Single particle nonlocality, geometric phases and time-dependent boundary conditions

We investigate the issue of single particle nonlocality in a quantum system subjected to
time-dependent boundary conditions. We discuss earlier claims according to which the quantum state
of a particle remaining localized at the center of an infinite well with moving walls would be
specifically modified by the change in boundary conditions due to the wall’s motion. We first prove
that the evolution of an initially localized Gaussian state is not affected nonlocally by a linearly
moving wall: as long as the quantum state has negligible amplitude near the wall, the boundary
motion has no effect. This result is further extended to related confined time-dependent oscillators
in which the boundary’s motion is known to give rise to geometric phases: for a Gaussian state
remaining localized far from the boundaries, the effect of the geometric phases is washed out and
the particle dynamics shows no traces of a nonlocal influence that would be induced by the moving
boundaries.

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