Quantum effective force and Bohmian approach for time-dependent traps

TL;DR

This paper investigates Bohmian trajectories and quantum effective forces for particles in time-dependent traps, revealing conditions where forces vanish and analyzing two-body systems with different quantum statistics.

Contribution

It introduces a Bohmian approach to analyze particles in dynamic traps and explores the effects of quantum statistics on two-body systems in such environments.

Findings

Quantum effective force can be zero for particles initially in energy eigenstates.

Trajectories differ for bosons and fermions, affecting particle separation.

Average separation aligns with quantum statistical expectations.

Abstract

Trajectories of a Bohmian particle confined in time-dependent cylindrical and spherical traps are computed for both contracting and expanding boxes. Quantum effective force is considered in arbitrary directions. It is seen that in contrast to the problem of a particle in an infinite rectangular box with one wall in motion, if particle initially is in an energy eigenstate of a tiny box the force is zero in all directions. Trajectories of a two-body system confined in the spherical trap are also computed for different statistics. Computations show that there are situations for which distance between bosons is greater than the fermions. However, results of average separation of the particles confirm our expectation about the statistics.