Lifshitz formulas for finite-density Casimir effect

TL;DR

This paper generalizes the Lifshitz formula to analyze the Casimir effect in systems with finite chemical potential, enabling studies in dense quark matter and Dirac/Weyl semimetals.

Contribution

The authors extend the Lifshitz formula to include finite chemical potential, broadening its applicability to new physical systems and conditions.

Findings

Derived a generalized Lifshitz formula for finite chemical potential

Applied the formula to systems like dense quark matter and semimetals

Demonstrated the formula's versatility across various boundary conditions and dimensions

Abstract

The Lifshitz formula is well known as a theoretical approach to investigate the Casimir effect at finite temperature. In this Letter, we generalize the Lifshitz formula to the Casimir effect originating from quantum fields at finite chemical potential. To demonstrate the versatility of this formula, we discuss the typical phenomena of the Casimir effect at finite chemical potential in various systems, such as some boundary conditions, finite temperatures, arbitrary spatial dimensions, and mismatched chemical potentials. This formula can be applied to the Casimir effect in dense quark matter and Dirac/Weyl semimetals, where the chemical potential is regarded as a parameter to control the Casimir effect.