Boundary dynamics and topology change in quantum mechanics

TL;DR

This paper explores how boundary conditions can dynamically induce topology changes in quantum systems by utilizing self-adjoint extensions and time-dependent Schrödinger equations.

Contribution

It introduces a method to control quantum topology transitions through boundary condition manipulation within a rigorous mathematical framework.

Findings

Boundary conditions can be used to induce topology change in quantum systems.

A framework for dynamical topology change using self-adjoint extensions is developed.

Examples illustrate how boundary-driven topology transitions can be realized.

Abstract

We show how to use boundary conditions to drive the evolution on a Quantum Mechanical system. We will see how this problem can be expressed in terms of a time-dependent Schr\"{o}dinger equation. In particular we will need the theory of self-adjoint extensions of differential operators in manifolds with boundary. An introduction of the latter as well as meaningful examples will be given. It is known that different boundary conditions can be used to describe different topologies of the associated quantum systems. We will use the previous results to study how this topology change can be accomplished in a dynamical way.