Casimir Effect for Quantum Field theory in Networks

TL;DR

This paper investigates the Casimir effect in quantum field theories on networks, introducing a new junction condition that allows control over the force's nature, with potential applications in quantum device design.

Contribution

It proposes a novel junction condition for quantum fields on networks and demonstrates how it enables control of the Casimir force, extending the analysis to various networks and dimensions.

Findings

Casimir force can be tuned from attractive to repulsive by adjusting edge lengths.

New junction condition ensures energy conservation at network nodes.

Extension of Casimir effect analysis to complex networks and higher dimensions.

Abstract

This paper studies quantum field theories defined in networks, which are the multi-branch generalizations of interface conformal field theory (ICFT). We propose a novel junction condition on the node and show that it is consistent with energy conservation in the sense that the total energy flow into the node is zero. As an application, we explore the Casimir effect on networks. Remarkably, the Casimir force on one edge can be changed from attractive to repulsive by adjusting the lengths of the other edges, providing a straightforward way to control the Casimir effect. We begin by discussing the Casimir effect for $(1+1)$-dimensional free massless scalars on a simple network. We then extend this discussion to various types of networks and higher dimensions. Finally, we offer brief comments on some open questions.