On the connection between Random Waves and Quantum Fields. Duality between nodal lines statistic and the Casimir energy

TL;DR

This paper reveals a connection between the statistics of nodal lines in random waves and quantum fields, linking their probabilities to Casimir energy calculations for specific conductor arrangements.

Contribution

It establishes a novel duality between nodal line statistics and Casimir energy, bridging concepts from random wave theory and quantum field theory.

Findings

Nodal line probability relates to Casimir energy of conductors.

Provides a new perspective on statistical properties of quantum fields.

Connects geometric configurations with quantum vacuum effects.

Abstract

Using the statistical description common to random waves and quantum fields we show how the probability of having a nodal line close to a (translationally symmetric) reference curve $\gamma$ is related to the Casimir energy of an appropriate configuration of conductors.