Dynamics of free time-dependent effective mass

TL;DR

This paper demonstrates that two free particles with time-dependent effective mass exhibit persistent quantum entanglement and non-separability in phase space, even with increasing mass profiles, challenging the expectation that large mass suppresses quantum behavior.

Contribution

It introduces an exact solution for the Schrödinger equation with time-dependent mass and shows persistent entanglement in the Wigner distribution for particles with increasing mass.

Findings

Wigner distribution shows eternal entanglement between particles.

Particles remain non-separated despite increasing mass.

Quantum features persist over time with quadratic mass growth.

Abstract

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 behavour forever for two spatially separated free TDEM. The time-dependent Schr\"{o}dinger equation for a free particle with TDEM is solved with the help of Lewis-Riesenfeld phase space invariant method. WQD for the system of two identical TDEM with quadratically increasing mass profile shows that the particles are never separated. In particular, their reminiscent is present at the origin of the phase-space forever.