A dynamical composition law for boundary conditions

TL;DR

This paper introduces a dynamical composition law for boundary conditions in quantum systems, showing that rapid boundary changes preserve unitarity and can lead to new boundary conditions, with potential experimental applications.

Contribution

It presents a novel dynamical composition law for boundary conditions in quantum mechanics, demonstrating unitarity preservation and the emergence of Dirichlet conditions as an attractor.

Findings

Rapid boundary changes preserve unitarity.

New boundary conditions emerge from superposition of topologies.

Dirichlet boundary condition acts as an attractor.

Abstract

We analyze the quantum dynamics of a non-relativistic particle moving in a bounded domain of physical space, when the boundary conditions are rapidly changed. In general, this yields new boundary conditions, via a dynamical composition law that is a very simple instance of superposition of different topologies. In all cases unitarity is preserved and the quick change of boundary conditions does not introduce any decoherence in the system. Among the emerging boundary conditions, the Dirichlet case (vanishing wave function at the boundary) plays the role of an attractor. Possible experimental implementations with superconducting quantum interference devices are explored and analyzed.