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

## TL;DR

This paper demonstrates that a single quantum particle in a well with moving walls is unaffected by boundary motion if initially localized away from the boundaries, showing no nonlocal influence or geometric phase effects.

## Contribution

It proves that boundary motion does not affect localized Gaussian states and extends this to systems with geometric phases, clarifying misconceptions about nonlocality.

## Key findings

- Localized states are unaffected by boundary motion.
- Geometric phases do not influence localized Gaussian states.
- No nonlocal effects are observed from moving boundaries.

## 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.