Quantum cavities with alternating boundary conditions

TL;DR

This paper investigates how rapid switching between boundary conditions in a quantum cavity creates a new effective boundary condition, revealing a composition law that governs the resulting quantum dynamics.

Contribution

It introduces a dynamical composition law for boundary conditions in quantum cavities resulting from rapid switching, a novel approach in quantum boundary dynamics.

Findings

Rapid switching induces a new effective boundary condition.

A composition law relates initial boundary conditions to the effective one.

The approach provides a method to engineer boundary conditions dynamically.

Abstract

We consider the quantum dynamics of a free nonrelativistic particle moving in a cavity and we analyze the effect of a rapid switching between two different boundary conditions. We show that this procedure induces, in the limit of infinitely frequent switchings, a new effective dynamics in the cavity related to a novel boundary condition. We obtain a dynamical composition law for boundary conditions which gives the emerging boundary condition in terms of the two initial ones.