# Sign Flip in the Casimir Force for Interacting Fermion Systems

## TL;DR

This paper investigates how interactions and boundary conditions in a finite fermionic chain can cause the Casimir force to switch from attractive to repulsive, revealing complex quantum vacuum effects.

## Contribution

It introduces a self-consistent method to analyze the Casimir force in interacting fermion systems with boundary conditions, highlighting a novel force flip phenomenon.

## Key findings

- Casimir force switches from attractive to repulsive
- Condensate interactions influence vacuum energy
- Boundary conditions alter fermionic Casimir effects

## Abstract

In this work we consider a fermionic chain of finite length $\ell$. Fermions are allowed to interact and are forced to obey boundary conditions, thus altering the process of condensation. Our goal is to explore how this affects the quantum vacuum energy for this system. We approach this problem by using a self-consistent method and observe a nontrivial behavior in the Casimir force, displaying a switch from an attractive to a repulsive regime. This flip stems from the competition between the attractive contribution from the usual fermionic Casimir effect and a repulsive one coming from the condensate.