Nonlocal Thermodynamics Properties of Position-Dependent Mass Particle in Magnetic and Aharonov-Bohm Flux Fields

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 Schrödinger 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.