Moving Walls and Geometric Phases

TL;DR

This paper explores the geometric Berry phase in a quantum particle confined in a one-dimensional box with moving walls, highlighting the importance of boundary conditions and renormalization for unitarity and phase calculation.

Contribution

It introduces a non-trivial Berry phase in a quantum system with moving boundaries and explicitly computes the geometric phase two-form considering boundary condition effects.

Findings

Berry phase exists for a quantum particle with moving walls

Proper boundary conditions are crucial for unitarity and phase calculation

Renormalization addresses divergences from boundary effects

Abstract

We unveil the existence of a non-trivial Berry phase associated to the dynamics of a quantum particle in a one dimensional box with moving walls. It is shown that a suitable choice of boundary conditions has to be made in order to preserve unitarity. For these boundary conditions we compute explicitly the geometric phase two-form on the parameter space. The unboundedness of the Hamiltonian describing the system leads to a natural prescription of renormalization for divergent contributions arising from the boundary.