Single particle nonlocality and time-dependent boundary conditions

Aephraim M. Steinberg

S. V. Mousavi, A. Matzkin

We investigate the issue of single particle nonlocality in a quantum system subjected to time-dependent boundary conditions. We first prove that contrary to earlier claims, there is no strong nonlocality: a quantum state localized at the center of a well with infinitely high moving walls is not modified by the wall's motion. We then show the existence of a weak form of nonlocality: when a quantum state is extended over the well, the wall's motion induces a current density all over the box instantaneously. We indicate how this current density can in principle be measured by performing weak measurements of the particle's momentum.

A. Matzkin

Abstract 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.

Günter Mahler A

Samuel Colin, A. Matzkin

The dynamics of a particle in an expanding cavity is investigated in the Klein-Gordon framework in a regime in which the single-particle picture remains valid. The cavity expansion represents a time-dependent boundary condition for the relativistic wave function. We show that this expansion induces a non-local effect on the current density throughout the cavity. Our results indicate that a relativistic treatment still contains apparently spurious effects traditionally associated with the unbounded velocities inherent in non-relativistic solutions obtained from the Schrödinger equation. Possible reasons for this behaviour are discussed.

Alexander P. Kasatkin