Dynamics of the free time-dependent effective mass

The consensus is that an object with a large mass will not manifest quantum behavior. Therefore, we expect that the quantumness of a time-dependent effective mass (TDEM) will erase after a long time when the mass profile continuously grows with time. However, the present article depicts that the Wigner quasi-probability distribution (WQD) will manifest an entanglement behavior forever for two spatially separated free TDEMs. The time-dependent Schrödinger equation for a free particle with TDEM has been solved with the help of the Lewis–Riesenfeld phase-space invariant method. WQD for the system of two identical TDEMs with quadratically increasing mass profiles shows that the particles are never separated. In particular, their reminiscent is present at the origin of the phase-space forever.