Abstract
The relativistic quantum motions of the oscillator field (via the Klein–Gordon oscillator equation) under a uniform magnetic field in a topologically non-trivial space-time geometry are analyzed. We solve the Klein–Gordon oscillator equation using the Nikiforov-Uvarov method and obtain the energy profile and the wave function. We discuss the effects of the non-trivial topology and the magnetic field on the energy eigenvalues. We find that the energy eigenvalues depend on the quantum flux field that shows an analogue of the Aharonov–Bohm effect. Furthermore, we obtain the persistent currents, the magnetization, and the magnetic susceptibility at zero temperature in the quantum system defined in a state and show that these magnetic parameters are modified by various factors.
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