In this study, we have constructed a generalized momentum operator based on the notion of backward–forward coordinates characterized by a low dynamical nonlocality decaying exponentially with position. We have derived the associated Schrodinger equation and we have studied the dynamics of a particle characterized by an exponentially decreasing position-dependent mass following the arguments of von Roos. In the absence of magnetic fields, it was observed that the dynamics of the particle is similar to the harmonic oscillator with damping and its energy state is affected by nonlocality. We have also studied the dynamics of a charged particle in the presence of Morse–Coulomb potentials and external magnetic and Aharonov-Bohm flux fields. Both the energy states and the thermodynamical properties were obtained. It was observed that all these physical quantities are affected by nonlocality and that for small magnetic fields and high quantum magnetic numbers, the entropy of the system decreases with increasing temperature unless the nonlocal parameter is negative. For positive value of the nonlocal parameter, it was found that the entropy increases with temperature and tends toward an asymptotically stable value similar to an isolated system.

中文翻译：

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位置相关质量粒子在磁场和 Aharonov-Bohm 通量场中的非局域热力学性质

在这项研究中，我们基于后向前坐标的概念构建了一个广义动量算子，其特征是低动态非定域性随位置呈指数衰减。我们已经导出了相关的薛定谔方程，并且我们已经研究了一个粒子的动力学，该粒子的特征是按照 von Roos 的论点呈指数下降的位置相关质量。在没有磁场的情况下，观察到粒子的动力学类似于具有阻尼的谐振子，其能量状态受非局域性影响。我们还研究了在莫尔斯-库仑势和外部磁场和 Aharonov-Bohm 通量场存在下带电粒子的动力学。获得了能态和热力学性质。观察到所有这些物理量都受非定域性的影响，对于小磁场和高量子磁数，除非非定域参数为负，否则系统的熵随着温度的升高而降低。对于非局部参数的正值，发现熵随温度增加并趋向于类似于孤立系统的渐近稳定值。