Ideal quantum gas in expanding cavity: nature of non-adiabatic force

TL;DR

This paper investigates the non-adiabatic force in an expanding quantum gas cavity, revealing it is quadratic in wall velocity and does not break time-reversal symmetry, using both perturbative and exact methods.

Contribution

It introduces a new understanding of non-adiabatic force as quadratic in velocity and validates the force operator through exact solutions using transitionless quantum states.

Findings

Non-adiabatic force is quadratic in wall velocity.

Force does not break time-reversal symmetry.

Exact solutions confirm perturbative results.

Abstract

We consider a quantum gas of non-interacting particles confined in the expanding cavity, and investigate the nature of the non-adiabatic force which is generated from the gas and acts on the cavity wall. Firstly, with use of the time-dependent canonical transformation which transforms the expanding cavity to the non-expanding one, we can define the force operator. Secondly, applying the perturbative theory which works when the cavity wall begins to move at time origin, we find that the non-adiabatic force is quadratic in the wall velocity and thereby does not break the time-reversal symmetry, in contrast with the general belief. Finally, using an assembly of the transitionless quantum states, we obtain the nonadiabatic force exactly. The exact result justifies the validity of both the definition of force operator and the issue of the perturbative theory. The mysterious mechanism of nonadiabatic transition with use of transitionless quantum states is also explained. The study is done on both cases of the hard-wall and soft-wall confinement with the time-dependent confining length.