外磁场中具有螺旋状位错时空的 Klein-Gordon 标量场振子
On the Klein-Gordon scalar field oscillators in a spacetime with spiral-like dislocations in external magnetic fields
AI总结：
研究了螺旋位错 I 和 II 对 Klein-Gordon 振子场相对论动力学的影响，发现位错 I 影响振子能量，而位错 II 仅在施加磁场时产生影响，且振子频率仅由磁场强度决定。
摘要：
我们研究了两种类型的螺旋位错（径向线的畸变，标记为螺旋位错 I，以及圆的畸变，标记为螺旋位错 II）对 Klein-Gordon (KG) 振子场相对论动力学的影响，包括存在和不存在外部磁场的情况。在此背景下，我们的研究表明，虽然螺旋位错 I 会影响 KG 振子的能量（无论有无磁场），但有趣的是，除非施加磁场，否则螺旋位错 II 对 KG 振子的能量没有影响。然而，对于两种类型的螺旋位错，我们观察到相应的波函数都包含了位错参数的影响。我们的发现基于螺旋位错 I 的 KG 振子（分别对应有磁场和无磁场）的精确可解性和条件精确可解性（与双合流 Heun 多项式相关），以及螺旋位错 II 的 KG 振子（无论有无磁场）的精确可解性。后者的精确可解性表明，振子的频率仅由磁场强度决定。
英文摘要：
We investigate the effects of two types of spiral dislocation (the distortion of the radial line, labeled as spiral dislocation I, and the distortion of a circle, labeled as spiral dislocation II) on the relativistic dynamics of the Klein-Gordon (KG) oscillator fields, both in the presence and absence of external magnetic fields. In this context, our investigations show that while spiral dislocation I affects the energies of the KG oscillators (with or without the magnetic field), spiral dislocation II has, interestingly, no effect on the KG oscillator's energies unless a magnetic field is applied. However, for both types of spiral dislocations, we observe that the corresponding wave functions incorporate the effects of the dislocation parameter. Our findings are based on the exact solvability and conditional exact solvability (associated with the biconfluent Heun polynomials) of the KG oscillators (with or without the magnetic field, respectively) for spiral dislocation I, and the exact solvability of the KG oscillators (with or without the magnetic field) for spiral dislocation II. The exact solvability of the latter suggests that the oscillator's frequency is solely determined by the magnetic field strength.
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