Nonlocal effects induced by the phase of the Schrödinger wavefunction for a particle in a cavity with moving boundaries

We investigate the dynamics of a particle in a confined periodic system — a time-dependent oscillator confined by infinitely high and moving walls — and focus on the evolution of the phase of the wavefunction. It is shown that for some specific initial states in this potential, the phase evolves nonlocally. We further elaborate a thought experiment devised to detect this form of single-particle nonlocality.

We point out that within the non-relativistic formalism based on the Schrödinger equation (SE), detecting this form of nonlocality can give rise to signaling. We believe this effect is an artifact, but the standard relativistic corrections to the SE do not appear to fix it. Specific illustrations are given, with analytical results in the adiabatic approximation, and numerical computations to show that contributions from high-energy states (corresponding to superluminal velocities) are negligible.

The article was published in: arXiv preprint arXiv:1909.06465.

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This work was supported (in part) by the Fetzer Franklin Fund of the John E. Fetzer Memorial Trust.