# Quantum particle in a split box: Excitations to the ground state

## TL;DR

This paper explores methods to split a quantum particle's wavefunction in a box into two parts, showing that non-adiabatic, asymmetric barriers can effectively approximate ideal symmetric splitting, which is relevant for quantum engines.

## Contribution

It introduces a non-adiabatic, asymmetric barrier approach to split the wavefunction, overcoming limitations of adiabatic, symmetric barriers in quantum systems.

## Key findings

- Non-adiabatic barriers induce excitations to the first excited state.
- As the barrier height increases, the excited state approximates the ground state of a partitioned box.
- Asymmetry in barrier placement still allows near-perfect probability splitting.

## Abstract

We discuss two different approaches for splitting the wavefunction of a single-particle-box (SPB) into two equal parts. Adiabatic insertion of a barrier in the center of a SPB in order to make two compartments which each have probability 1/2 to find the particle in it is one of the key steps for a Szilard engine. However, any asymmetry between the volume of the compartments due to an off-center insertion of the barrier results in a particle that is fully localized in the larger compartment, in the adiabatic limit. We show that rather than exactly splitting the eigenfunctions in half by a symmetric barrier, one can use a non-adiabatic insertion of an asymmetric barrier to induce excitations to the first excited state of the full box. As the barrier height goes to infinity the excited state of the full box becomes the ground state of one of the new boxes. Thus, we can achieve close to exact splitting of the probability between the two compartments using the more realistic non-adiabatic, not perfectly centered barrier, rather than the idealized adiabatic and central barrier normally assumed.