# Vacuum energy for generalised Dirac combs at $T = 0$

## TL;DR

This paper calculates the quantum vacuum energy for a periodic array of Dirac delta and delta-prime potentials at zero temperature, revealing a non-perturbative energy function that is non-analytical for small couplings.

## Contribution

It introduces a method to compute vacuum energy for generalized Dirac combs using zeta functions and highlights the non-perturbative nature of the energy at small couplings.

## Key findings

- Vacuum energy is expressed as a sum over the dual primitive cell of Bloch quasi-momenta.
- The energy function exhibits non-analytic behavior for small coupling constants.
- The approach generalizes previous models to hybrid comb potentials.

## Abstract

The quantum vacuum energy for a hybrid comb of Dirac $\delta$-$\delta'$ potentials is computed using the energy of the single $\delta$-$\delta'$ potential over the real line that makes up the comb. The zeta function of a comb periodic potential is the continuous sum of zeta functions over the dual primitive cell of Bloch quasi-momenta. The result obtained for the quantum vacuum energy is non-perturbative in the sense that the energy function is not analytical for small couplings