ1κ2(3) group manifold to the SUκ1κ2(3)SUκ1(2)Ω5 quotient space and considering the three Fourier transformations, the particle is reduced to two-dimensional space (Ω2=S2,H2ordS1+1) depending on the contraction parameter κ. Then with overlapping the reduced coordinates in the Eulerian parameterization with the canonical coordinates, we incorporate them into the Lagrangian. Therefore, we find three constant integrals of motion from the vector fields and we construct the superintegrable Hamiltonian. However, we obtain the wave function and the energy spectrum of the system by separating the variables and their solutions. Finally, by applying the resulting energy, for the two special cases of the produced topological space, we investigate and compare their thermodynamic properties.



中文翻译:

约束粒子对二维复杂Cayley-Klein空间超可积性的行为及其热力学性质

在本文中,我们研究了Cayley–Klein空间中the族的一个超可积分哈密顿量族上的粒子运动。通过来自其各自组的发电机之间的一般换向器关系来提供这种可能性。因此,通过将笛卡尔空间中的坐标转换为欧拉参数化,就新坐标而言,所获得的度量等于测地运动的同一拉格朗日坐标。另一方面,通过减少小号üκ1个κ2个3 组流形到 小号üκ1个κ2个3小号üκ1个2个Ω5 商空间并考虑三个傅里叶变换,粒子被简化为二维空间 Ω2个=小号2个H2个Ø[Rd小号1个+1个 取决于收缩参数 κ。然后将欧拉参数化中的简化坐标与规范坐标重叠,将它们合并到拉格朗日坐标中。因此,我们从矢量场中找到三个恒定的运动积分,并构造了超积分哈密顿量。但是,我们通过分离变量及其解来获得系统的波函​​数和能谱。最后,通过应用所产生的能量,针对产生的拓扑空间的两种特殊情况,我们研究并比较了它们的热力学性质。

更新日期:2021-04-01
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